View Full Version : Is State Vector Reduction a 'Process'?
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Is state-vector reduction (or collapse of the wavefunction) a physical\nprocess? Or is it really an artefact of our procedure of canonical\nquantisation?\n\nIn the Feynman path integral approach to Quantum Theory, state-vector\nreduction doesn\'t seem to be a process any more than asking the\nquestion: What is the amplitude of going from a certain initial state\nto a final state?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Is state-vector reduction (or collapse of the wavefunction) a physical
process? Or is it really an artefact of our procedure of canonical
quantisation?
In the Feynman path integral approach to Quantum Theory, state-vector
reduction doesn't seem to be a process any more than asking the
question: What is the amplitude of going from a certain initial state
to a final state?
Aaron Bergman
May16-05, 02:20 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1116090071.291677.269500@g14g2000cwa.googlegroups .com>,\n"Souvik" <souvik1982@gmail.com> wrote:\n\n> Is state-vector reduction (or collapse of the wavefunction) a physical\n> process?\n\nNo one knows.\n\n> Or is it really an artefact of our procedure of canonical\n> quantisation?\n\nIt has nothing to do with canonical quantizations, path integrals or\nwhatever. Quantum mechanics does not include state-vector reduction as a\nphysical process.\n\nIt does include, however, something called decoherence which makes the\nobservation of macroscopic superpositions occur with only infinitesimal\nprobability. Thus, even if state reduction were a physical process,\nnature has conspired to make it incredibly difficult to observe it.\n\nBut that doesn\'t mean that it\'s impossible. It\'s not pointed out enough,\nI think, that collapse vs. no-collapse scenarios for quantum mechanics\nis *not* an issue of interpretation; it\'s a real physical question.\nExperiments have been done to entangle and then disentangle increasingly\ncomplex objects, so it might be possible to eventually observe state\nreduction if it does exist.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1116090071.291677.269500@g14g2000cwa.googlegroups. com>,
"Souvik" <souvik1982@gmail.com> wrote:
> Is state-vector reduction (or collapse of the wavefunction) a physical
> process?
No one knows.
> Or is it really an artefact of our procedure of canonical
> quantisation?
It has nothing to do with canonical quantizations, path integrals or
whatever. Quantum mechanics does not include state-vector reduction as a
physical process.
It does include, however, something called decoherence which makes the
observation of macroscopic superpositions occur with only infinitesimal
probability. Thus, even if state reduction were a physical process,
nature has conspired to make it incredibly difficult to observe it.
But that doesn't mean that it's impossible. It's not pointed out enough,
I think, that collapse vs. no-collapse scenarios for quantum mechanics
is *not* an issue of interpretation; it's a real physical question.
Experiments have been done to entangle and then disentangle increasingly
complex objects, so it might be possible to eventually observe state
reduction if it does exist.
Aaron
Arnold Neumaier
May16-05, 02:20 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Souvik wrote:\n> Is state-vector reduction (or collapse of the wavefunction) a physical\n> process? Or is it really an artefact of our procedure of canonical\n> quantisation?\n\nIt is an artifact of the description of a quantum system by\na limited number of observables rather than by the state of\nthe whole universe. Once one projects to a subsystem, one\nmust ignore the details of the interaction with the unmodelled\nenvironment and gets some dissipative effects. These are\nresponsible for the collapse.\n\nBut since we cannot know the full state of the whole universe,\nwe are doomed to such reduced descriptions and hence to the\ncollapse. Actually it is a big help in using QM...\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Souvik wrote:
> Is state-vector reduction (or collapse of the wavefunction) a physical
> process? Or is it really an artefact of our procedure of canonical
> quantisation?
It is an artifact of the description of a quantum system by
a limited number of observables rather than by the state of
the whole universe. Once one projects to a subsystem, one
must ignore the details of the interaction with the unmodelled
environment and gets some dissipative effects. These are
responsible for the collapse.
But since we cannot know the full state of the whole universe,
we are doomed to such reduced descriptions and hence to the
collapse. Actually it is a big help in using QM...
Arnold Neumaier
You'd think that having your state vectors reduced would prevent your wave equations from working.
When I was young, I naively thought that the reason that Green's functions worked was that they modeled state vector collapse. For example, in a position representation, a state vector collapse should lose all information about momentum (because of the Heisenberg uncertainty principle), and this is exactly how the Green's function computes the contribution from one point to another.
In this sense, state vector reduction is invisible in QM because it is consistent with the assumption of linear superposition.
Carl
The question of how wave function collapse can be compatible with wave function evolution is a particularly interesting one.
A simple but ugly interpretation is to suppose that wave function collapse does exist, but that it is somehow transparent to wave function evolution. That way we would be unable to detect the effect of wave function collapse by noticing a failure of our usual wave equations.
One way this could happen is by making the assumption that wave function collapse happens in a fashion that is identical to the action of the usual propagators. If the position representations are taken to be the fundamental representations, then this says that during wave function collapse, a particle must lose all memory of its momentum. This is compatible with the Heisenberg uncertainty principle, but it implies that momentum eigenstates are only approximations.
This also implies that a unified field theory might not be compatible with conservation of momentum, even when written in the momentum representation. If this is the case, then the Higgs mechanism can be replaced with a simpler method of giving the elementary particles mass. Namely, just cut the Higgs from all the diagrams involved with it and let the left and right handed fermion propagators turn themselves into each other with vertex values given by the mass. The resummation turns massless fermion propagators into massive ones.
Carl
rof@maths.tcd.ie
May20-05, 03:55 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman <abergman@physics.utexas.edu> writes:\n\n>In article <1116090071.291677.269500@g14g2000cwa.googlegroups .com>,\n> "Souvik" <souvik1982@gmail.com> wrote:\n\n>> Is state-vector reduction (or collapse of the wavefunction) a physical\n>> process?\n\n>No one knows.\n\nIndeed, although there are a lot of people who claim they do. Quantum\nmechanics has a psychological effect similar to metaphysics - when\notherwise honest people talk about it, they omit, distort and twist\nthe truth to promote their own interpretation. They\'ll give you\na firm but confusing answer, without informing you that a significant\nfraction of physicists (say, over 50%) disagree with it. They\'ll\nsay that those who disagree with them are unreasonable, illogical.\n\nEven very intelligent people do this. It\'s quite a bizarre social\nphenomenon to have physicists turning into politicians like this,\nattempting to manipulate and confuse others into sharing their\nview. Part of it may stem from the fact that there\'s a lot of\ndogma (belief taught as fact) in quantum mechanics textbooks,\nand in undergraduate quantum mechanics classes. It\'s also\npossible that this is a result and not a cause of the problem.\nPhysicists are aware that there\'s something odd going on;\na lot of them won\'t want to discuss it.\n\nIf you\'re interested in my opinion, which I don\'t suggest you\nshould be, it seems to me that quantum mechanics is like a piece\nof alien technology that fell from space. We have no idea\nwhy it works; many say they do, but it\'s rare that two people\nagree on a reason. Nobody has ever deduced the mathematical\nformalism by showing that, based on their interpretation,\nthe formalism that we do use is the formalism that we should\nuse. Rather, people look at the mathematical formalism\nand then invent stories about what it means, some involving\nparallel worlds, some involving consciousness.\n\nThis is different from the "shut up and calculate" approach,\nwhich is appropriate for somebody who wants to follow a\ncareer in physics but who has no motivation to actually\nunderstand why the calculations he is doing are the right\nones to do. I advocate looking for a derivation of the\nformalism of quantum mechanics, without assuming it in\nadvance. I haven\'t found one, but neither has anybody\nelse.\n\nYou may hear it said from various physicists that the\nproblem of reconciling quantum mechanics with gravity\ndoes not require any better understanding of why\nquantum mechanics works. This is dogma.\n\n>... even if state reduction were a physical process,\n>nature has conspired to make it incredibly difficult to observe it.\n\n>But that doesn\'t mean that it\'s impossible. It\'s not pointed out enough,\n>I think, that collapse vs. no-collapse scenarios for quantum mechanics\n>is *not* an issue of interpretation; it\'s a real physical question.\n>Experiments have been done to entangle and then disentangle increasingly\n>complex objects, so it might be possible to eventually observe state\n>reduction if it does exist.\n\nThere are some interpretations involving collapse, such as the GRW\nspontaneous collapse interpretation, or Penrose\'s gravitational\ncollapse interpretation, which give different predictions to\n"orthodox" quantum mechanics, which is the Hilbert space recipe for\ncalculating the probabilities of various experimental results.\nThese are testable in principle, and the experiment to test Penrose\'s\nis currently being constructed.\n\nThe no-collapse interpretations (many worlds, Bohmian mechanics, and\nso on) typically agree with orthodox QM on every prediction.\n\nOrthodox QM itself, or the Copenhagen interpretation, features\ncollapse but doesn\'t consider it physical. From the Copenhagen point\nof view, the wavefunction encodes knowledge about the system, and\nit collapses when a measurement is performed; that is, when we\nacquire new knowledge, we have to update the mathematical object\nwhich we use to represent knowledge. Hence different observers will\nuse different wavefunctions to describe the same system. The\nCopenhagen view is still the officially recognised majority view,\nbut I doubt there are many physicists today who would agree that,\nfor example, the ground state orbital of an electron in a hydrogen\natom represents knowledge. Physicists dislike knowledge because\nknowledge is subjective, and subjective things are bad.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman <abergman@physics.utexas.edu> writes:
>In article <1116090071.291677.269500@g14g2000cwa.googlegroups. com>,
> "Souvik" <souvik1982@gmail.com> wrote:
>> Is state-vector reduction (or collapse of the wavefunction) a physical
>> process?
>No one knows.
Indeed, although there are a lot of people who claim they do. Quantum
mechanics has a psychological effect similar to metaphysics - when
otherwise honest people talk about it, they omit, distort and twist
the truth to promote their own interpretation. They'll give you
a firm but confusing answer, without informing you that a significant
fraction of physicists (say, over 50%) disagree with it. They'll
say that those who disagree with them are unreasonable, illogical.
Even very intelligent people do this. It's quite a bizarre social
phenomenon to have physicists turning into politicians like this,
attempting to manipulate and confuse others into sharing their
view. Part of it may stem from the fact that there's a lot of
dogma (belief taught as fact) in quantum mechanics textbooks,
and in undergraduate quantum mechanics classes. It's also
possible that this is a result and not a cause of the problem.
Physicists are aware that there's something odd going on;
a lot of them won't want to discuss it.
If you're interested in my opinion, which I don't suggest you
should be, it seems to me that quantum mechanics is like a piece
of alien technology that fell from space. We have no idea
why it works; many say they do, but it's rare that two people
agree on a reason. Nobody has ever deduced the mathematical
formalism by showing that, based on their interpretation,
the formalism that we do use is the formalism that we should
use. Rather, people look at the mathematical formalism
and then invent stories about what it means, some involving
parallel worlds, some involving consciousness.
This is different from the "shut up and calculate" approach,
which is appropriate for somebody who wants to follow a
career in physics but who has no motivation to actually
understand why the calculations he is doing are the right
ones to do. I advocate looking for a derivation of the
formalism of quantum mechanics, without assuming it in
advance. I haven't found one, but neither has anybody
else.
You may hear it said from various physicists that the
problem of reconciling quantum mechanics with gravity
does not require any better understanding of why
quantum mechanics works. This is dogma.
>... even if state reduction were a physical process,
>nature has conspired to make it incredibly difficult to observe it.
>But that doesn't mean that it's impossible. It's not pointed out enough,
>I think, that collapse vs. no-collapse scenarios for quantum mechanics
>is *not* an issue of interpretation; it's a real physical question.
>Experiments have been done to entangle and then disentangle increasingly
>complex objects, so it might be possible to eventually observe state
>reduction if it does exist.
There are some interpretations involving collapse, such as the GRW
spontaneous collapse interpretation, or Penrose's gravitational
collapse interpretation, which give different predictions to
"orthodox" quantum mechanics, which is the Hilbert space recipe for
calculating the probabilities of various experimental results.
These are testable in principle, and the experiment to test Penrose's
is currently being constructed.
The no-collapse interpretations (many worlds, Bohmian mechanics, and
so on) typically agree with orthodox QM on every prediction.
Orthodox QM itself, or the Copenhagen interpretation, features
collapse but doesn't consider it physical. From the Copenhagen point
of view, the wavefunction encodes knowledge about the system, and
it collapses when a measurement is performed; that is, when we
acquire new knowledge, we have to update the mathematical object
which we use to represent knowledge. Hence different observers will
use different wavefunctions to describe the same system. The
Copenhagen view is still the officially recognised majority view,
but I doubt there are many physicists today who would agree that,
for example, the ground state orbital of an electron in a hydrogen
atom represents knowledge. Physicists dislike knowledge because
knowledge is subjective, and subjective things are bad.
R.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Souvik wrote:\n> Is state-vector reduction (or collapse of the wavefunction) a physical\n> process? Or is it really an artefact of our procedure of canonical\n> quantisation?\n>\n> In the Feynman path integral approach to Quantum Theory, state-vector\n> reduction doesn\'t seem to be a process any more than asking the\n> question: What is the amplitude of going from a certain initial state\n> to a final state?\n>\n\nAs you see different opinions arise. My take on it is this.\nWhen you view the wave function as a statistical description,\n(analogous to a probability distribution) then the assumption\nof new information changes your description changes.\n\nThus even classical probability distributions "collapse".\nE.g, your probability of winning the raffle can jump from\na small positive probability to either of certainty or absolute zero\nupon the drawing. This occurs "instantaneously for all tickets".\nThis happens "non-locally" because the\nstate of "winning the raffle" does not describe the state\nof your ticket but the correlation between your ticket and\nthe state of a ticket drawn in the raffle office.\n\nSo I would argue that collapsing wave functions are not physical\nprocesses but rather occur "on paper".\n\n\nBill Hobba posted a link:\nhttp://quantum.phys.cmu.edu/quest.html\nto another "interpretation" of QM called "Consistent Histories"\nwhich makes this point.\n\nIt may help in parsing the various thought experiments to remember\nthat when you are considering a "one particle experiment" there\nis a global non-causal constraint being applied to the system definition\nwhich excludes cases where a second or third particle enters the\nexperimental domain. So for example when you measure one electron\nin position x you are in this act measuring also zero electrons\nat every other position. The measurement action is non-local,\nand you toss out instances when you get more than one electron total.\nThis "tossing out of instances" tells you that the collapse\nis not occuring "to the particle" but rather "to your description".\n\nThis you may relate also to Arnold Neumaier\'s point about restriction\nto a small part of "the whole universe". However I think this point\nmisleading in that "the wave function of the whole universe"\nis not operationally meaningful. There is only one instance of "the\nwhole universe" so probabilities are meaningless and you cannot\ninterpret such a "wave function" quantum mechanically,\nThat is unless you use a 1-dimensional Hilbert space, with one\nphysical observable "does it exist" which has expectation value 1.\n\n\nRegards,\nJames Baugh\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Souvik wrote:
> Is state-vector reduction (or collapse of the wavefunction) a physical
> process? Or is it really an artefact of our procedure of canonical
> quantisation?
>
> In the Feynman path integral approach to Quantum Theory, state-vector
> reduction doesn't seem to be a process any more than asking the
> question: What is the amplitude of going from a certain initial state
> to a final state?
>
As you see different opinions arise. My take on it is this.
When you view the wave function as a statistical description,
(analogous to a probability distribution) then the assumption
of new information changes your description changes.
Thus even classical probability distributions "collapse".
E.g, your probability of winning the raffle can jump from
a small positive probability to either of certainty or absolute zero
upon the drawing. This occurs "instantaneously for all tickets".
This happens "non-locally" because the
state of "winning the raffle" does not describe the state
of your ticket but the correlation between your ticket and
the state of a ticket drawn in the raffle office.
So I would argue that collapsing wave functions are not physical
processes but rather occur "on paper".
Bill Hobba posted a link:
http://quantum.phys.cmu.edu/quest.html
to another "interpretation" of QM called "Consistent Histories"
which makes this point.
It may help in parsing the various thought experiments to remember
that when you are considering a "one particle experiment" there
is a global non-causal constraint being applied to the system definition
which excludes cases where a second or third particle enters the
experimental domain. So for example when you measure one electron
in position x you are in this act measuring also zero electrons
at every other position. The measurement action is non-local,
and you toss out instances when you get more than one electron total.
This "tossing out of instances" tells you that the collapse
is not occuring "to the particle" but rather "to your description".
This you may relate also to Arnold Neumaier's point about restriction
to a small part of "the whole universe". However I think this point
misleading in that "the wave function of the whole universe"
is not operationally meaningful. There is only one instance of "the
whole universe" so probabilities are meaningless and you cannot
interpret such a "wave function" quantum mechanically,
That is unless you use a 1-dimensional Hilbert space, with one
physical observable "does it exist" which has expectation value 1.
Regards,
James Baugh
Arnold Neumaier
May21-05, 03:42 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Baugh wrote:\n\n> This you may relate also to Arnold Neumaier\'s point about restriction\n> to a small part of "the whole universe". However I think this point\n> misleading in that "the wave function of the whole universe"\n> is not operationally meaningful. There is only one instance of "the\n> whole universe" so probabilities are meaningless and you cannot\n> interpret such a "wave function" quantum mechanically,\n\nThis is not true. Quantum mechanics not only provides probabilities\nbut also expectations. And these are _not_ meaningless,\neven though only one instance of the universe exists.\n\nFor example, if we measure the mass of a piece of metal, we actually\nmeasure the expectation of the mass operator <M> (M is the sum of\nall the particle masses). Similarly, as any discussion of the\ngrand canonical ensemble can convince you, all the quantities discussed\nin thermodynamics are either expectations, or numbers computed from\nsuch expectations. And these are measured routinely for single objects.\nQuantum mechanics just asserts that the accuraccy one can obtain is limited.\n\nGoing deeper into statistical mechanics shows that the quantities\nhandled by hydrodynamics (and this is much of our everyday life!)\nare also expectations and functions of expectations, and apply to\nsingle objects, such as the motor of the car you are driving.\n\n\nOnly the probabilistic interpretation of QM goes down the drain when\nthe whole universe is considered. But essentially everything else\nremains intact. Those who can read German can find more discussion\nof this in\nhttp://www.mat.univie.ac.at/~neum/physik-faq.tex\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Baugh wrote:
> This you may relate also to Arnold Neumaier's point about restriction
> to a small part of "the whole universe". However I think this point
> misleading in that "the wave function of the whole universe"
> is not operationally meaningful. There is only one instance of "the
> whole universe" so probabilities are meaningless and you cannot
> interpret such a "wave function" quantum mechanically,
This is not true. Quantum mechanics not only provides probabilities
but also expectations. And these are _not_ meaningless,
even though only one instance of the universe exists.
For example, if we measure the mass of a piece of metal, we actually
measure the expectation of the mass operator <M> (M is the sum of
all the particle masses). Similarly, as any discussion of the
grand canonical ensemble can convince you, all the quantities discussed
in thermodynamics are either expectations, or numbers computed from
such expectations. And these are measured routinely for single objects.
Quantum mechanics just asserts that the accuraccy one can obtain is limited.
Going deeper into statistical mechanics shows that the quantities
handled by hydrodynamics (and this is much of our everyday life!)
are also expectations and functions of expectations, and apply to
single objects, such as the motor of the car you are driving.
Only the probabilistic interpretation of QM goes down the drain when
the whole universe is considered. But essentially everything else
remains intact. Those who can read German can find more discussion
of this in
http://www.mat.univie.ac.at/~neum/physik-faq.tex
Arnold Neumaier
Arnold Neumaier
May21-05, 03:43 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Aaron Bergman <abergman@physics.utexas.edu> writes:\n>\n>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups .com>,\n>>"Souvik" <souvik1982@gmail.com> wrote:\n>\n>>>Is state-vector reduction (or collapse of the wavefunction) a physical\n>>>process?\n>\n>>No one knows.\n>\n> Indeed, although there are a lot of people who claim they do. Quantum\n> mechanics has a psychological effect similar to metaphysics - when\n> otherwise honest people talk about it, they omit, distort and twist\n> the truth to promote their own interpretation. They\'ll give you\n> a firm but confusing answer, without informing you that a significant\n> fraction of physicists (say, over 50%) disagree with it.\n\nDo you think truth is a matter of majority votes???\nTruth is rather a matter of listening to the different sides\nof a controversy and then choosing the best.\n\n\nIt is obvious that whatever a person claims is first and foremost\nhis or her personal opinion, and not a fact. Who takes it for a\nfact is simply misleading himself or herself. Thus there is no\nneed to qualify each of one\'s statements by clumsy phrases like\n\'in my opinion\', or \'according to what I have read/understood\', or\n\'as far as I am informed\' or \'since this makes most sense to me\'.\nThese phrases accompany silently any statement by anyone.\n\nIt is also obvious that an opinion doesn\'t become a fact because\nit is believed by half the number of people from a particular\nensemble; truth would otherwise become dependent on the choice\nof this ensemble.\n\nHonesty therefore only requires that one asserts what one thinks\nis true, and gives one\'s reasons upon request. This is the scientific\napproach, since it lets others check upon the trustworthiness of\na claim.\n\n\n> They\'ll\n> say that those who disagree with them are unreasonable, illogical.\n>\n> Even very intelligent people do this. It\'s quite a bizarre social\n> phenomenon to have physicists turning into politicians like this,\n> attempting to manipulate and confuse others into sharing their\n> view.\n\nI don\'t think this is a fair assessment. Everything called\nknowledge is in fact a set of beliefs of the person claiming it.\nAnd this set of beliefs is more or less close to the objective\ntruth, depending on the standards of that persons.\n\nTelling others what one thinks is true in no way manipulates\nothers any more than feeding others what one thinks is nourishing.\nBut as we shouldn\'t accept being fed by those with poor judgment\nabout food, we shouldn\'t accept an opinion for the truth if offered\nby someone with poor judgment about the relevant areas.\n\nThus one needs to check the claims, to listen to different sides\nof a controversy, to ask for sources or justification of an opinion.\nIn this way, anyone who wants to get a clear picture soon notices\nwhich claims are trustworthy, which ones are tenable but somewhat\nshaky, and which ones are poorly founded.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Aaron Bergman <abergman@physics.utexas.edu> writes:
>
>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups. com>,
>>"Souvik" <souvik1982@gmail.com> wrote:
>
>>>Is state-vector reduction (or collapse of the wavefunction) a physical
>>>process?
>
>>No one knows.
>
> Indeed, although there are a lot of people who claim they do. Quantum
> mechanics has a psychological effect similar to metaphysics - when
> otherwise honest people talk about it, they omit, distort and twist
> the truth to promote their own interpretation. They'll give you
> a firm but confusing answer, without informing you that a significant
> fraction of physicists (say, over 50%) disagree with it.
Do you think truth is a matter of majority votes???
Truth is rather a matter of listening to the different sides
of a controversy and then choosing the best.
It is obvious that whatever a person claims is first and foremost
his or her personal opinion, and not a fact. Who takes it for a
fact is simply misleading himself or herself. Thus there is no
need to qualify each of one's statements by clumsy phrases like
'in my opinion', or 'according to what I have read/understood', or
'as far as I am informed' or 'since this makes most sense to me'.
These phrases accompany silently any statement by anyone.
It is also obvious that an opinion doesn't become a fact because
it is believed by half the number of people from a particular
ensemble; truth would otherwise become dependent on the choice
of this ensemble.
Honesty therefore only requires that one asserts what one thinks
is true, and gives one's reasons upon request. This is the scientific
approach, since it lets others check upon the trustworthiness of
a claim.
> They'll
> say that those who disagree with them are unreasonable, illogical.
>
> Even very intelligent people do this. It's quite a bizarre social
> phenomenon to have physicists turning into politicians like this,
> attempting to manipulate and confuse others into sharing their
> view.
I don't think this is a fair assessment. Everything called
knowledge is in fact a set of beliefs of the person claiming it.
And this set of beliefs is more or less close to the objective
truth, depending on the standards of that persons.
Telling others what one thinks is true in no way manipulates
others any more than feeding others what one thinks is nourishing.
But as we shouldn't accept being fed by those with poor judgment
about food, we shouldn't accept an opinion for the truth if offered
by someone with poor judgment about the relevant areas.
Thus one needs to check the claims, to listen to different sides
of a controversy, to ask for sources or justification of an opinion.
In this way, anyone who wants to get a clear picture soon notices
which claims are trustworthy, which ones are tenable but somewhat
shaky, and which ones are poorly founded.
Arnold Neumaier
Seratend
May21-05, 11:48 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nArnold Neumaier a écrit :\n\n>\n> For example, if we measure the mass of a piece of metal, we actually\n> measure the expectation of the mass operator <M> (M is the sum of\n> all the particle masses).\n>\nThis is only true, in the absolute, if the piece of metal is made of an\ninfinite number of particle masses (convergence in law). What we really\nmeasure is the value of M= sum_i Mi and not <M>.\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier a écrit :
>
> For example, if we measure the mass of a piece of metal, we actually
> measure the expectation of the mass operator <M> (M is the sum of
> all the particle masses).
>
This is only true, in the absolute, if the piece of metal is made of an
infinite number of particle masses (convergence in law). What we really
measure is the value of M= sum_i Mi and not <M>.
Seratend.
Seratend
May21-05, 11:48 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nrof@maths.tcd.ie a écrit :\n> Aaron Bergman <abergman@physics.utexas.edu> writes:\n> Orthodox QM itself, or the Copenhagen interpretation, features\n> collapse but doesn\'t consider it physical. From the Copenhagen point\n> of view, the wavefunction encodes knowledge about the system, and\n> it collapses when a measurement is performed; that is, when we\n> acquire new knowledge, we have to update the mathematical object\n> which we use to represent knowledge. Hence different observers will\n> use different wavefunctions to describe the same system. The\n> Copenhagen view is still the officially recognised majority view,\n> but I doubt there are many physicists today who would agree that,\n> for example, the ground state orbital of an electron in a hydrogen\n> atom represents knowledge. Physicists dislike knowledge because\n> knowledge is subjective, and subjective things are bad.\n>\n> R.\n\nYes this is the formal point of view of the quantum results\nmeasurements. However, this does not explain the selection of the\neingenbasis used to match the computed results with the experimental\nresults.\nIn other words, for the collapse postulate, every eigenbasis is ok to\nexpress statistical results (the born rules), but in the lab, we just\nhave one basis where the statistics apply. Why?\n\nSeratend.\n\n(and please do not use the decoherence as the way to solve this issue)\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie a écrit :
> Aaron Bergman <abergman@physics.utexas.edu> writes:
> Orthodox QM itself, or the Copenhagen interpretation, features
> collapse but doesn't consider it physical. From the Copenhagen point
> of view, the wavefunction encodes knowledge about the system, and
> it collapses when a measurement is performed; that is, when we
> acquire new knowledge, we have to update the mathematical object
> which we use to represent knowledge. Hence different observers will
> use different wavefunctions to describe the same system. The
> Copenhagen view is still the officially recognised majority view,
> but I doubt there are many physicists today who would agree that,
> for example, the ground state orbital of an electron in a hydrogen
> atom represents knowledge. Physicists dislike knowledge because
> knowledge is subjective, and subjective things are bad.
>
> R.
Yes this is the formal point of view of the quantum results
measurements. However, this does not explain the selection of the
eingenbasis used to match the computed results with the experimental
results.
In other words, for the collapse postulate, every eigenbasis is ok to
express statistical results (the born rules), but in the lab, we just
have one basis where the statistics apply. Why?
Seratend.
(and please do not use the decoherence as the way to solve this issue)
Aaron Bergman
May21-05, 06:05 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> In other words, for the collapse postulate, every eigenbasis is ok to\n> express statistical results (the born rules), but in the lab, we just\n> have one basis where the statistics apply. Why?\n\nBecause we\'re entangling with a specific classical observable.\n\n> (and please do not use the decoherence as the way to solve this issue)\n\nDecoherence really does solve this issue up until you start to ask\nquestions about the human brain. At that point, I advocating throwing up\none\'s arms and being happy that we seem to get the right answer.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
Seratend <ser_monmail@yahoo.fr> wrote:
> In other words, for the collapse postulate, every eigenbasis is ok to
> express statistical results (the born rules), but in the lab, we just
> have one basis where the statistics apply. Why?
Because we're entangling with a specific classical observable.
> (and please do not use the decoherence as the way to solve this issue)
Decoherence really does solve this issue up until you start to ask
questions about the human brain. At that point, I advocating throwing up
one's arms and being happy that we seem to get the right answer.
Aaron
Arnold Neumaier
May22-05, 10:34 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier a écrit :\n>\n>>For example, if we measure the mass of a piece of metal, we actually\n>>measure the expectation of the mass operator <M> (M is the sum of\n>>all the particle masses).\n>>\n> This is only true, in the absolute, if the piece of metal is made of an\n> infinite number of particle masses (convergence in law). What we really\n> measure is the value of M= sum_i Mi and not <M>.\n\nNo. What we measure is an approximation of\n<integral_Omega dx a^*(x)Ma(x)> over the region Omega of interest.\nThis is the expression that figures in statistical mechanics\nderivations of macroscopic elasticity theory.\n\nStatistical mechanics must use the grand canonical ensemble\nfor calculations in local equilibrium such as elasticity theory\nor hydrodynamics, since the cell boundaries in the coarse graining\nare vague and hence the number of particles cannot be assumed\nconstant in each cell. Hence all fields are expectations.\n\nPlease resume discussion of this in the new thread\n\'\'Wave Function of the Universe?\'\' opened by Baugh,\nwhere I copied this answer.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier a écrit :
>
>>For example, if we measure the mass of a piece of metal, we actually
>>measure the expectation of the mass operator <M> (M is the sum of
>>all the particle masses).
>>
> This is only true, in the absolute, if the piece of metal is made of an
> infinite number of particle masses (convergence in law). What we really
> measure is the value of M= sum_i Mi and not <M>.
No. What we measure is an approximation of
<integral_Omega dx a^*(x)Ma(x)> over the region \Omega of interest.
This is the expression that figures in statistical mechanics
derivations of macroscopic elasticity theory.
Statistical mechanics must use the grand canonical ensemble
for calculations in local equilibrium such as elasticity theory
or hydrodynamics, since the cell boundaries in the coarse graining
are vague and hence the number of particles cannot be assumed
constant in each cell. Hence all fields are expectations.
Please resume discussion of this in the new thread
''Wave Function of the Universe?'' opened by Baugh,
where I copied this answer.
Arnold Neumaier
Frank Hellmann
May23-05, 03:57 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n>\n> Yes this is the formal point of view of the quantum results\n> measurements. However, this does not explain the selection of the\n> eingenbasis used to match the computed results with the experimental\n> results.\n> In other words, for the collapse postulate, every eigenbasis is ok to\n> express statistical results (the born rules), but in the lab, we just\n> have one basis where the statistics apply. Why?\n>\n> Seratend.\n>\n> (and please do not use the decoherence as the way to solve this\nissue)\n\nI have seen this argument quite a few times, do you have any good\nconcise review papers on this?\nA meassurement is represented by a Projection operator, and you can\ndevelop the whole apparatus of the statistical interpretation of QM\nwithout ever refferring to a basis, so I really don\'t see where this\nproblem comes into things.\n\nFrank.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
>
> Yes this is the formal point of view of the quantum results
> measurements. However, this does not explain the selection of the
> eingenbasis used to match the computed results with the experimental
> results.
> In other words, for the collapse postulate, every eigenbasis is ok to
> express statistical results (the born rules), but in the lab, we just
> have one basis where the statistics apply. Why?
>
> Seratend.
>
> (and please do not use the decoherence as the way to solve this
issue)
I have seen this argument quite a few times, do you have any good
concise review papers on this?
A meassurement is represented by a Projection operator, and you can
develop the whole apparatus of the statistical interpretation of QM
without ever refferring to a basis, so I really don't see where this
problem comes into things.
Frank.
Frank Hellmann
May23-05, 03:58 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Souvik wrote:\n> > Is state-vector reduction (or collapse of the wavefunction) a\nphysical\n> > process? Or is it really an artefact of our procedure of canonical\n> > quantisation?\n>\n> It is an artifact of the description of a quantum system by\n> a limited number of observables rather than by the state of\n> the whole universe. Once one projects to a subsystem, one\n> must ignore the details of the interaction with the unmodelled\n> environment and gets some dissipative effects. These are\n> responsible for the collapse.\n>\n\nUnless I\'m mistaken you are describing decoherence, which is not\nequivalent to collapse.\n\nFrank.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Souvik wrote:
> > Is state-vector reduction (or collapse of the wavefunction) a
physical
> > process? Or is it really an artefact of our procedure of canonical
> > quantisation?
>
> It is an artifact of the description of a quantum system by
> a limited number of observables rather than by the state of
> the whole universe. Once one projects to a subsystem, one
> must ignore the details of the interaction with the unmodelled
> environment and gets some dissipative effects. These are
> responsible for the collapse.
>
Unless I'm mistaken you are describing decoherence, which is not
equivalent to collapse.
Frank.
Seratend
May23-05, 03:59 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman a =E9crit :\n> In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\n> Seratend <ser_monmail@yahoo.fr> wrote:\n>\n> > In other words, for the collapse postulate, every eigenbasis is ok\nto\n> > express statistical results (the born rules), but in the lab, we\njust\n> > have one basis where the statistics apply. Why?\n>\n> Because we\'re entangling with a specific classical observable.\n>\nWhy? I mean the entanglement does not choose a basis. Every basis is ok\nto express the statistics of the entanglement.\nFor example, in statiscal classical mechanics we use to choose by\ndefault, A(p,q) as an observable (in the formulation a la Von Neumann,\n[q,p]=3D0). What does prevent us to choose another basis and other\nobservables to express the statistics? From this point, why in\nclassical mechanics do we seem to have the superselection rule\n(prefered basis=3D p,q)for the experiments?\n\n> > (and please do not use the decoherence as the way to solve this\nissue)\n>\n> Decoherence really does solve this issue up until you start to ask\n> questions about the human brain. At that point, I advocating throwing\nup\n> one\'s arms and being happy that we seem to get the right answer.\n>\n> Aaron\n\nYou can remove the human brain and just stay with events and outcomes\n(in order to avoid philosophical questions). Your point of view seems\nto be the selection of the basis (to express the results) after the\nexperiment: an a posteriori selection (no prediction).\nIn this case, you are implicitly saying (in my understanding) the QM\nframework does not give (a prediction) an answer to the preferred basis\nof experiment results. We must do before the experiment to know/learn\nwhat is the preferred basis. (We must have/construct a collection of\nexperiments where we know the preferred basis of the statistics in\norder to build other experiments for predictions - statistics on a\ngiven basis).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman a =E9crit :
> In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
> Seratend <ser_monmail@yahoo.fr> wrote:
>
> > In other words, for the collapse postulate, every eigenbasis is ok
to
> > express statistical results (the born rules), but in the lab, we
just
> > have one basis where the statistics apply. Why?
>
> Because we're entangling with a specific classical observable.
>
Why? I mean the entanglement does not choose a basis. Every basis is ok
to express the statistics of the entanglement.
For example, in statiscal classical mechanics we use to choose by
default, A(p,q) as an observable (in the formulation a la Von Neumann,
[q,p]=3D0). What does prevent us to choose another basis and other
observables to express the statistics? From this point, why in
classical mechanics do we seem to have the superselection rule
(prefered basis=3D p,q)for the experiments?
> > (and please do not use the decoherence as the way to solve this
issue)
>
> Decoherence really does solve this issue up until you start to ask
> questions about the human brain. At that point, I advocating throwing
up
> one's arms and being happy that we seem to get the right answer.
>
> Aaron
You can remove the human brain and just stay with events and outcomes
(in order to avoid philosophical questions). Your point of view seems
to be the selection of the basis (to express the results) after the
experiment: an a posteriori selection (no prediction).
In this case, you are implicitly saying (in my understanding) the QM
framework does not give (a prediction) an answer to the preferred basis
of experiment results. We must do before the experiment to know/learn
what is the preferred basis. (We must have/construct a collection of
experiments where we know the preferred basis of the statistics in
order to build other experiments for predictions - statistics on a
given basis).
Seratend.
rof@maths.tcd.ie
May23-05, 04:00 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend <ser_monmail@yahoo.fr> writes:\n\n>rof@maths.tcd.ie a crit :\n>> From the Copenhagen point\n>> of view, the wavefunction encodes knowledge about the system, and\n>> it collapses when a measurement is performed; that is, when we\n>> acquire new knowledge, we have to update the mathematical object\n>> which we use to represent knowledge.\n\n>Yes this is the formal point of view of the quantum results\n>measurements. However, this does not explain the selection of the\n>eingenbasis used to match the computed results with the experimental\n>results.\n>In other words, for the collapse postulate, every eigenbasis is ok to\n>express statistical results (the born rules), but in the lab, we just\n>have one basis where the statistics apply. Why?\n\n>(and please do not use the decoherence as the way to solve this issue)\n\nI\'m not sure I understand the question very clearly, but I\'ll try\nto answer it. There is a special basis - the position basis, although\nthis isn\'t an entire basis for the Hilbert space, since it doesn\'t\nspan the spin part of the Hilbert space, for example. Anyway, all\nmeasurements are ultimately measurements of position, as Bell\nwas fond of saying, for example the positions of instrument\npointers. To measure spin we separate the spin-up part of the beam\nfrom the spin-down part and then measure position. Because\nall interactions which can serve as measurements are local,\nmeaning that if system A wants to exchange information with system\nB it has to be in the same region of space, interactions with\nneighboring objects tend to act as position measurements.\n\nI hope this was what you were asking.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend <ser_monmail@yahoo.fr> writes:
>rof@maths.tcd.ie a crit :
>> From the Copenhagen point
>> of view, the wavefunction encodes knowledge about the system, and
>> it collapses when a measurement is performed; that is, when we
>> acquire new knowledge, we have to update the mathematical object
>> which we use to represent knowledge.
>Yes this is the formal point of view of the quantum results
>measurements. However, this does not explain the selection of the
>eingenbasis used to match the computed results with the experimental
>results.
>In other words, for the collapse postulate, every eigenbasis is ok to
>express statistical results (the born rules), but in the lab, we just
>have one basis where the statistics apply. Why?
>(and please do not use the decoherence as the way to solve this issue)
I'm not sure I understand the question very clearly, but I'll try
to answer it. There is a special basis - the position basis, although
this isn't an entire basis for the Hilbert space, since it doesn't
span the spin part of the Hilbert space, for example. Anyway, all
measurements are ultimately measurements of position, as Bell
was fond of saying, for example the positions of instrument
pointers. To measure spin we separate the spin-up part of the beam
from the spin-down part and then measure position. Because
all interactions which can serve as measurements are local,
meaning that if system A wants to exchange information with system
B it has to be in the same region of space, interactions with
neighboring objects tend to act as position measurements.
I hope this was what you were asking.
R.
rof@maths.tcd.ie
May23-05, 04:02 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n>rof@maths.tcd.ie wrote:\n\n>> Aaron Bergman <abergman@physics.utexas.edu> writes:\n>>\n>>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups .com>,\n>>>"Souvik" <souvik1982@gmail.com> wrote:\n>>\n>>>>Is state-vector reduction (or collapse of the wavefunction) a physical\n>>>>process?\n>>\n>>>No one knows.\n>>\n>> Indeed, although there are a lot of people who claim they do. Quantum\n>> mechanics has a psychological effect similar to metaphysics - when\n>> otherwise honest people talk about it, they omit, distort and twist\n>> the truth to promote their own interpretation. They\'ll give you\n>> a firm but confusing answer, without informing you that a significant\n>> fraction of physicists (say, over 50%) disagree with it.\n\n>Do you think truth is a matter of majority votes???\n>Truth is rather a matter of listening to the different sides\n>of a controversy and then choosing the best.\n\nThere are some things, like the canon of mathematics, classical\nmechanics, and the formalism of quantum mechanics which are\nwell-established. There are other things, like the interpretation\nof quantum mechanics, which aren\'t. It is difficult for a non-expert\nto know in advance which areas are well-established, where is no\ncontroversy, and in which areas there is a controversy among experts. If\nsuch a person asks a question like "Is state-vector reduction a\nphysical process?", then a physicist who responds by saying "No it\nisn\'t," without adding that this answer is merely his own opinion,\nis doing the inquirer a disservice.\n\nMost questions about physics have a clear, well-established\nanswer which can be found simply by asking a physicist, and only\nthe expert can be expected to know which questions are\nexceptions to this general rule. A physicist who gives an\napparently straightforward, if slightly confusing, answer\nto a question about physics, without making it clear that\nthis question has an unusual status in physics, that,\nunlike most questions in physics, this one has no\nwell-established answer, is implicitly telling the\nperson that this question is just like other questions\nin physics, that is has a well-established answer, and\nthat in fact the answer being given is the well-established\none.\n\nNow this is what you did, and you interpreted my post as an attack\non you, became angry, and treated me to three question marks and a\nlecture about how everything is mere opinion and belief:\n\n>Everything called\n>knowledge is in fact a set of beliefs of the person claiming it.\n\nReaders of this post will be very well aware that certain knowledge,\nfor example knowledge of definitions, of mathematical theorems of\nwhich one has seen the proof, and of many statements about physics,\nare not merely beliefs. When I say that Newton\'s third law states\nthat action and reaction are equal in magnitude, I am not merely\nexpressing my personal belief, for that is exactly what the third\nlaw says. When I say that a Banach space is a normed, complete\nvector space, I am not merely giving my opinion on the matter.\nClaiming that everything is opinion and nothing is well-established\nis a practice of those who oppose science. "Evolution is a theory\nnot a fact," they say.\n\nThis is, of course, all beside the point, but serves to illustrate\nmy original point, which was that, when it comes to interpreting\nquantum mechanics, otherwise honest people become less honest. I\nnoticed this first in myself and then in others. Only by explicitly\nacknowledging this and trying to overcome it are we likely to make\nprogress. Pretending that it\'s not true and trying to promote our\nown views through fighting against others with aggressive punctuation\nonly makes the situation worse.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>rof@maths.tcd.ie wrote:
>> Aaron Bergman <abergman@physics.utexas.edu> writes:
>>
>>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups. com>,
>>>"Souvik" <souvik1982@gmail.com> wrote:
>>
>>>>Is state-vector reduction (or collapse of the wavefunction) a physical
>>>>process?
>>
>>>No one knows.
>>
>> Indeed, although there are a lot of people who claim they do. Quantum
>> mechanics has a psychological effect similar to metaphysics - when
>> otherwise honest people talk about it, they omit, distort and twist
>> the truth to promote their own interpretation. They'll give you
>> a firm but confusing answer, without informing you that a significant
>> fraction of physicists (say, over 50%) disagree with it.
>Do you think truth is a matter of majority votes???
>Truth is rather a matter of listening to the different sides
>of a controversy and then choosing the best.
There are some things, like the canon of mathematics, classical
mechanics, and the formalism of quantum mechanics which are
well-established. There are other things, like the interpretation
of quantum mechanics, which aren't. It is difficult for a non-expert
to know in advance which areas are well-established, where is no
controversy, and in which areas there is a controversy among experts. If
such a person asks a question like "Is state-vector reduction a
physical process?", then a physicist who responds by saying "No it
isn't," without adding that this answer is merely his own opinion,
is doing the inquirer a disservice.
Most questions about physics have a clear, well-established
answer which can be found simply by asking a physicist, and only
the expert can be expected to know which questions are
exceptions to this general rule. A physicist who gives an
apparently straightforward, if slightly confusing, answer
to a question about physics, without making it clear that
this question has an unusual status in physics, that,
unlike most questions in physics, this one has no
well-established answer, is implicitly telling the
person that this question is just like other questions
in physics, that is has a well-established answer, and
that in fact the answer being given is the well-established
one.
Now this is what you did, and you interpreted my post as an attack
on you, became angry, and treated me to three question marks and a
lecture about how everything is mere opinion and belief:
>Everything called
>knowledge is in fact a set of beliefs of the person claiming it.
Readers of this post will be very well aware that certain knowledge,
for example knowledge of definitions, of mathematical theorems of
which one has seen the proof, and of many statements about physics,
are not merely beliefs. When I say that Newton's third law states
that action and reaction are equal in magnitude, I am not merely
expressing my personal belief, for that is exactly what the third
law says. When I say that a Banach space is a normed, complete
vector space, I am not merely giving my opinion on the matter.
Claiming that everything is opinion and nothing is well-established
is a practice of those who oppose science. "Evolution is a theory
not a fact," they say.
This is, of course, all beside the point, but serves to illustrate
my original point, which was that, when it comes to interpreting
quantum mechanics, otherwise honest people become less honest. I
noticed this first in myself and then in others. Only by explicitly
acknowledging this and trying to overcome it are we likely to make
progress. Pretending that it's not true and trying to promote our
own views through fighting against others with aggressive punctuation
only makes the situation worse.
R.
Aaron Bergman
May23-05, 11:12 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1116754314.909405.119910@z14g2000cwz.googlegroups .com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman a =E9crit :\n> > In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\n> > Seratend <ser_monmail@yahoo.fr> wrote:\n> >\n> > > In other words, for the collapse postulate, every eigenbasis is ok\n> to\n> > > express statistical results (the born rules), but in the lab, we\n> just\n> > > have one basis where the statistics apply. Why?\n> >\n> > Because we\'re entangling with a specific classical observable.\n> >\n> Why? I mean the entanglement does not choose a basis. Every basis is ok\n> to express the statistics of the entanglement.\n\nThis isn\'t just entanglement; it\'s entanglement with a classical\nobservable. That selects a basis, the one in which the classical\nobservable is diagonal.\n\n[...]\n\n> You can remove the human brain and just stay with events and outcomes\n> (in order to avoid philosophical questions). Your point of view seems\n> to be the selection of the basis (to express the results) after the\n> experiment: an a posteriori selection (no prediction).\n> In this case, you are implicitly saying (in my understanding) the QM\n> framework does not give (a prediction) an answer to the preferred basis\n> of experiment results. We must do before the experiment to know/learn\n> what is the preferred basis. (We must have/construct a collection of\n> experiments where we know the preferred basis of the statistics in\n> order to build other experiments for predictions - statistics on a\n> given basis).\n\nNot at all. Decoherence shows us how the basis is selected.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1116754314.909405.119910@z14g2000cwz.googlegroups. com>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman a =E9crit :
> > In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
> > Seratend <ser_monmail@yahoo.fr> wrote:
> >
> > > In other words, for the collapse postulate, every eigenbasis is ok
> to
> > > express statistical results (the born rules), but in the lab, we
> just
> > > have one basis where the statistics apply. Why?
> >
> > Because we're entangling with a specific classical observable.
> >
> Why? I mean the entanglement does not choose a basis. Every basis is ok
> to express the statistics of the entanglement.
This isn't just entanglement; it's entanglement with a classical
observable. That selects a basis, the one in which the classical
observable is diagonal.
[...]
> You can remove the human brain and just stay with events and outcomes
> (in order to avoid philosophical questions). Your point of view seems
> to be the selection of the basis (to express the results) after the
> experiment: an a posteriori selection (no prediction).
> In this case, you are implicitly saying (in my understanding) the QM
> framework does not give (a prediction) an answer to the preferred basis
> of experiment results. We must do before the experiment to know/learn
> what is the preferred basis. (We must have/construct a collection of
> experiments where we know the preferred basis of the statistics in
> order to build other experiments for predictions - statistics on a
> given basis).
Not at all. Decoherence shows us how the basis is selected.
Aaron
Arnold Neumaier
May24-05, 01:26 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>rof@maths.tcd.ie wrote:\n>\n>>>Aaron Bergman <abergman@physics.utexas.edu> writes:\n>>>\n>>>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups .com>,\n>>>>"Souvik" <souvik1982@gmail.com> wrote:\n>>>\n>>>>>Is state-vector reduction (or collapse of the wavefunction) a physical\n>>>>>process?\n>>>\n>>>>No one knows.\n>>>\n>>>Indeed, although there are a lot of people who claim they do. Quantum\n>>>mechanics has a psychological effect similar to metaphysics - when\n>>>otherwise honest people talk about it, they omit, distort and twist\n>>>the truth to promote their own interpretation. They\'ll give you\n>>>a firm but confusing answer, without informing you that a significant\n>>>fraction of physicists (say, over 50%) disagree with it.\n>\n>\n>>Do you think truth is a matter of majority votes???\n>>Truth is rather a matter of listening to the different sides\n>>of a controversy and then choosing the best.\n>\n>\n> There are some things, like the canon of mathematics, classical\n> mechanics, and the formalism of quantum mechanics which are\n> well-established. There are other things, like the interpretation\n> of quantum mechanics, which aren\'t. It is difficult for a non-expert\n> to know in advance which areas are well-established, where is no\n> controversy, and in which areas there is a controversy among experts. If\n> such a person asks a question like "Is state-vector reduction a\n> physical process?", then a physicist who responds by saying "No it\n> isn\'t," without adding that this answer is merely his own opinion,\n> is doing the inquirer a disservice.\n>\n> Most questions about physics have a clear, well-established\n> answer which can be found simply by asking a physicist, and only\n> the expert can be expected to know which questions are\n> exceptions to this general rule. A physicist who gives an\n> apparently straightforward, if slightly confusing, answer\n> to a question about physics, without making it clear that\n> this question has an unusual status in physics, that,\n> unlike most questions in physics, this one has no\n> well-established answer, is implicitly telling the\n> person that this question is just like other questions\n> in physics, that is has a well-established answer, and\n> that in fact the answer being given is the well-established\n> one.\n>\n> Now this is what you did, and you interpreted my post as an attack\n> on you, became angry, and treated me to three question marks and a\n> lecture about how everything is mere opinion and belief:\n>\n>\n>>Everything called\n>>knowledge is in fact a set of beliefs of the person claiming it.\n>\n>\n> Readers of this post will be very well aware that certain knowledge,\n> for example knowledge of definitions, of mathematical theorems of\n> which one has seen the proof, and of many statements about physics,\n> are not merely beliefs. When I say that Newton\'s third law states\n> that action and reaction are equal in magnitude, I am not merely\n> expressing my personal belief, for that is exactly what the third\n> law says. When I say that a Banach space is a normed, complete\n> vector space, I am not merely giving my opinion on the matter.\n> Claiming that everything is opinion and nothing is well-established\n> is a practice of those who oppose science. "Evolution is a theory\n> not a fact," they say.\n>\n> This is, of course, all beside the point, but serves to illustrate\n> my original point, which was that, when it comes to interpreting\n> quantum mechanics, otherwise honest people become less honest. I\n> noticed this first in myself and then in others. Only by explicitly\n> acknowledging this and trying to overcome it are we likely to make\n> progress. Pretending that it\'s not true and trying to promote our\n> own views through fighting against others with aggressive punctuation\n> only makes the situation worse.\n\nYou seem to be projecting _your_ anger onto me.\n\nThat you find three question marks and a short essay on learning\ntruth in controversial matters an aggressive behavior in a context\nwhere controversial things are discussed is a sign of your emotional\nstate rather than a property of my contribution.\n\nI wasn\'t angry at all when I wrote the mail you find so objectionable,\nbut simply thought that your assessment of the situation (namely,\ncharacterizing otherwise honest people as people who \'omit, distort\nand twist the truth\' was far off the mark.\n\nTo say that \'\'Everything called knowledge is in fact a set\nof beliefs of the person claiming it.\'\' does not contradict the\nobjectivity of mathematical definitions. When I say that a Banach\nspace is a normed, complete vector space, I both state my belief\nand happen to coincide with the social consensus of the guild of\nmathematicians. And when I say that state reduction is a\nphysical process, I both state my belief and happen to coincide with\nfamous physicists like von Neumann and many others, and this is good\nenough to make this statement honestly.\n\nIt is ridiculous to require a percentage of people in a field\nto agree with you before you utter a statement without adding\na qualification like \'I believe\' or \'Some physisicts believe\'.\nThere would never be an agreement on the percentage required\nto do so.\n\nIn any case, such a requirement is _not_ part of the social agreement\nof what constitutes ethical behavior of scientists. Thus you have\nno right to accuse them of omitting, distorting and twisting\nthe truth.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>rof@maths.tcd.ie wrote:
>
>>>Aaron Bergman <abergman@physics.utexas.edu> writes:
>>>
>>>>In article <1116090071.291677.269500@g14g2000cwa.googlegroups. com>,
>>>>"Souvik" <souvik1982@gmail.com> wrote:
>>>
>>>>>Is state-vector reduction (or collapse of the wavefunction) a physical
>>>>>process?
>>>
>>>>No one knows.
>>>
>>>Indeed, although there are a lot of people who claim they do. Quantum
>>>mechanics has a psychological effect similar to metaphysics - when
>>>otherwise honest people talk about it, they omit, distort and twist
>>>the truth to promote their own interpretation. They'll give you
>>>a firm but confusing answer, without informing you that a significant
>>>fraction of physicists (say, over 50%) disagree with it.
>
>
>>Do you think truth is a matter of majority votes???
>>Truth is rather a matter of listening to the different sides
>>of a controversy and then choosing the best.
>
>
> There are some things, like the canon of mathematics, classical
> mechanics, and the formalism of quantum mechanics which are
> well-established. There are other things, like the interpretation
> of quantum mechanics, which aren't. It is difficult for a non-expert
> to know in advance which areas are well-established, where is no
> controversy, and in which areas there is a controversy among experts. If
> such a person asks a question like "Is state-vector reduction a
> physical process?", then a physicist who responds by saying "No it
> isn't," without adding that this answer is merely his own opinion,
> is doing the inquirer a disservice.
>
> Most questions about physics have a clear, well-established
> answer which can be found simply by asking a physicist, and only
> the expert can be expected to know which questions are
> exceptions to this general rule. A physicist who gives an
> apparently straightforward, if slightly confusing, answer
> to a question about physics, without making it clear that
> this question has an unusual status in physics, that,
> unlike most questions in physics, this one has no
> well-established answer, is implicitly telling the
> person that this question is just like other questions
> in physics, that is has a well-established answer, and
> that in fact the answer being given is the well-established
> one.
>
> Now this is what you did, and you interpreted my post as an attack
> on you, became angry, and treated me to three question marks and a
> lecture about how everything is mere opinion and belief:
>
>
>>Everything called
>>knowledge is in fact a set of beliefs of the person claiming it.
>
>
> Readers of this post will be very well aware that certain knowledge,
> for example knowledge of definitions, of mathematical theorems of
> which one has seen the proof, and of many statements about physics,
> are not merely beliefs. When I say that Newton's third law states
> that action and reaction are equal in magnitude, I am not merely
> expressing my personal belief, for that is exactly what the third
> law says. When I say that a Banach space is a normed, complete
> vector space, I am not merely giving my opinion on the matter.
> Claiming that everything is opinion and nothing is well-established
> is a practice of those who oppose science. "Evolution is a theory
> not a fact," they say.
>
> This is, of course, all beside the point, but serves to illustrate
> my original point, which was that, when it comes to interpreting
> quantum mechanics, otherwise honest people become less honest. I
> noticed this first in myself and then in others. Only by explicitly
> acknowledging this and trying to overcome it are we likely to make
> progress. Pretending that it's not true and trying to promote our
> own views through fighting against others with aggressive punctuation
> only makes the situation worse.
You seem to be projecting _your_ anger onto me.
That you find three question marks and a short essay on learning
truth in controversial matters an aggressive behavior in a context
where controversial things are discussed is a sign of your emotional
state rather than a property of my contribution.
I wasn't angry at all when I wrote the mail you find so objectionable,
but simply thought that your assessment of the situation (namely,
characterizing otherwise honest people as people who 'omit, distort
and twist the truth' was far off the mark.
To say that ''Everything called knowledge is in fact a set
of beliefs of the person claiming it.'' does not contradict the
objectivity of mathematical definitions. When I say that a Banach
space is a normed, complete vector space, I both state my belief
and happen to coincide with the social consensus of the guild of
mathematicians. And when I say that state reduction is a
physical process, I both state my belief and happen to coincide with
famous physicists like von Neumann and many others, and this is good
enough to make this statement honestly.
It is ridiculous to require a percentage of people in a field
to agree with you before you utter a statement without adding
a qualification like 'I believe' or 'Some physisicts believe'.
There would never be an agreement on the percentage required
to do so.
In any case, such a requirement is _not_ part of the social agreement
of what constitutes ethical behavior of scientists. Thus you have
no right to accuse them of omitting, distorting and twisting
the truth.
Arnold Neumaier
rof@maths.tcd.ie
May24-05, 01:26 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman <abergman@physics.utexas.edu> writes:\n\n>In article <1116754314.909405.119910@z14g2000cwz.googlegroups .com>,\n> "Seratend" <ser_monmail@yahoo.fr> wrote:\n\n>> Aaron Bergman a =E9crit :\n>> > In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\n>> > Seratend <ser_monmail@yahoo.fr> wrote:\n>> >\n>> > > In other words, for the collapse postulate, every eigenbasis is ok\n>> to\n>> > > express statistical results (the born rules), but in the lab, we\n>> just\n>> > > have one basis where the statistics apply. Why?\n>> >\n>> > Because we\'re entangling with a specific classical observable.\n>> >\n>> Why? I mean the entanglement does not choose a basis. Every basis is ok\n>> to express the statistics of the entanglement.\n\n>This isn\'t just entanglement; it\'s entanglement with a classical\n>observable. That selects a basis, the one in which the classical\n>observable is diagonal.\n\nYou don\'t even need the observable to be classical to get a\npreferred basis; a decomposition of the Hilbert space, H, into\ntwo factors, H_a and H_b, corresponding to "system" and "environment",\nor "system" and "measuring device" will be enough to select\na special basis, in the sense that an overall state |psi>\nof H can be decomposed into \\sum_i l_i |a_i>|b_i>, where\nthe |a_i> are an orthonormal basis for H_a and |b_i> are an\northonormal basis for H_b. The bases selected by the decomposition\ndepend on |psi>.\n\nIt\'s called the Schmidt decomposition, and the l_i are called\nthe Schmidt coefficients. If there\'s an initial state\nwhich factorises into the state of the system and\nthe state of the measuring device, say, |psi_0>=|a_0>|b_0>,\nthen after an interaction between them, that state of\nthe system, |psi> can be decomposed according to the\nSchmidt decomposition, which gives a preferred basis\nfor that interaction (there are pathological cases\nwhere the decomposition isn\'t unique, but these are\n"of measure zero"). Because of the locality of information\ntransfer, this tends to pick out basis states which\nare fairly localised (presuming that spatial degrees\nof freedom are included in the system and that all\ninteractions are, in fact, local), or rather, were\nlocalised at the time of the interaction.\n\n>> You can remove the human brain and just stay with events and outcomes\n>> (in order to avoid philosophical questions). Your point of view seems\n>> to be the selection of the basis (to express the results) after the\n>> experiment: an a posteriori selection (no prediction).\n>> In this case, you are implicitly saying (in my understanding) the QM\n>> framework does not give (a prediction) an answer to the preferred basis\n>> of experiment results. We must do before the experiment to know/learn\n>> what is the preferred basis. (We must have/construct a collection of\n>> experiments where we know the preferred basis of the statistics in\n>> order to build other experiments for predictions - statistics on a\n>> given basis).\n\n>Not at all. Decoherence shows us how the basis is selected.\n\nPretty much; the above process, repeated many times, with\nlocal interactions of many systems with one another, gives\nyou decoherence, with the various systems "telling each other"\nwhere they are with respect to one another, leading to\na preferred basis which is approximately the position basis,\nalthough it\'s not exactly a complete basis.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman <abergman@physics.utexas.edu> writes:
>In article <1116754314.909405.119910@z14g2000cwz.googlegroups. com>,
> "Seratend" <ser_monmail@yahoo.fr> wrote:
>> Aaron Bergman a =E9crit :>> > In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
>> > Seratend <ser_monmail@yahoo.fr> wrote:
>> >
>> > > In other words, for the collapse postulate, every eigenbasis is ok
>> to
>> > > express statistical results (the born rules), but in the lab, we
>> just
>> > > have one basis where the statistics apply. Why?
>> >
>> > Because we're entangling with a specific classical observable.
>> >
>> Why? I mean the entanglement does not choose a basis. Every basis is ok
>> to express the statistics of the entanglement.
>This isn't just entanglement; it's entanglement with a classical
>observable. That selects a basis, the one in which the classical
>observable is diagonal.
You don't even need the observable to be classical to get a
preferred basis; a decomposition of the Hilbert space, H, into
two factors, H_a and H_b, corresponding to "system" and "environment",
or "system" and "measuring device" will be enough to select
a special basis, in the sense that an overall state |\psi>
of H can be decomposed into \sum_i l_i |a_i>|b_i>, where
the |a_i> are an orthonormal basis for H_a and |b_i> are an
orthonormal basis for H_b. The bases selected by the decomposition
depend on |\psi>.
It's called the Schmidt decomposition, and the l_i are called
the Schmidt coefficients. If there's an initial state
which factorises into the state of the system and
the state of the measuring device, say, |\psi_0>=|a_0>|b_0>,
then after an interaction between them, that state of
the system, |\psi> can be decomposed according to the
Schmidt decomposition, which gives a preferred basis
for that interaction (there are pathological cases
where the decomposition isn't unique, but these are
"of measure zero"). Because of the locality of information
transfer, this tends to pick out basis states which
are fairly localised (presuming that spatial degrees
of freedom are included in the system and that all
interactions are, in fact, local), or rather, were
localised at the time of the interaction.
>> You can remove the human brain and just stay with events and outcomes
>> (in order to avoid philosophical questions). Your point of view seems
>> to be the selection of the basis (to express the results) after the
>> experiment: an a posteriori selection (no prediction).
>> In this case, you are implicitly saying (in my understanding) the QM
>> framework does not give (a prediction) an answer to the preferred basis
>> of experiment results. We must do before the experiment to know/learn
>> what is the preferred basis. (We must have/construct a collection of
>> experiments where we know the preferred basis of the statistics in
>> order to build other experiments for predictions - statistics on a
>> given basis).
>Not at all. Decoherence shows us how the basis is selected.
Pretty much; the above process, repeated many times, with
local interactions of many systems with one another, gives
you decoherence, with the various systems "telling each other"
where they are with respect to one another, leading to
a preferred basis which is approximately the position basis,
although it's not exactly a complete basis.
R.
markwh04@yahoo.com
May24-05, 08:02 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> But since we cannot know the full state of the whole universe,\n> we are doomed to such reduced descriptions and hence to the\n> collapse.\n\nOr more strongly: as Smolin has pointed out, there may not even *be*\nsuch a thing as a state for the whole universe, not even a\nconfiguration space! This necessarily forces one into a local\ndescription and relative states cease to be merely an expedient, and\nbecome a fundamental part of the whole enterprise.\n\nIn that case, collapse is there from the outset because reduced states\nare all you have.\n\nTo put it more clearly: in the absence of a universal state or even a\nuniversal configuration space, the universe in effect becomes an open\nsystem.\n\nA second account, not mutually exclusive (and in fact closely related),\nfor the collapse comes from the fact that the most general quantum\ntheory [see note 1] admits both quantum AND classical degrees of\nfreedom; the latter playing the role of superselection parameters.\n\nIn the most general case, a relative state obtained by tracing out the\nenvironmental modes will cut across the superselection boundaries and\ngive you a state which is a mixture with respect to the classical\ndegrees.\n\nStates that lie in different superselection sectors combine only\nclassically, never by superposition. By itself, a system can\'t evolve\nin such a way as to transmit information from the quantum to the\nclassical degrees (i.e. a Schroedinger or automorphic evolution\nautomatically precludes collapse-through-superselection). That\'s what\nwould be required to get a "measurement" type event. But when combined\nwith the feature of there being a cut-off at the boundary of the\nenvironment, you get the desired result of\ncollapse-through-superselection.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> But since we cannot know the full state of the whole universe,
> we are doomed to such reduced descriptions and hence to the
> collapse.
Or more strongly: as Smolin has pointed out, there may not even *be*
such a thing as a state for the whole universe, not even a
configuration space! This necessarily forces one into a local
description and relative states cease to be merely an expedient, and
become a fundamental part of the whole enterprise.
In that case, collapse is there from the outset because reduced states
are all you have.
To put it more clearly: in the absence of a universal state or even a
universal configuration space, the universe in effect becomes an open
system.
A second account, not mutually exclusive (and in fact closely related),
for the collapse comes from the fact that the most general quantum
theory [see note 1] admits both quantum AND classical degrees of
freedom; the latter playing the role of superselection parameters.
In the most general case, a relative state obtained by tracing out the
environmental modes will cut across the superselection boundaries and
give you a state which is a mixture with respect to the classical
degrees.
States that lie in different superselection sectors combine only
classically, never by superposition. By itself, a system can't evolve
in such a way as to transmit information from the quantum to the
classical degrees (i.e. a Schroedinger or automorphic evolution
automatically precludes collapse-through-superselection). That's what
would be required to get a "measurement" type event. But when combined
with the feature of there being a cut-off at the boundary of the
environment, you get the desired result of
collapse-through-superselection.
Seratend
May25-05, 11:21 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman a écrit :\n> > Aaron Bergman a =E9crit :\n> > > In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\n> > > Seratend <ser_monmail@yahoo.fr> wrote:\n> > > > In other words, for the collapse postulate, every eigenbasis is ok to\n> > > > express statistical results (the born rules), but in the lab, we just\n> > > > have one basis where the statistics apply. Why?\n> > >\n> > > Because we\'re entangling with a specific classical observable.\n> > >\n> > Why? I mean the entanglement does not choose a basis. Every basis is ok\n> > to express the statistics of the entanglement.\n>\n> This isn\'t just entanglement; it\'s entanglement with a classical\n> observable. That selects a basis, the one in which the classical\n> observable is diagonal.\n>\nWell if your answer is simply the preferred eigenbasis is the\neigenbasis of the classical observable, you are just saying that we\nonly know the preferred basis after the experiment as QM does not\ndescribe what the classical observable is and the born rules do not\nselect a preferred basis (every basis is ok for the born rules).\nTherefore, you are saying that QM theory does not give a prediction of\nthe preferred basis in an experiment (what is this classical observable\nfor this experiment). Therefore, we need to make at least an experiment\nto learn the preferred basis of this classical observable.\n\n> Not at all. Decoherence shows us how the basis is selected.\n\nNo, as you\'ve said above, in this case, it is the classical observable\nthat gives the preferred basis of the experiment (the one where we\nreally measure the born rule statistics).\nAs long as QM does not predict the preferred observable of an\nexperiment (the born rules), I don\'t know how you can say that\ndecoherence show us how the basis is selected.\n\nSeratend\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman a écrit :
> > Aaron Bergman a =E9crit :
> > > In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
> > > Seratend <ser_monmail@yahoo.fr> wrote:
> > > > In other words, for the collapse postulate, every eigenbasis is ok to
> > > > express statistical results (the born rules), but in the lab, we just
> > > > have one basis where the statistics apply. Why?
> > >
> > > Because we're entangling with a specific classical observable.
> > >
> > Why? I mean the entanglement does not choose a basis. Every basis is ok
> > to express the statistics of the entanglement.
>
> This isn't just entanglement; it's entanglement with a classical
> observable. That selects a basis, the one in which the classical
> observable is diagonal.
>
Well if your answer is simply the preferred eigenbasis is the
eigenbasis of the classical observable, you are just saying that we
only know the preferred basis after the experiment as QM does not
describe what the classical observable is and the born rules do not
select a preferred basis (every basis is ok for the born rules).
Therefore, you are saying that QM theory does not give a prediction of
the preferred basis in an experiment (what is this classical observable
for this experiment). Therefore, we need to make at least an experiment
to learn the preferred basis of this classical observable.
> Not at all. Decoherence shows us how the basis is selected.
No, as you've said above, in this case, it is the classical observable
that gives the preferred basis of the experiment (the one where we
really measure the born rule statistics).
As long as QM does not predict the preferred observable of an
experiment (the born rules), I don't know how you can say that
decoherence show us how the basis is selected.
Seratend
Arnold Neumaier
May25-05, 11:21 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>markwh04@yahoo.com wrote:\n> Arnold Neumaier wrote:\n>\n>>But since we cannot know the full state of the whole universe,\n>>we are doomed to such reduced descriptions and hence to the\n>>collapse.\n>\n>\n> Or more strongly: as Smolin has pointed out, there may not even *be*\n> such a thing as a state for the whole universe, not even a\n> configuration space! This necessarily forces one into a local\n> description and relative states cease to be merely an expedient, and\n> become a fundamental part of the whole enterprise.\n>\n> In that case, collapse is there from the outset because reduced states\n> are all you have.\n>\n> To put it more clearly: in the absence of a universal state or even a\n> universal configuration space, the universe in effect becomes an open\n> system.\n\nI prefer to view this situation as an indication of missing degrees of\nfreedom.\n\n\n> A second account, not mutually exclusive (and in fact closely related),\n> for the collapse comes from the fact that the most general quantum\n> theory [see note 1] admits both quantum AND classical degrees of\n> freedom; the latter playing the role of superselection parameters.\n\nWhere is note 1?\n\n\n> In the most general case, a relative state obtained by tracing out the\n> environmental modes will cut across the superselection boundaries and\n> give you a state which is a mixture with respect to the classical\n> degrees.\n\nHow can this be? Traditionally, superselection rules refer to\noperators that are always in an eigenstate. A relative trace is\nthen in the same state with respect to these operators.\nThus the classical degrees of freedom would not mix.\nOr do you have something different in mind?\n\n\n> States that lie in different superselection sectors combine only\n> classically, never by superposition. By itself, a system can\'t evolve\n> in such a way as to transmit information from the quantum to the\n> classical degrees (i.e. a Schroedinger or automorphic evolution\n> automatically precludes collapse-through-superselection). That\'s what\n> would be required to get a "measurement" type event.\n\nThis happens in nonlinear quantum dynamics.\n\n> But when combined\n> with the feature of there being a cut-off at the boundary of the\n> environment, you get the desired result of\n> collapse-through-superselection.\n\nCould you please provide a good reference?\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>markwh04@yahoo.com wrote:
> Arnold Neumaier wrote:
>
>>But since we cannot know the full state of the whole universe,
>>we are doomed to such reduced descriptions and hence to the
>>collapse.
>
>
> Or more strongly: as Smolin has pointed out, there may not even *be*
> such a thing as a state for the whole universe, not even a
> configuration space! This necessarily forces one into a local
> description and relative states cease to be merely an expedient, and
> become a fundamental part of the whole enterprise.
>
> In that case, collapse is there from the outset because reduced states
> are all you have.
>
> To put it more clearly: in the absence of a universal state or even a
> universal configuration space, the universe in effect becomes an open
> system.
I prefer to view this situation as an indication of missing degrees of
freedom.
> A second account, not mutually exclusive (and in fact closely related),
> for the collapse comes from the fact that the most general quantum
> theory [see note 1] admits both quantum AND classical degrees of
> freedom; the latter playing the role of superselection parameters.
Where is note 1?
> In the most general case, a relative state obtained by tracing out the
> environmental modes will cut across the superselection boundaries and
> give you a state which is a mixture with respect to the classical
> degrees.
How can this be? Traditionally, superselection rules refer to
operators that are always in an eigenstate. A relative trace is
then in the same state with respect to these operators.
Thus the classical degrees of freedom would not mix.
Or do you have something different in mind?
> States that lie in different superselection sectors combine only
> classically, never by superposition. By itself, a system can't evolve
> in such a way as to transmit information from the quantum to the
> classical degrees (i.e. a Schroedinger or automorphic evolution
> automatically precludes collapse-through-superselection). That's what
> would be required to get a "measurement" type event.
This happens in nonlinear quantum dynamics.
> But when combined
> with the feature of there being a cut-off at the boundary of the
> environment, you get the desired result of
> collapse-through-superselection.
Could you please provide a good reference?
Arnold Neumaier
Aaron Bergman
May25-05, 04:17 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117014495.964319.125450@z14g2000cwz.googlegroups .com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman a écrit :\n> > > Aaron Bergman a =E9crit :\n> > > > In article <1116673523.731545.15140@g49g2000cwa.googlegroups. com>,\n> > > > Seratend <ser_monmail@yahoo.fr> wrote:\n> > > > > In other words, for the collapse postulate, every eigenbasis is ok to\n> > > > > express statistical results (the born rules), but in the lab, we just\n> > > > > have one basis where the statistics apply. Why?\n> > > >\n> > > > Because we\'re entangling with a specific classical observable.\n> > > >\n> > > Why? I mean the entanglement does not choose a basis. Every basis is ok\n> > > to express the statistics of the entanglement.\n> >\n> > This isn\'t just entanglement; it\'s entanglement with a classical\n> > observable. That selects a basis, the one in which the classical\n> > observable is diagonal.\n> >\n> Well if your answer is simply the preferred eigenbasis is the\n> eigenbasis of the classical observable, you are just saying that we\n> only know the preferred basis after the experiment as QM does not\n> describe what the classical observable is and the born rules do not\n> select a preferred basis (every basis is ok for the born rules).\n> Therefore, you are saying that QM theory does not give a prediction of\n> the preferred basis in an experiment (what is this classical observable\n> for this experiment). Therefore, we need to make at least an experiment\n> to learn the preferred basis of this classical observable.\n\nWhen you describe an experiment in quantum mechanics, you separate out\nthe world into classical and quantum components. The classical component\ncomes with a preferred basis given by the macrostates of the measurement\napparatus. When you entangle the measuring device with the quantum\nsystem, decoherence tells you that the entangled states essentially no\nlonger interfere. Now, why we only perceive one branch of the decoherent\nwavefunction is a complete mystery, but the basis is completely\ndeteremined by the experimental setup.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117014495.964319.125450@z14g2000cwz.googlegroups. com>,
Seratend <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman a écrit :
> > > Aaron Bergman a =E9crit :
> > > > In article <1116673523.731545.15140@g49g2000cwa.googlegroups.c om>,
> > > > Seratend <ser_monmail@yahoo.fr> wrote:
> > > > > In other words, for the collapse postulate, every eigenbasis is ok to
> > > > > express statistical results (the born rules), but in the lab, we just
> > > > > have one basis where the statistics apply. Why?
> > > >
> > > > Because we're entangling with a specific classical observable.
> > > >
> > > Why? I mean the entanglement does not choose a basis. Every basis is ok
> > > to express the statistics of the entanglement.
> >
> > This isn't just entanglement; it's entanglement with a classical
> > observable. That selects a basis, the one in which the classical
> > observable is diagonal.
> >
> Well if your answer is simply the preferred eigenbasis is the
> eigenbasis of the classical observable, you are just saying that we
> only know the preferred basis after the experiment as QM does not
> describe what the classical observable is and the born rules do not
> select a preferred basis (every basis is ok for the born rules).
> Therefore, you are saying that QM theory does not give a prediction of
> the preferred basis in an experiment (what is this classical observable
> for this experiment). Therefore, we need to make at least an experiment
> to learn the preferred basis of this classical observable.
When you describe an experiment in quantum mechanics, you separate out
the world into classical and quantum components. The classical component
comes with a preferred basis given by the macrostates of the measurement
apparatus. When you entangle the measuring device with the quantum
system, decoherence tells you that the entangled states essentially no
longer interfere. Now, why we only perceive one branch of the decoherent
wavefunction is a complete mystery, but the basis is completely
deteremined by the experimental setup.
Aaron
> Is state-vector reduction (or collapse of the wavefunction) a physical
> process? Or is it really an artefact of our procedure of canonical
> quantisation?[/color]
It is an artifact of the description of a quantum system by
a limited number of observables rather than by the state of
the whole universe. Once one projects to a subsystem, one
must ignore the details of the interaction with the unmodelled
environment and gets some dissipative effects. These are
responsible for the collapse.
But since we cannot know the full state of the whole universe,
we are doomed to such reduced descriptions and hence to the
collapse. Actually it is a big help in using QM...
Arnold Neumaier
Could you explain this more ? maybe give an example :smile:
Seratend
May26-05, 01:34 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nAaron Bergman a écrit :\n> In article <1117014495.964319.125450@z14g2000cwz.googlegroups .com>,\n>\n> When you describe an experiment in quantum mechanics, you separate out\n> the world into classical and quantum components. The classical component\n> comes with a preferred basis given by the macrostates of the measurement\n> apparatus. When you entangle the measuring device with the quantum\n> system, decoherence tells you that the entangled states essentially no\n> longer interfere.\n\nI understand you seem to adopt the copenhagen interpretation. If this\nis the case, once again, CI does not explain the preferred basis, this\nis an an external data compatible with the postulates of QM, but not\nexplained by QM theory (the classical apparatus and its eigen basis in\nCI is not explained) . I understand decoherence tells us that there is\na local basis where there is no interference (the projected density\nmatric is diagonal in this eigenbasis), providing a sufficient\ninteraction with the environment. However, nothing in QM, prevents one\nto choose another eigenbasis where we have interferences, otherwise, it\nwould be impossible to observe interference in quantum experiments\n(e.g. double slits interferences, squizz, etc ...). Therefore, I really\ndo not understand how you can say that the basis where the local\ndensity matrix is diagonal is the preferred eigenbasis of the\nexperiment and that this basis may be or not the one choosen by the\nclassical apparatus (what in QM postulates infere this result) .\n\n> Now, why we only perceive one branch of the decoherent\n> wavefunction is a complete mystery, but the basis is completely\n> deteremined by the experimental setup.\n>\n> Aaron\n\nI understand what you call one branch of the decoherent wavefunction as\nan outcome of the experiment (the state after the experiment given by\nthe outcome). If this is the case, I have no problem with this part as\nQM theory deals explicitely with statistical predictions of experiment\noutcomes and not with the prediction of the outcomes (the born rules).\nIt is mainly a matter of choice (statistical versus deterministic\ndescription) in a theory.\n\nMy question regarding this theory remains: does QM theory explain the\npreferred basis or not?\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman a écrit :
> In article <1117014495.964319.125450@z14g2000cwz.googlegroups. com>,
>
> When you describe an experiment in quantum mechanics, you separate out
> the world into classical and quantum components. The classical component
> comes with a preferred basis given by the macrostates of the measurement
> apparatus. When you entangle the measuring device with the quantum
> system, decoherence tells you that the entangled states essentially no
> longer interfere.
I understand you seem to adopt the copenhagen interpretation. If this
is the case, once again, CI does not explain the preferred basis, this
is an an external data compatible with the postulates of QM, but not
explained by QM theory (the classical apparatus and its eigen basis in
CI is not explained) . I understand decoherence tells us that there is
a local basis where there is no interference (the projected density
matric is diagonal in this eigenbasis), providing a sufficient
interaction with the environment. However, nothing in QM, prevents one
to choose another eigenbasis where we have interferences, otherwise, it
would be impossible to observe interference in quantum experiments
(e.g. double slits interferences, squizz, etc ...). Therefore, I really
do not understand how you can say that the basis where the local
density matrix is diagonal is the preferred eigenbasis of the
experiment and that this basis may be or not the one choosen by the
classical apparatus (what in QM postulates infere this result) .
> Now, why we only perceive one branch of the decoherent
> wavefunction is a complete mystery, but the basis is completely
> deteremined by the experimental setup.
>
> Aaron
I understand what you call one branch of the decoherent wavefunction as
an outcome of the experiment (the state after the experiment given by
the outcome). If this is the case, I have no problem with this part as
QM theory deals explicitely with statistical predictions of experiment
outcomes and not with the prediction of the outcomes (the born rules).
It is mainly a matter of choice (statistical versus deterministic
description) in a theory.
My question regarding this theory remains: does QM theory explain the
preferred basis or not?
Seratend.
Arnold Neumaier
May26-05, 02:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Frank Hellmann wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Souvik wrote:\n>>\n>>>Is state-vector reduction (or collapse of the wavefunction) a physical\n>>>process? Or is it really an artefact of our procedure of canonical\n>>>quantisation?\n>>\n>>It is an artifact of the description of a quantum system by\n>>a limited number of observables rather than by the state of\n>>the whole universe. Once one projects to a subsystem, one\n>>must ignore the details of the interaction with the unmodelled\n>>environment and gets some dissipative effects. These are\n>>responsible for the collapse.\n>>\n> Unless I\'m mistaken you are describing decoherence, which is not\n> equivalent to collapse.\n\nThe two are not equivalent but related. Decoherence is the\napparent collapse due to entanglement with the environment.\nIt does not lead to state reduction and does not solve the\nmeasurement problem. See my paper\nA. Neumaier,\nCollapse challenge for interpretations of quantum mechanics\nquant-ph/0505172\nand the recent survey\nM. Schlosshauer,\nDecoherence, the Measurement Problem, and Interpretations of\nQuantum Mechanics\nRev. Mod. Phys. 76 (2004), 1267--1305.\nquant-ph/0312059.\n\nCollapse is the result of approximating the entangled dynamics\nby a Markov approximation, resulting in a dissipative master\nequation of Lindblad type. The latter have built in collapse.\nThe validity of the Markov approximation is an additional\nassumption beyond decoherence. It is responsible for the\ncollapse.\n\nQuantum optics and hence all high quality experiments for\nthe foundations of quantum mechanics are unthinkable without\nthe Markov approximation.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann wrote:
> Arnold Neumaier wrote:
>
>>Souvik wrote:
>>
>>>Is state-vector reduction (or collapse of the wavefunction) a physical
>>>process? Or is it really an artefact of our procedure of canonical
>>>quantisation?
>>
>>It is an artifact of the description of a quantum system by
>>a limited number of observables rather than by the state of
>>the whole universe. Once one projects to a subsystem, one
>>must ignore the details of the interaction with the unmodelled
>>environment and gets some dissipative effects. These are
>>responsible for the collapse.
>>
> Unless I'm mistaken you are describing decoherence, which is not
> equivalent to collapse.
The two are not equivalent but related. Decoherence is the
apparent collapse due to entanglement with the environment.
It does not lead to state reduction and does not solve the
measurement problem. See my paper
A. Neumaier,
Collapse challenge for interpretations of quantum mechanics
http://www.arxiv.org/abs/quant-ph/0505172
and the recent survey
M. Schlosshauer,
Decoherence, the Measurement Problem, and Interpretations of
Quantum Mechanics
Rev. Mod. Phys. 76 (2004), 1267--1305.
http://www.arxiv.org/abs/quant-ph/0312059.
Collapse is the result of approximating the entangled dynamics
by a Markov approximation, resulting in a dissipative master
equation of Lindblad type. The latter have built in collapse.
The validity of the Markov approximation is an additional
assumption beyond decoherence. It is responsible for the
collapse.
Quantum optics and hence all high quality experiments for
the foundations of quantum mechanics are unthinkable without
the Markov approximation.
Arnold Neumaier
rof@maths.tcd.ie
May26-05, 02:06 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n>rof@maths.tcd.ie wrote:\n\n>> A physicist who gives an\n>> apparently straightforward, if slightly confusing, answer\n>> to a question about physics, without making it clear that\n>> this question has an unusual status in physics, that,\n>> unlike most questions in physics, this one has no\n>> well-established answer, is implicitly telling the\n>> person that this question is just like other questions\n>> in physics, that is has a well-established answer, and\n>> that in fact the answer being given is the well-established\n>> one.\n>>\n>> Now this is what you did, and you interpreted my post as an attack\n>> on you, became angry, and treated me to three question marks and a\n>> lecture about how everything is mere opinion and belief:\n>>\n>>>Everything called\n>>>knowledge is in fact a set of beliefs of the person claiming it.\n\n>You seem to be projecting _your_ anger onto me.\n\nPerhaps it seems that way to you; I assure you that I\'m not.\n\n>That you find three question marks and a short essay on learning\n>truth in controversial matters an aggressive behavior in a context\n>where controversial things are discussed is a sign of your emotional\n>state rather than a property of my contribution.\n\nPerhaps you use three question marks and assertions that everything\nis mere opinion and belief all the time, but I read quite a lot\nof your posts, and often enjoy reading them, and it seems that\nyou rarely do that. Your behaviour in this case seemed to be\nan exception to your normal tone.\n\n>To say that \'\'Everything called knowledge is in fact a set\n>of beliefs of the person claiming it.\'\' does not contradict the\n>objectivity of mathematical definitions. When I say that a Banach\n>space is a normed, complete vector space, I both state my belief\n>and happen to coincide with the social consensus of the guild of\n>mathematicians.\n\nIndeed, but the question is how it appears to the person for whom\nyour reply was intended. You are saying that one can adopt a\nparticular point of view, namely that everything anybody ever\nsays is their opinion and must be considered that way, and that it\nmight or might not coincide with what is well-established, and that\nthe onus is on the reader to determine whether what is said\nis well-established or not. From this point of view, you weren\'t\nbeing dishonest; I agree.\n\n>And when I say that state reduction is a\n>physical process, I both state my belief and happen to coincide with\n>famous physicists like von Neumann and many others, and this is good\n>enough to make this statement honestly.\n\nWell, von Neumann was actually of the opinion that state reduction\nwasn\'t a physical process, as far as I can determine from reading\nhis papers. In your post, you also said (more or less) that it\nwasn\'t a physical process, so I presume you left out a "not"\nabove.\n\nI happen to also think it\'s unlikely that state vector collapse is\na physical process, although I wouldn\'t presume to dogmatically\nstate that it isn\'t if asked by somebody who wasn\'t already familiar\nwith the subject. If I did that, I would be presenting what\nis merely my opinion as though I were certain that it was\ntrue.\n\nConsider, for example, somebody who liked Penrose\'s gravitational\ncollapse interpretation. According to your criteria of honesty,\nthat person could say "Yes, collapse is a physical process,"\nwhile being perfectly honest, since his opinion coincides\nwith that of a famous physicist. The poor person who asked\nthe question in the first place would have gotten two "honest"\nanswers to his question, one saying no (from you) and one\nsaying yes. Neither of the answerers would have given any\nindication that their answer was merely their opinion,\nand so the questioner would be left confused, and would\nhave to distrust future answers that he got from supposedly\nrespectable physicists.\n\nYou may very well say that this is a harsh lesson that he needs to\nlearn. I would say that it would be better if people clearly\ndistinguished between what was merely their opinion and\nwhat is well-established, and then those who ask questions\nwould be able to trust the answers that physicists give them.\n\nAs another example, if somebody asks "Is Riemann hypothesis true?",\nmost knowledgeable people would reply that it isn\'t known whether\nor not it is true, although it is widely believed that it is.\nSomebody who simply says "Yes, it\'s true," would be being honest\nby your criteria, but not by mine.\n\n>It is ridiculous to require a percentage of people in a field\n>to agree with you before you utter a statement without adding\n>a qualification like \'I believe\' or \'Some physisicts believe\'.\n>There would never be an agreement on the percentage required\n>to do so.\n\nI agree. I never suggested that one should require a\nspecific percentage of physicists to agree with one before\nsaying something. I do think, however, that if one knows\nthat a statement is merely an opinion, and that more than\n50% of physicists hold the opposite opinion, one can\nsay that it is controversial, and that it shouldn\'t\nbe stated as though it were a fact. I gave 50% as an example\nof a figure which would indicate a controversy, not as\na boundary between controversy and non-controversy.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>rof@maths.tcd.ie wrote:
>> A physicist who gives an
>> apparently straightforward, if slightly confusing, answer
>> to a question about physics, without making it clear that
>> this question has an unusual status in physics, that,
>> unlike most questions in physics, this one has no
>> well-established answer, is implicitly telling the
>> person that this question is just like other questions
>> in physics, that is has a well-established answer, and
>> that in fact the answer being given is the well-established
>> one.
>>
>> Now this is what you did, and you interpreted my post as an attack
>> on you, became angry, and treated me to three question marks and a
>> lecture about how everything is mere opinion and belief:
>>
>>>Everything called
>>>knowledge is in fact a set of beliefs of the person claiming it.
>You seem to be projecting _your_ anger onto me.
Perhaps it seems that way to you; I assure you that I'm not.
>That you find three question marks and a short essay on learning
>truth in controversial matters an aggressive behavior in a context
>where controversial things are discussed is a sign of your emotional
>state rather than a property of my contribution.
Perhaps you use three question marks and assertions that everything
is mere opinion and belief all the time, but I read quite a lot
of your posts, and often enjoy reading them, and it seems that
you rarely do that. Your behaviour in this case seemed to be
an exception to your normal tone.
>To say that ''Everything called knowledge is in fact a set
>of beliefs of the person claiming it.'' does not contradict the
>objectivity of mathematical definitions. When I say that a Banach
>space is a normed, complete vector space, I both state my belief
>and happen to coincide with the social consensus of the guild of
>mathematicians.
Indeed, but the question is how it appears to the person for whom
your reply was intended. You are saying that one can adopt a
particular point of view, namely that everything anybody ever
says is their opinion and must be considered that way, and that it
might or might not coincide with what is well-established, and that
the onus is on the reader to determine whether what is said
is well-established or not. From this point of view, you weren't
being dishonest; I agree.
>And when I say that state reduction is a
>physical process, I both state my belief and happen to coincide with
>famous physicists like von Neumann and many others, and this is good
>enough to make this statement honestly.
Well, von Neumann was actually of the opinion that state reduction
wasn't a physical process, as far as I can determine from reading
his papers. In your post, you also said (more or less) that it
wasn't a physical process, so I presume you left out a "not"
above.
I happen to also think it's unlikely that state vector collapse is
a physical process, although I wouldn't presume to dogmatically
state that it isn't if asked by somebody who wasn't already familiar
with the subject. If I did that, I would be presenting what
is merely my opinion as though I were certain that it was
true.
Consider, for example, somebody who liked Penrose's gravitational
collapse interpretation. According to your criteria of honesty,
that person could say "Yes, collapse is a physical process,"
while being perfectly honest, since his opinion coincides
with that of a famous physicist. The poor person who asked
the question in the first place would have gotten two "honest"
answers to his question, one saying no (from you) and one
saying yes. Neither of the answerers would have given any
indication that their answer was merely their opinion,
and so the questioner would be left confused, and would
have to distrust future answers that he got from supposedly
respectable physicists.
You may very well say that this is a harsh lesson that he needs to
learn. I would say that it would be better if people clearly
distinguished between what was merely their opinion and
what is well-established, and then those who ask questions
would be able to trust the answers that physicists give them.
As another example, if somebody asks "Is Riemann hypothesis true?",
most knowledgeable people would reply that it isn't known whether
or not it is true, although it is widely believed that it is.
Somebody who simply says "Yes, it's true," would be being honest
by your criteria, but not by mine.
>It is ridiculous to require a percentage of people in a field
>to agree with you before you utter a statement without adding
>a qualification like 'I believe' or 'Some physisicts believe'.
>There would never be an agreement on the percentage required
>to do so.
I agree. I never suggested that one should require a
specific percentage of physicists to agree with one before
saying something. I do think, however, that if one knows
that a statement is merely an opinion, and that more than
50% of physicists hold the opposite opinion, one can
say that it is controversial, and that it shouldn't
be stated as though it were a fact. I gave 50% as an example
of a figure which would indicate a controversy, not as
a boundary between controversy and non-controversy.
R.
Aaron Bergman
May26-05, 02:06 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1116962439.668290.161080@g14g2000cwa.googlegroups .com>,\nmarkwh04@yahoo.com wrote:\n\n> Arnold Neumaier wrote:\n> > But since we cannot know the full state of the whole universe,\n> > we are doomed to such reduced descriptions and hence to the\n> > collapse.\n>\n> Or more strongly: as Smolin has pointed out, there may not even *be*\n> such a thing as a state for the whole universe, not even a\n> configuration space! This necessarily forces one into a local\n> description and relative states cease to be merely an expedient, and\n> become a fundamental part of the whole enterprise.\n\nOf course, it would be nice to have a theory that could describe the\nwhole universe.\n\n> In that case, collapse is there from the outset because reduced states\n> are all you have.\n\nI don\'t agree with this formulation. If you have unitary evolution, you\ndon\'t have collapse. Or, put another way, pure states never evolve into\nmixed states.\n\n> To put it more clearly: in the absence of a universal state or even a\n> universal configuration space, the universe in effect becomes an open\n> system.\n>\n> A second account, not mutually exclusive (and in fact closely related),\n> for the collapse comes from the fact that the most general quantum\n> theory [see note 1]\n\nNote one appears to be missing.\n\n> admits both quantum AND classical degrees of\n> freedom; the latter playing the role of superselection parameters.\n\nI\'d find such a thing very difficult to implement.\n\n> In the most general case, a relative state obtained by tracing out the\n> environmental modes will cut across the superselection boundaries and\n> give you a state which is a mixture with respect to the classical\n> degrees.\n>\n> States that lie in different superselection sectors combine only\n> classically, never by superposition. By itself, a system can\'t evolve\n> in such a way as to transmit information from the quantum to the\n> classical degrees (i.e. a Schroedinger or automorphic evolution\n> automatically precludes collapse-through-superselection). That\'s what\n> would be required to get a "measurement" type event. But when combined\n> with the feature of there being a cut-off at the boundary of the\n> environment, you get the desired result of\n> collapse-through-superselection.\n\nI\'d prefer to ditch the superselection. If the world was how I wanted it\nto be, there\'d be an actual physical nonunitary collapse process that\nmakes things classical at large scales. Unfortunately, the world has no\nobligation to conform to my needs. But I can hope.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1116962439.668290.161080@g14g2000cwa.googlegroups. com>,
markwh04@yahoo.com wrote:
> Arnold Neumaier wrote:
> > But since we cannot know the full state of the whole universe,
> > we are doomed to such reduced descriptions and hence to the
> > collapse.
>
> Or more strongly: as Smolin has pointed out, there may not even *be*
> such a thing as a state for the whole universe, not even a
> configuration space! This necessarily forces one into a local
> description and relative states cease to be merely an expedient, and
> become a fundamental part of the whole enterprise.
Of course, it would be nice to have a theory that could describe the
whole universe.
> In that case, collapse is there from the outset because reduced states
> are all you have.
I don't agree with this formulation. If you have unitary evolution, you
don't have collapse. Or, put another way, pure states never evolve into
mixed states.
> To put it more clearly: in the absence of a universal state or even a
> universal configuration space, the universe in effect becomes an open
> system.
>
> A second account, not mutually exclusive (and in fact closely related),
> for the collapse comes from the fact that the most general quantum
> theory [see note 1]
Note one appears to be missing.
> admits both quantum AND classical degrees of
> freedom; the latter playing the role of superselection parameters.
I'd find such a thing very difficult to implement.
> In the most general case, a relative state obtained by tracing out the
> environmental modes will cut across the superselection boundaries and
> give you a state which is a mixture with respect to the classical
> degrees.
>
> States that lie in different superselection sectors combine only
> classically, never by superposition. By itself, a system can't evolve
> in such a way as to transmit information from the quantum to the
> classical degrees (i.e. a Schroedinger or automorphic evolution
> automatically precludes collapse-through-superselection). That's what
> would be required to get a "measurement" type event. But when combined
> with the feature of there being a cut-off at the boundary of the
> environment, you get the desired result of
> collapse-through-superselection.
I'd prefer to ditch the superselection. If the world was how I wanted it
to be, there'd be an actual physical nonunitary collapse process that
makes things classical at large scales. Unfortunately, the world has no
obligation to conform to my needs. But I can hope.
Aaron
Seratend
May26-05, 02:07 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie a =E9crit :\n> Seratend <ser_monmail@yahoo.fr> writes:\n>\n> >rof@maths.tcd.ie a crit :\n\n> >In other words, for the collapse postulate, every eigenbasis is ok to\n> >express statistical results (the born rules), but in the lab, we just\n> >have one basis where the statistics apply. Why?\n>\n> >(and please do not use the decoherence as the way to solve this issue)\n>\n> I\'m not sure I understand the question very clearly, but I\'ll try\n> to answer it. There is a special basis - the position basis, although\n> this isn\'t an entire basis for the Hilbert space, since it doesn\'t\n> span the spin part of the Hilbert space, for example. Anyway, all\n> measurements are ultimately measurements of position, as Bell\n> was fond of saying, for example the positions of instrument\n> pointers.\n\nI do not know how you can come to such a conclusion (for the position).\nThe postulates of QM are clear (formally). Born rules may be applied to\nany eigenbasis (i.e. any observable). If position becomes the preferred\nbasis for the observation, this postulate has to be changed (with\nadditional postulates or anything else). If this is the case, I would\nlike to know it explicitly.\n\n\n> Because all interactions which can serve as measurements are local,\n> meaning that if system A wants to exchange information with system\n> B it has to be in the same region of space, interactions with\n> neighboring objects tend to act as position measurements.\n>\nI think you are mixing the unitary time evolution of the global system\nthat is impacted by the type of interaction (always local) with the\nborn rules that may be applied to any eigenbasis of this system\n(locally or globally).\nFor example, in the classical hydrogen atom, I just have a position\ninteraction (coulombian interaction), however, what I usually measure\nis an energy (the radiation induced by the transitions between 2 energy\neigen states) and not position. How do you explain that?\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie a =E9crit :
> Seratend <ser_monmail@yahoo.fr> writes:
>
> >rof@maths.tcd.ie a crit :
> >In other words, for the collapse postulate, every eigenbasis is ok to
> >express statistical results (the born rules), but in the lab, we just
> >have one basis where the statistics apply. Why?
>
> >(and please do not use the decoherence as the way to solve this issue)
>
> I'm not sure I understand the question very clearly, but I'll try
> to answer it. There is a special basis - the position basis, although
> this isn't an entire basis for the Hilbert space, since it doesn't
> span the spin part of the Hilbert space, for example. Anyway, all
> measurements are ultimately measurements of position, as Bell
> was fond of saying, for example the positions of instrument
> pointers.
I do not know how you can come to such a conclusion (for the position).
The postulates of QM are clear (formally). Born rules may be applied to
any eigenbasis (i.e. any observable). If position becomes the preferred
basis for the observation, this postulate has to be changed (with
additional postulates or anything else). If this is the case, I would
like to know it explicitly.
> Because all interactions which can serve as measurements are local,
> meaning that if system A wants to exchange information with system
> B it has to be in the same region of space, interactions with
> neighboring objects tend to act as position measurements.
>
I think you are mixing the unitary time evolution of the global system
that is impacted by the type of interaction (always local) with the
born rules that may be applied to any eigenbasis of this system
(locally or globally).
For example, in the classical hydrogen atom, I just have a position
interaction (coulombian interaction), however, what I usually measure
is an energy (the radiation induced by the transitions between 2 energy
eigen states) and not position. How do you explain that?
Seratend.
Seratend
May26-05, 02:07 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Frank Hellmann a =E9crit :\n>\n> I have seen this argument quite a few times, do you have any good\n> concise review papers on this?\n> A meassurement is represented by a Projection operator, and you can\n> develop the whole apparatus of the statistical interpretation of QM\n> without ever refferring to a basis, so I really don\'t see where this\n> problem comes into things.\n>\n> Frank.\n\nWe may also view the measurement problem as the quest for a generic\nsuperselection rule (the selection of the preferred basis): the\nprediction of the preferred basis of a given experiment (what does not\nseem to be given by the current QM postulates). However, I do not know\nif one has ever proved that such a rule exists (either by tests or by a\ntheorem).\n\nI may propose you the following papers:\n\n* Elements of Environmental Decoherence, Joos 1999,\narXiv:quant-ph/9908008 (short one)\n* Decoherence, the Measurement Problem, and Interpretations of Quantum\nMechanics, Schlosshauer 2003, arXiv:quant-ph/0312059 (extensive review\nof the problem end of 2003, very complete and lot of pointers to other\npapers)\n\nIf someone has other recent papers, do not hesitate to post them : ).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann a =E9crit :
>
> I have seen this argument quite a few times, do you have any good
> concise review papers on this?
> A meassurement is represented by a Projection operator, and you can
> develop the whole apparatus of the statistical interpretation of QM
> without ever refferring to a basis, so I really don't see where this
> problem comes into things.
>
> Frank.
We may also view the measurement problem as the quest for a generic
superselection rule (the selection of the preferred basis): the
prediction of the preferred basis of a given experiment (what does not
seem to be given by the current QM postulates). However, I do not know
if one has ever proved that such a rule exists (either by tests or by a
theorem).
I may propose you the following papers:
* Elements of Environmental Decoherence, Joos 1999,
arXiv:http://www.arxiv.org/abs/quant-ph/9908008 (short one)
* Decoherence, the Measurement Problem, and Interpretations of Quantum
Mechanics, Schlosshauer 2003, arXiv:http://www.arxiv.org/abs/quant-ph/0312059 (extensive review
of the problem end of 2003, very complete and lot of pointers to other
papers)
If someone has other recent papers, do not hesitate to post them : ).
Seratend.
Aaron Bergman
May26-05, 07:22 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117095659.166639.149930@o13g2000cwo.googlegroups .com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman a écrit :\n> > In article <1117014495.964319.125450@z14g2000cwz.googlegroups .com>,\n> >\n> > When you describe an experiment in quantum mechanics, you separate out\n> > the world into classical and quantum components. The classical component\n> > comes with a preferred basis given by the macrostates of the measurement\n> > apparatus. When you entangle the measuring device with the quantum\n> > system, decoherence tells you that the entangled states essentially no\n> > longer interfere.\n>\n> I understand you seem to adopt the copenhagen interpretation.\n\nI don\'t believe in any \'interpretation\' of quantum mechanics. I\'m just\nconfused by all of it. As I said elsewhere, in my ideal world, there\nwould be a physical collapse process leading to the emergence of a\nclassical world. Unfortunately, I\'m not sure I believe that\'s likely.\n\n> If this\n> is the case, once again, CI does not explain the preferred basis, this\n> is an an external data compatible with the postulates of QM, but not\n> explained by QM theory (the classical apparatus and its eigen basis in\n> CI is not explained) . I understand decoherence tells us that there is\n> a local basis where there is no interference (the projected density\n> matric is diagonal in this eigenbasis), providing a sufficient\n> interaction with the environment. However, nothing in QM, prevents one\n> to choose another eigenbasis where we have interferences, otherwise, it\n> would be impossible to observe interference in quantum experiments\n> (e.g. double slits interferences, squizz, etc ...). Therefore, I really\n> do not understand how you can say that the basis where the local\n> density matrix is diagonal is the preferred eigenbasis of the\n> experiment and that this basis may be or not the one choosen by the\n> classical apparatus (what in QM postulates infere this result) .\n\nI\'m not sure I understand what you\'re asking. Let me try to answer\nsomething, then. The question of what why we observe what we observe is\ncompletely unanswered by quantum mechanics. This, however, is a\ndifferent issue of the existence of the basis for observation. As you\nseem to agree, the diagonalization of the density matrix in a given\nexperimental setup determines a preferred basis. The connection between\nthis basis and our perception of reality is too hard a question for me,\nbut it seems to be right.\n\n[...]\n\n> My question regarding this theory remains: does QM theory explain the\n> preferred basis or not?\n\nQM (ie, decoherence) explains how preferred bases arise in experiments.\nIt does not explain why we perceive what we perceive.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117095659.166639.149930@o13g2000cwo.googlegroups. com>,
Seratend <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman a écrit :
> > In article <1117014495.964319.125450@z14g2000cwz.googlegroups. com>,
> >
> > When you describe an experiment in quantum mechanics, you separate out
> > the world into classical and quantum components. The classical component
> > comes with a preferred basis given by the macrostates of the measurement
> > apparatus. When you entangle the measuring device with the quantum
> > system, decoherence tells you that the entangled states essentially no
> > longer interfere.
>
> I understand you seem to adopt the copenhagen interpretation.
I don't believe in any 'interpretation' of quantum mechanics. I'm just
confused by all of it. As I said elsewhere, in my ideal world, there
would be a physical collapse process leading to the emergence of a
classical world. Unfortunately, I'm not sure I believe that's likely.
> If this
> is the case, once again, CI does not explain the preferred basis, this
> is an an external data compatible with the postulates of QM, but not
> explained by QM theory (the classical apparatus and its eigen basis in
> CI is not explained) . I understand decoherence tells us that there is
> a local basis where there is no interference (the projected density
> matric is diagonal in this eigenbasis), providing a sufficient
> interaction with the environment. However, nothing in QM, prevents one
> to choose another eigenbasis where we have interferences, otherwise, it
> would be impossible to observe interference in quantum experiments
> (e.g. double slits interferences, squizz, etc ...). Therefore, I really
> do not understand how you can say that the basis where the local
> density matrix is diagonal is the preferred eigenbasis of the
> experiment and that this basis may be or not the one choosen by the
> classical apparatus (what in QM postulates infere this result) .
I'm not sure I understand what you're asking. Let me try to answer
something, then. The question of what why we observe what we observe is
completely unanswered by quantum mechanics. This, however, is a
different issue of the existence of the basis for observation. As you
seem to agree, the diagonalization of the density matrix in a given
experimental setup determines a preferred basis. The connection between
this basis and our perception of reality is too hard a question for me,
but it seems to be right.
[...]
> My question regarding this theory remains: does QM theory explain the
> preferred basis or not?
QM (ie, decoherence) explains how preferred bases arise in experiments.
It does not explain why we perceive what we perceive.
Aaron
Seratend
May28-05, 04:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman a =E9crit :\n> In article <1117095659.166639.149930@o13g2000cwo.googlegroups .com>,\n> Seratend <ser_monmail@yahoo.fr> wrote:\n>\n> >\n> > I understand you seem to adopt the copenhagen interpretation.\n>\n> I don\'t believe in any \'interpretation\' of quantum mechanics. I\'m just\n> confused by all of it. As I said elsewhere, in my ideal world, there\n> would be a physical collapse process leading to the emergence of a\n> classical world. Unfortunately, I\'m not sure I believe that\'s likely.\n>\nOk, I also prefer to leave interpretation to philosophy : ).\nI have another question: what do you call a classical world. Frankly I\ndo not understand that. QM deals only with statitistics of outcomes\nand, in my opinion, outcomes are the "classical world" (what we "see").\nTherefore, it is relatively difficult for me to understand people who\nwant to demonstrate that there is a physical collapse leading to the\noutcomes.\nI can only understand this sentence as the quest for a deterministic\n(causal) description of outcomes compatible with the statistics of QM.\nIf this is the case, we already have such a description, bohmian\nmechanics for the position eigen basis (and equivelent formulations in\ndifferent eigenbasis).\n\nAs in classical probability, I can work with the statistical\ndescription it provides whenever its results are more practical than\nthe ones of a deterministic description explaining the outcomes. I have\na mathematical separation in the desciption of outcomes: statistical or\ndeterministic. Both are ok. Choosing one versus the other is only a\nmatter of taste rather than a necessity.\nHence my non understanding of the quest of a physical collapse behing\nthe outcomes of QM.\n\nThis subject as you have already noticed is different from the problem\nof the preferred eigenbasis and the decoherence (the analog of the law\nof large numbers in QM).\n\n> I\'m not sure I understand what you\'re asking. Let me try to answer\n> something, then. The question of what why we observe what we observe is\n> completely unanswered by quantum mechanics.\n\nSo you are saying that QM theory does not explain the preferred basis.\n\n> This, however, is a different issue of the existence of the basis for o=\nbservation.\nI do not understand you. To describe the observation of something I\nneed a basis. For example, in the deterministic world, a signal s(t) is\nwell described by s(t) or its fourier transform ^s(w). However, I\nusually see the values of the signal at every time (s(t) and not the\nvalues at a given frequency).\n\n> As you seem to agree, the diagonalization of the density matrix in a gi=\nven\n> experimental setup determines a preferred basis.\nNo, I just say that we obtain a basis. I just question, if it is\nanother postulate. As if I take QM postulates, I may apply the collapse\npostulate to this local state in any basis I want (especially one\ndifferent from the eigenbasis:\n\nfor any diagonal density matrix I have: rho=3D sum_i pi|ai><ai|\nChoosing another basis:\n|ai>=3D sum cij|bj>\n\n=3D> rho=3D sum_i pi.cij.cik* |bj><bi|\n\nrho is no more diagonal. Both eigen basis are possible for the\nmeasurement outcomes as expressed by the QM postulates.\n\n> The connection between this basis and our perception of reality is too =\nhard a question for me,\n> but it seems to be right.\n>\nWell if you accept decoherence, you may accept the situations where the\ninteraction between the environment and the system is so weak, that in\na first approximation, no entanglment as occured. In this case, what\neigenbasis do we select?\n\n> [...]\n>\n> > My question regarding this theory remains: does QM theory explain the\n> > preferred basis or not?\n>\n> QM (ie, decoherence) explains how preferred bases arise in experiments.\n> It does not explain why we perceive what we perceive.\n>\nIf I take 2 experiments: the observation of double slits interference\nand the emission of radiation of an hidrogen gas. In one case I see,\nthe position (an interference) and in the second case the energy\neigenstate of the H atoms. Frankly, I see no common preferred basis and\nthe last observer is the human (the projector) in this example.\nHow decoherence is able to explain/solve this difference in this\npreferred eigen basis observation?\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman a =E9crit :
> In article <1117095659.166639.149930@o13g2000cwo.googlegroups. com>,
> Seratend <ser_monmail@yahoo.fr> wrote:
>
> >
> > I understand you seem to adopt the copenhagen interpretation.
>
> I don't believe in any 'interpretation' of quantum mechanics. I'm just
> confused by all of it. As I said elsewhere, in my ideal world, there
> would be a physical collapse process leading to the emergence of a
> classical world. Unfortunately, I'm not sure I believe that's likely.
>
Ok, I also prefer to leave interpretation to philosophy : ).
I have another question: what do you call a classical world. Frankly I
do not understand that. QM deals only with statitistics of outcomes
and, in my opinion, outcomes are the "classical world" (what we "see").
Therefore, it is relatively difficult for me to understand people who
want to demonstrate that there is a physical collapse leading to the
outcomes.
I can only understand this sentence as the quest for a deterministic
(causal) description of outcomes compatible with the statistics of QM.
If this is the case, we already have such a description, bohmian
mechanics for the position eigen basis (and equivelent formulations in
different eigenbasis).
As in classical probability, I can work with the statistical
description it provides whenever its results are more practical than
the ones of a deterministic description explaining the outcomes. I have
a mathematical separation in the desciption of outcomes: statistical or
deterministic. Both are ok. Choosing one versus the other is only a
matter of taste rather than a necessity.
Hence my non understanding of the quest of a physical collapse behing
the outcomes of QM.
This subject as you have already noticed is different from the problem
of the preferred eigenbasis and the decoherence (the analog of the law
of large numbers in QM).
> I'm not sure I understand what you're asking. Let me try to answer
> something, then. The question of what why we observe what we observe is
> completely unanswered by quantum mechanics.
So you are saying that QM theory does not explain the preferred basis.
> This, however, is a different issue of the existence of the basis for o=
bservation.
I do not understand you. To describe the observation of something I
need a basis. For example, in the deterministic world, a signal s(t) is
well described by s(t) or its fourier transform ^s(w). However, I
usually see the values of the signal at every time (s(t) and not the
values at a given frequency).
> As you seem to agree, the diagonalization of the density matrix in a gi=
ven
> experimental setup determines a preferred basis.
No, I just say that we obtain a basis. I just question, if it is
another postulate. As if I take QM postulates, I may apply the collapse
postulate to this local state in any basis I want (especially one
different from the eigenbasis:
for any diagonal density matrix I have: \rho=3D sum_i \pi|ai><ai|
Choosing another basis:
|ai>=3D sum cij|bj>
=3D> \rho=3D sum_i \pi.cij.cik* |bj><bi|
\rho is no more diagonal. Both eigen basis are possible for the
measurement outcomes as expressed by the QM postulates.
> The connection between this basis and our perception of reality is too =
hard a question for me,
> but it seems to be right.
>
Well if you accept decoherence, you may accept the situations where the
interaction between the environment and the system is so weak, that in
a first approximation, no entanglment as occured. In this case, what
eigenbasis do we select?
> [...]
>
> > My question regarding this theory remains: does QM theory explain the
> > preferred basis or not?
>
> QM (ie, decoherence) explains how preferred bases arise in experiments.
> It does not explain why we perceive what we perceive.
>
If I take 2 experiments: the observation of double slits interference
and the emission of radiation of an hidrogen gas. In one case I see,
the position (an interference) and in the second case the energy
eigenstate of the H atoms. Frankly, I see no common preferred basis and
the last observer is the human (the projector) in this example.
How decoherence is able to explain/solve this difference in this
preferred eigen basis observation?
Seratend.
Arnold Neumaier
May28-05, 04:15 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n\n> In article <1116962439.668290.161080@g14g2000cwa.googlegroups .com>,\n> markwh04@yahoo.com wrote:\n>\n>>Arnold Neumaier wrote:\n>>\n>>>But since we cannot know the full state of the whole universe,\n>>>we are doomed to such reduced descriptions and hence to the\n>>>collapse.\n>>\n>>Or more strongly: as Smolin has pointed out, there may not even *be*\n>>such a thing as a state for the whole universe, not even a\n>>configuration space! This necessarily forces one into a local\n>>description and relative states cease to be merely an expedient, and\n>>become a fundamental part of the whole enterprise.\n>\n> Of course, it would be nice to have a theory that could describe the\n> whole universe.\n\nThe standard model claims to be a theory of the whole universe\nin a flat, gravitationless spacetime. It specifies expectations of\nall fields and correlations at all possible combinations of\npositions and times, and hence describes the world anywhere.\n(That it is not in complete agreement with observation because it\ndoes not treat gravity correctly does not invalidate the general\nobservation.)\n\n\n>>In that case, collapse is there from the outset because reduced states\n>>are all you have.\n>\n> I don\'t agree with this formulation. If you have unitary evolution, you\n> don\'t have collapse. Or, put another way, pure states never evolve into\n> mixed states.\n\nBut if you have unitary evolution, you have the whole universe.\nFor in that case nothing outside that system can interact with it\n(by unitarity), so all observations are restricted to this system\nitself. Which means, it contains us and everything we interact with,\nhence the whole universe.\n\n\n> I\'d prefer to ditch the superselection. If the world was how I wanted it\n> to be, there\'d be an actual physical nonunitary collapse process that\n> makes things classical at large scales. Unfortunately, the world has no\n> obligation to conform to my needs. But I can hope.\n\nThere are some such scenarios that are not yet contradicted by\nexperiment....\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1116962439.668290.161080@g14g2000cwa.googlegroups. com>,
> markwh04@yahoo.com wrote:
>
>>Arnold Neumaier wrote:
>>
>>>But since we cannot know the full state of the whole universe,
>>>we are doomed to such reduced descriptions and hence to the
>>>collapse.
>>
>>Or more strongly: as Smolin has pointed out, there may not even *be*
>>such a thing as a state for the whole universe, not even a
>>configuration space! This necessarily forces one into a local
>>description and relative states cease to be merely an expedient, and
>>become a fundamental part of the whole enterprise.
>
> Of course, it would be nice to have a theory that could describe the
> whole universe.
The standard model claims to be a theory of the whole universe
in a flat, gravitationless spacetime. It specifies expectations of
all fields and correlations at all possible combinations of
positions and times, and hence describes the world anywhere.
(That it is not in complete agreement with observation because it
does not treat gravity correctly does not invalidate the general
observation.)
>>In that case, collapse is there from the outset because reduced states
>>are all you have.
>
> I don't agree with this formulation. If you have unitary evolution, you
> don't have collapse. Or, put another way, pure states never evolve into
> mixed states.
But if you have unitary evolution, you have the whole universe.
For in that case nothing outside that system can interact with it
(by unitarity), so all observations are restricted to this system
itself. Which means, it contains us and everything we interact with,
hence the whole universe.
> I'd prefer to ditch the superselection. If the world was how I wanted it
> to be, there'd be an actual physical nonunitary collapse process that
> makes things classical at large scales. Unfortunately, the world has no
> obligation to conform to my needs. But I can hope.
There are some such scenarios that are not yet contradicted by
experiment....
Arnold Neumaier
Arnold Neumaier
May28-05, 04:15 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>rof@maths.tcd.ie wrote:\n>\n\n>>>Now this is what you did, and you interpreted my post as an attack\n>>>on you, became angry, and treated me to three question marks and a\n>>>lecture about how everything is mere opinion and belief:\n>>>\n>>>\n>>>>Everything called\n>>>>knowledge is in fact a set of beliefs of the person claiming it.\n>\n>>You seem to be projecting _your_ anger onto me.\n>\n> Perhaps it seems that way to you; I assure you that I\'m not.\n\nThen it must have been an artifact of the medium usenet.\nIt seems to make statements to look more emotional than they\nare meant, which occasionally (and in unmoderated groups often)\nleads to an involuntary rise in aggression.\n\n\n> Perhaps you use three question marks and assertions that everything\n> is mere opinion and belief all the time, but I read quite a lot\n> of your posts, and often enjoy reading them,\n\nThanks for the compliment. I try to be readable, informative,\nand polite, though sometimes I am quite explicit about what I\nthink of a poor contribution.\n\n\n> and it seems that\n> you rarely do that. Your behaviour in this case seemed to be\n> an exception to your normal tone.\n\nI raise three question mark when I find something really unbelievable\nthough (because it is not about something formal) one cannot describe it\nas wrong.\n\n\n>>To say that \'\'Everything called knowledge is in fact a set\n>>of beliefs of the person claiming it.\'\' does not contradict the\n>>objectivity of mathematical definitions. When I say that a Banach\n>>space is a normed, complete vector space, I both state my belief\n>>and happen to coincide with the social consensus of the guild of\n>>mathematicians.\n>\n> Indeed, but the question is how it appears to the person for whom\n> your reply was intended. You are saying that one can adopt a\n> particular point of view, namely that everything anybody ever\n> says is their opinion and must be considered that way,\n\nAt least this is the way I take what others say. It is a very\nefficient way of looking at communication. Then I sieve through\nwhat nourishes my hunger for truth and understanding - independent\nof whether the speaker spoke the truth or a prejudice. From an\ninteresting statement I sometimes learn even when the speaker does\nnot recognize its faults, and a true statement may fail to interest\nme if it is phrased in a way that I cannot recognize its relevance.\n\n\n> and that it\n> might or might not coincide with what is well-established, and that\n> the onus is on the reader to determine whether what is said\n> is well-established or not. From this point of view, you weren\'t\n> being dishonest; I agree.\n>\n>\n>>And when I say that state reduction is a\n>>physical process, I both state my belief and happen to coincide with\n>>famous physicists like von Neumann and many others, and this is good\n>>enough to make this statement honestly.\n>\n> Well, von Neumann was actually of the opinion that state reduction\n> wasn\'t a physical process, as far as I can determine from reading\n> his papers. In your post, you also said (more or less) that it\n> wasn\'t a physical process, so I presume you left out a "not"\n> above.\n\nNo. I meant \'\'state reduction is a physical process\'\' since this is\nwhat I said and what physicists observe. See\nA. Neumaier,\nCollapse challenge for interpretations of quantum mechanics\nquant-ph/0505172\n(see also http://www.mat.univie.ac.at/~neum/collapse.html).\nVon Neumann takes the collapse as an axiom, hence also testifies to its\nreality. I\'d appreciate getting a clear reference where he states\nthe contrary (if he does so).\n\n\n> Consider, for example, somebody who liked Penrose\'s gravitational\n> collapse interpretation. According to your criteria of honesty,\n> that person could say "Yes, collapse is a physical process,"\n> while being perfectly honest, since his opinion coincides\n> with that of a famous physicist.\n\nYes.\n\n> The poor person who asked\n> the question in the first place would have gotten two "honest"\n> answers to his question, one saying no (from you) and one\n> saying yes.\n\nThis is the typical situation one finds when controversy prevails.\nIndeed, in some sense, controversy _is_ the coexistence of\ndisagreeing honest statements.\n\n\n> Neither of the answerers would have given any\n> indication that their answer was merely their opinion,\n> and so the questioner would be left confused,\n\nNo. If the questioner is only a little intelligent, he would\nbe left with the impression that either at least one of the\nspeakers was incompetent, or that the topic is controversial.\n\n\n> and would\n> have to distrust future answers that he got from supposedly\n> respectable physicists.\n\nThis is indeed healthy. One should not trust a statement without\ngood reason, independently of whether it carries the label\n\'this is the truth\' or \'this is my personal opinion\'. In fact,\nthe first may be a lie and the second the truth.\n\n\n> You may very well say that this is a harsh lesson that he needs to\n> learn. I would say that it would be better if people clearly\n> distinguished between what was merely their opinion and\n> what is well-established, and then those who ask questions\n> would be able to trust the answers that physicists give them.\n\nOnly if they have no prejudice, and if he recognizes that he speaks\nwith a person without prejudice. But both requirements are very rarely\nmet. So he is right to be cautious. Indeed, we learn it from the\nearliest age not to trust too early.\n\n\n> As another example, if somebody asks "Is Riemann hypothesis true?",\n> most knowledgeable people would reply that it isn\'t known whether\n> or not it is true, although it is widely believed that it is.\n> Somebody who simply says "Yes, it\'s true," would be being honest\n> by your criteria,\n\nOnly if he really thinks it is true, according to the standards\nof mathematics. For example, I think that Louis de Branges\ncan say it with honesty.\nhttp://www.math.columbia.edu/~woit/blog/archives/000035.html\n\n\n\n>\n>>It is ridiculous to require a percentage of people in a field\n>>to agree with you before you utter a statement without adding\n>>a qualification like \'I believe\' or \'Some physisicts believe\'.\n>>There would never be an agreement on the percentage required\n>>to do so.\n>\n>\n> I agree. I never suggested that one should require a\n> specific percentage of physicists to agree with one before\n> saying something.\n\nYou suggested that one should require 50% in the mail which\ncaused my three question marks.\n\n\n> I do think, however, that if one knows\n> that a statement is merely an opinion, and that more than\n> 50% of physicists hold the opposite opinion, one can\n> say that it is controversial,\n\nShould Einstein have declared his theory controversial\nuntil he convinced haldf of the physicsists? (or of the\ntheoretical phyicsts only? Or of the astrophysicists\nonly? ...)\n\nNo. He was convinced it was right, and he was right to\nhaving aserted it without scruples. It is part of the\nscientific process that finding out the truth takes time.\nBut often it is being found by bold people who know what\nthey know, even being in a minority.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>rof@maths.tcd.ie wrote:
>
>>>Now this is what you did, and you interpreted my post as an attack
>>>on you, became angry, and treated me to three question marks and a
>>>lecture about how everything is mere opinion and belief:
>>>
>>>
>>>>Everything called
>>>>knowledge is in fact a set of beliefs of the person claiming it.
>
>>You seem to be projecting _your_ anger onto me.
>
> Perhaps it seems that way to you; I assure you that I'm not.
Then it must have been an artifact of the medium usenet.
It seems to make statements to look more emotional than they
are meant, which occasionally (and in unmoderated groups often)
leads to an involuntary rise in aggression.
> Perhaps you use three question marks and assertions that everything
> is mere opinion and belief all the time, but I read quite a lot
> of your posts, and often enjoy reading them,
Thanks for the compliment. I try to be readable, informative,
and polite, though sometimes I am quite explicit about what I
think of a poor contribution.
> and it seems that
> you rarely do that. Your behaviour in this case seemed to be
> an exception to your normal tone.
I raise three question mark when I find something really unbelievable
though (because it is not about something formal) one cannot describe it
as wrong.
>>To say that ''Everything called knowledge is in fact a set
>>of beliefs of the person claiming it.'' does not contradict the
>>objectivity of mathematical definitions. When I say that a Banach
>>space is a normed, complete vector space, I both state my belief
>>and happen to coincide with the social consensus of the guild of
>>mathematicians.
>
> Indeed, but the question is how it appears to the person for whom
> your reply was intended. You are saying that one can adopt a
> particular point of view, namely that everything anybody ever
> says is their opinion and must be considered that way,
At least this is the way I take what others say. It is a very
efficient way of looking at communication. Then I sieve through
what nourishes my hunger for truth and understanding - independent
of whether the speaker spoke the truth or a prejudice. From an
interesting statement I sometimes learn even when the speaker does
not recognize its faults, and a true statement may fail to interest
me if it is phrased in a way that I cannot recognize its relevance.
> and that it
> might or might not coincide with what is well-established, and that
> the onus is on the reader to determine whether what is said
> is well-established or not. From this point of view, you weren't
> being dishonest; I agree.
>
>
>>And when I say that state reduction is a
>>physical process, I both state my belief and happen to coincide with
>>famous physicists like von Neumann and many others, and this is good
>>enough to make this statement honestly.
>
> Well, von Neumann was actually of the opinion that state reduction
> wasn't a physical process, as far as I can determine from reading
> his papers. In your post, you also said (more or less) that it
> wasn't a physical process, so I presume you left out a "not"
> above.
No. I meant ''state reduction is a physical process'' since this is
what I said and what physicists observe. See
A. Neumaier,
Collapse challenge for interpretations of quantum mechanics
http://www.arxiv.org/abs/quant-ph/0505172
(see also http://www.mat.univie.ac.at/~neum/collapse.html).
Von Neumann takes the collapse as an axiom, hence also testifies to its
reality. I'd appreciate getting a clear reference where he states
the contrary (if he does so).
> Consider, for example, somebody who liked Penrose's gravitational
> collapse interpretation. According to your criteria of honesty,
> that person could say "Yes, collapse is a physical process,"
> while being perfectly honest, since his opinion coincides
> with that of a famous physicist.
Yes.
> The poor person who asked
> the question in the first place would have gotten two "honest"
> answers to his question, one saying no (from you) and one
> saying yes.
This is the typical situation one finds when controversy prevails.
Indeed, in some sense, controversy _is_ the coexistence of
disagreeing honest statements.
> Neither of the answerers would have given any
> indication that their answer was merely their opinion,
> and so the questioner would be left confused,
No. If the questioner is only a little intelligent, he would
be left with the impression that either at least one of the
speakers was incompetent, or that the topic is controversial.
> and would
> have to distrust future answers that he got from supposedly
> respectable physicists.
This is indeed healthy. One should not trust a statement without
good reason, independently of whether it carries the label
'this is the truth' or 'this is my personal opinion'. In fact,
the first may be a lie and the second the truth.
> You may very well say that this is a harsh lesson that he needs to
> learn. I would say that it would be better if people clearly
> distinguished between what was merely their opinion and
> what is well-established, and then those who ask questions
> would be able to trust the answers that physicists give them.
Only if they have no prejudice, and if he recognizes that he speaks
with a person without prejudice. But both requirements are very rarely
met. So he is right to be cautious. Indeed, we learn it from the
earliest age not to trust too early.
> As another example, if somebody asks "Is Riemann hypothesis true?",
> most knowledgeable people would reply that it isn't known whether
> or not it is true, although it is widely believed that it is.
> Somebody who simply says "Yes, it's true," would be being honest
> by your criteria,
Only if he really thinks it is true, according to the standards
of mathematics. For example, I think that Louis de Branges
can say it with honesty.
http://www.math.columbia.edu/~woit/blog/archives/000035.html
>
>>It is ridiculous to require a percentage of people in a field
>>to agree with you before you utter a statement without adding
>>a qualification like 'I believe' or 'Some physisicts believe'.
>>There would never be an agreement on the percentage required
>>to do so.
>
>
> I agree. I never suggested that one should require a
> specific percentage of physicists to agree with one before
> saying something.
You suggested that one should require 50% in the mail which
caused my three question marks.
> I do think, however, that if one knows
> that a statement is merely an opinion, and that more than
> 50% of physicists hold the opposite opinion, one can
> say that it is controversial,
Should Einstein have declared his theory controversial
until he convinced haldf of the physicsists? (or of the
theoretical phyicsts only? Or of the astrophysicists
only? ...)
No. He was convinced it was right, and he was right to
having aserted it without scruples. It is part of the
scientific process that finding out the truth takes time.
But often it is being found by bold people who know what
they know, even being in a minority.
Arnold Neumaier
Seratend
May28-05, 01:44 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie a écrit :\n>\n> It\'s called the Schmidt decomposition, and the l_i are called\n> the Schmidt coefficients. If there\'s an initial state\n> which factorises into the state of the system and\n> the state of the measuring device, say, |psi_0>=|a_0>|b_0>,\n> then after an interaction between them, that state of\n> the system, |psi> can be decomposed according to the\n> Schmidt decomposition, which gives a preferred basis\n> for that interaction (there are pathological cases\n> where the decomposition isn\'t unique, but these are\n> "of measure zero").\n\nOh, yes? So you are claming that the degenerated states are seldom.\nEspecially in the system?\nIf this is the case, observing the unpolarized radiation of an atom in\na given energy eigen state, EPR would not be possible etc ...\n\nThe schmidt decomposition principle is a nice "trick" to quiclky say\nyou have a preferred eigenbasis in a measurement. However, each time I\nlook deeper into this decomposition, I see not so many difference\nbetween claiming, a posteriori, the prefered basis of the measurement\n(we kown the basis when we do the measurement)and choosing a psteriori\nan environment basis and interactions such that the density matrix is\ndiagonal in the basis of the measurement.\n\n\n> Because of the locality of information\n> transfer, this tends to pick out basis states which\n> are fairly localised (presuming that spatial degrees\n> of freedom are included in the system and that all\n> interactions are, in fact, local), or rather, were\n> localised at the time of the interaction.\n>\nPlease, if you use the word information, try to connect it (replace it)\nwith the formal objects of QM theory. There is so many confusion (at\nleast for me) with this word especially when applied to QM and\nmeasurement that for me it has not a defined signification.\n\n>Not at all. Decoherence shows us how the basis is selected.\n>\n> Pretty much; the above process, repeated many times, with\n> local interactions of many systems with one another, gives\n> you decoherence, with the various systems "telling each other"\n> where they are with respect to one another, leading to\n> a preferred basis which is approximately the position basis,\n> although it\'s not exactly a complete basis.\n>\n> R.\n\nDecoherence explains why we may not see so easily interferences in the\nclassical world (the unitary evolution of the system with the\nenvironment through interactions). However, I do not see how\ndecoherence can explain the preferred basis (and surely not the ad hoc\nschmidt decomposition). If this is the case, I think the collapse\npostulate must be completed by another postulate. However, may be, QM\ndoes not explain the preferred basis at all(out the scope of the\ntheory)?\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie a écrit :
>
> It's called the Schmidt decomposition, and the l_i are called
> the Schmidt coefficients. If there's an initial state
> which factorises into the state of the system and
> the state of the measuring device, say, |\psi_0>=|a_0>|b_0>,
> then after an interaction between them, that state of
> the system, |\psi> can be decomposed according to the
> Schmidt decomposition, which gives a preferred basis
> for that interaction (there are pathological cases
> where the decomposition isn't unique, but these are
> "of measure zero").
Oh, yes? So you are claming that the degenerated states are seldom.
Especially in the system?
If this is the case, observing the unpolarized radiation of an atom in
a given energy eigen state, EPR would not be possible etc ...
The schmidt decomposition principle is a nice "trick" to quiclky say
you have a preferred eigenbasis in a measurement. However, each time I
look deeper into this decomposition, I see not so many difference
between claiming, a posteriori, the prefered basis of the measurement
(we kown the basis when we do the measurement)and choosing a psteriori
an environment basis and interactions such that the density matrix is
diagonal in the basis of the measurement.
> Because of the locality of information
> transfer, this tends to pick out basis states which
> are fairly localised (presuming that spatial degrees
> of freedom are included in the system and that all
> interactions are, in fact, local), or rather, were
> localised at the time of the interaction.
>
Please, if you use the word information, try to connect it (replace it)
with the formal objects of QM theory. There is so many confusion (at
least for me) with this word especially when applied to QM and
measurement that for me it has not a defined signification.
>Not at all. Decoherence shows us how the basis is selected.
>
> Pretty much; the above process, repeated many times, with
> local interactions of many systems with one another, gives
> you decoherence, with the various systems "telling each other"
> where they are with respect to one another, leading to
> a preferred basis which is approximately the position basis,
> although it's not exactly a complete basis.
>
> R.
Decoherence explains why we may not see so easily interferences in the
classical world (the unitary evolution of the system with the
environment through interactions). However, I do not see how
decoherence can explain the preferred basis (and surely not the ad hoc
schmidt decomposition). If this is the case, I think the collapse
postulate must be completed by another postulate. However, may be, QM
does not explain the preferred basis at all(out the scope of the
theory)?
Seratend.
Aaron Bergman
May29-05, 01:26 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117183732.077481.57630@z14g2000cwz.googlegroups. com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman a =E9crit :\n> > In article <1117095659.166639.149930@o13g2000cwo.googlegroups .com>,\n> > Seratend <ser_monmail@yahoo.fr> wrote:\n> >\n> > >\n> > > I understand you seem to adopt the copenhagen interpretation.\n> >\n> > I don\'t believe in any \'interpretation\' of quantum mechanics. I\'m just\n> > confused by all of it. As I said elsewhere, in my ideal world, there\n> > would be a physical collapse process leading to the emergence of a\n> > classical world. Unfortunately, I\'m not sure I believe that\'s likely.\n> >\n> Ok, I also prefer to leave interpretation to philosophy : ).\n> I have another question: what do you call a classical world. Frankly I\n> do not understand that. QM deals only with statitistics of outcomes\n> and, in my opinion, outcomes are the "classical world" (what we "see").\n> Therefore, it is relatively difficult for me to understand people who\n> want to demonstrate that there is a physical collapse leading to the\n> outcomes.\n\nWhy do we observe outcomes with probability |<a|psi>|^2? QM has no\nanswer for this question.\n\n> I can only understand this sentence as the quest for a deterministic\n> (causal) description of outcomes compatible with the statistics of QM.\n\nQM is deterministic and causal. That\'s the problem.\n\n> If this is the case, we already have such a description, bohmian\n> mechanics for the position eigen basis (and equivelent formulations in\n> different eigenbasis).\n\nBohmian mechanics has no relativistic generalization that I know of.\n\n[...]\n\n> > I\'m not sure I understand what you\'re asking. Let me try to answer\n> > something, then. The question of what why we observe what we observe is\n> > completely unanswered by quantum mechanics.\n>\n> So you are saying that QM theory does not explain the preferred basis.\n\nYou\'ll have to communicate to me better what you mean by \'preferred\nbasis\'. Given an experimental setup with a classical measuring device\n(where classical means large numbers of microstates per macrostate), I\ncan describe to you a preferred basis in that setup.\n\n[...]\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117183732.077481.57630@z14g2000cwz.googlegroups.c om>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman a =E9crit :
> > In article <1117095659.166639.149930@o13g2000cwo.googlegroups. com>,
> > Seratend <ser_monmail@yahoo.fr> wrote:
> >
> > >
> > > I understand you seem to adopt the copenhagen interpretation.
> >
> > I don't believe in any 'interpretation' of quantum mechanics. I'm just
> > confused by all of it. As I said elsewhere, in my ideal world, there
> > would be a physical collapse process leading to the emergence of a
> > classical world. Unfortunately, I'm not sure I believe that's likely.
> >
> Ok, I also prefer to leave interpretation to philosophy : ).
> I have another question: what do you call a classical world. Frankly I
> do not understand that. QM deals only with statitistics of outcomes
> and, in my opinion, outcomes are the "classical world" (what we "see").
> Therefore, it is relatively difficult for me to understand people who
> want to demonstrate that there is a physical collapse leading to the
> outcomes.
Why do we observe outcomes with probability |<a|\psi>|^2? QM has no
answer for this question.
> I can only understand this sentence as the quest for a deterministic
> (causal) description of outcomes compatible with the statistics of QM.
QM is deterministic and causal. That's the problem.
> If this is the case, we already have such a description, bohmian
> mechanics for the position eigen basis (and equivelent formulations in
> different eigenbasis).
Bohmian mechanics has no relativistic generalization that I know of.
[...]
> > I'm not sure I understand what you're asking. Let me try to answer
> > something, then. The question of what why we observe what we observe is
> > completely unanswered by quantum mechanics.
>
> So you are saying that QM theory does not explain the preferred basis.
You'll have to communicate to me better what you mean by 'preferred
basis'. Given an experimental setup with a classical measuring device
(where classical means large numbers of microstates per macrostate), I
can describe to you a preferred basis in that setup.
[...]
Aaron
Arnold Neumaier
May30-05, 12:18 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> QM deals only with statistics of outcomes\n> and, in my opinion, outcomes are the "classical world" (what we "see").\n\nIn my opinion, the "classical world" (what we "see") is the world\nas seen after irreversible effects have set in, i.e., the world\nas described by nonequilibrium thermodynamics (including hydromechanics\nand kinetic theory). Everything in thermodynamics and kinetic theory\nis real, objective, without any of the dubiosities that characterize\nthe traditional interpretations of the quantum world.\n\n\n> Therefore, it is relatively difficult for me to understand people who\n> want to demonstrate that there is a physical collapse leading to the\n> outcomes.\n\nThe quest is to show that the interaction of a quantum system with\na macroscopic detector describable by thermodynamics (and hence,\nthrough statistical mechanics, by quantum theory) gives rise to\nmacroscopic, observable effects in the detector that can be regarded\nas the physical equivalent of an objective record of measurements.\n\nI gave a concise formulation of a specific case of this quest in\nmy recent paper quant-ph/0505172.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> QM deals only with statistics of outcomes
> and, in my opinion, outcomes are the "classical world" (what we "see").
In my opinion, the "classical world" (what we "see") is the world
as seen after irreversible effects have set in, i.e., the world
as described by nonequilibrium thermodynamics (including hydromechanics
and kinetic theory). Everything in thermodynamics and kinetic theory
is real, objective, without any of the dubiosities that characterize
the traditional interpretations of the quantum world.
> Therefore, it is relatively difficult for me to understand people who
> want to demonstrate that there is a physical collapse leading to the
> outcomes.
The quest is to show that the interaction of a quantum system with
a macroscopic detector describable by thermodynamics (and hence,
through statistical mechanics, by quantum theory) gives rise to
macroscopic, observable effects in the detector that can be regarded
as the physical equivalent of an objective record of measurements.
I gave a concise formulation of a specific case of this quest in
my recent paper http://www.arxiv.org/abs/quant-ph/0505172.
Arnold Neumaier
rof@maths.tcd.ie
May30-05, 12:21 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n>rof@maths.tcd.ie wrote:\n\n>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>\n>>>rof@maths.tcd.ie wrote:\n>>\n\n>>>You seem to be projecting _your_ anger onto me.\n>>\n>> Perhaps it seems that way to you; I assure you that I\'m not.\n\n>Then it must have been an artifact of the medium usenet.\n>It seems to make statements to look more emotional than they\n>are meant, which occasionally (and in unmoderated groups often)\n>leads to an involuntary rise in aggression.\n\nIndeed; this happens far too often. In diplomacy, people\nhave developed formalized rules to avoid involuntary\nrises in aggression like this, and refer to it as\nprotocol. Usenet hasn\'t got anything similar yet, excapt\nfor the vague rule that one shold be polite.\n\n>>>And when I say that state reduction is a\n>>>physical process, I both state my belief and happen to coincide with\n>>>famous physicists like von Neumann and many others, and this is good\n>>>enough to make this statement honestly.\n>>\n>> Well, von Neumann was actually of the opinion that state reduction\n>> wasn\'t a physical process, as far as I can determine from reading\n>> his papers. In your post, you also said (more or less) that it\n>> wasn\'t a physical process, so I presume you left out a "not"\n>> above.\n\n>No. I meant \'\'state reduction is a physical process\'\' since this is\n>what I said and what physicists observe.\n\nPerhaps you are using the word "physical" in a way with which I\'m\nnot familiar. You referred, in your original post to collapse\nas "an artifact of the description of a quantum system by\na limited number of observables". To me, that sounds very\nmuch like saying that collapse isn\'t a physical process.\n\n>See\n> A. Neumaier,\n> Collapse challenge for interpretations of quantum mechanics\n> quant-ph/0505172\n> (see also http://www.mat.univie.ac.at/~neum/collapse.html).\n\nThe latter link appears to be broken. Your treatment of the Copenhagen\ninterpretation in the article claims that the "unresolved\nquantum-classical interface issue (including the missing definition\nof which situations constitute a measurement) is a serious defect\nof the Copenhagen interpretation when viewed as a fundamental\ninterpretation of quantum mechanics."\n\nThis is slightly unfair to the Copenhagen interpretation, in\nwhich the wavefunction is understood to represent knowledge\nabout the system, rather than the system itself. A definition\nof measurement isn\'t missing because measurement is the\nacquisition of new knowledge. State vector reduction happens\nbecause the observer acquires new knowledge and then updates\nthe mathematical representation of his knowledge to reflect\nthe new knowledge that he has.\n\nIt is only if we ignore this, and suppose that the Copenhagen\ninterpretation asserts the opposite, namely that the wavefunction\ndoesn\'t represent knowledge, but represents the state of the\nsystem, that the discontinuous change in the wavefunction\nlooks problematic, since that would mean that the system\nitself changes discontinuously.\n\n>Von Neumann takes the collapse as an axiom, hence also testifies to its\n>reality.\n\nHe uses it as an axiom, but that doesn\'t mean that he claimed that\nthe wavefunction didn\'t represent knowledge.\n\n>I\'d appreciate getting a clear reference where he states\n>the contrary (if he does so).\n\nHe is less clear about it than Bohr or Heisenberg, but, for\nexample, in his 1938 paper with Birkhoff, "The Logic of\nQuantum Mechanics", for example, he expresses the view\nthat the formalism of quantum mechanics is the way it\nis because the algebra of Hilbert-space subspaces is\nthat of a non-distributive orthomodular lattice, which\nmatches the structure of the collection of experimentally\nverifiable propositions about a system. This seems to\nme to be an indication that he considered rays of Hilbert\nspace to be associated with propositions (knowledge), rather\nthan with the actual configuration of the system.\n\nMore concretely, in chapter 4 of his "Mathematical\nFoundations of Quantum Mechanics", he says:\n\n"Let us assume that we do not know the state of a\nsystem, S, but that we have made certain measurements\nabout the state of S and know their results. In reality,\nit always happens this way, because we can learn something\nabout the state of S only from the results of measurements.\nMore precisely, the states are only a theoretical construction,\nonly the results of measurements are actually available, and\nthe problem of physics is to furnish relationships between\nthe results of past and future measurements." p. 337\n\nIn addition, he credits Bohr on page 420 with the insight\nthat quantum mechanics can only be understood in terms\nof the relationship between the physical and the psychical,\nwhich seems to me to be a direct indication that he\nunderstood and agreed with the idea that the mathematical\nrepresentations that quantum mechanics uses refer to\nknowledge about the system and not to the system itself.\n\nHe devotes chapter 6 to explaining that it doesn\'t\nmatter where the boundary between the system and\nthe observer is placed, whether at the pointer\non the measuring device or at the eye of the\nobserver. The reason that he does this is that, as\nhe says, "the danger lies in the fact that the\nprinciple of psycho-physical parallelism is\nviolated, so long as it is not shown that the\nboundary between the observed system and the observer\ncan be displaced arbitrarily..." (p. 421).\n\nNow, the principle of psycho-physical parallelism is\nunderstood by Von Neumann to be "that it must\nbe possible to describe the subjective experience\nas if it were in reality in the physical world", and\nthat "that [the] boundary can be pushed arbitrarily\ninto the body of the actual observer is the content\nof the principle of psycho-physical parallelism" (p. 420).\n\nWhat this means (as I understand it) is, firstly,\nthat the ray of the Hilbert space in quantum\nmechanics represents knowledge, and the question\n"Knowledge about what?" can be given many answers,\nsuch as "knowledge about the position of the\ninstrument pointer", "knowledge about the momentum\nof the particle", or "knowledge about the conditions\ninside of my body." The principle of psycho-physical\nparallelism tells us that, whatever we claim to know\nabout the physical world, what we actually know about\nis what\'s going on inside our body, and Von Neumann\nis observing that pushing the boundary between the\nobserver and the observed inside the body of the\nobserver works just fine with quantum mechanics.\n\nI\'d be interested to hear any conflicting interpretations\nof the above quotes regarding psycho-physical parallelism\nand pushing the boundary inside the body of the observer.\n\nYou might also want to read the paper by Lon Becker:\n"That von Neumann Did Not Believe in a Physical Collapse",\nhttp://bjps.oupjournals.org/cgi/content/abstract/55/1/121\n\n>> You may very well say that this is a harsh lesson that he needs to\n>> learn. I would say that it would be better if people clearly\n>> distinguished between what was merely their opinion and\n>> what is well-established, and then those who ask questions\n>> would be able to trust the answers that physicists give them.\n\n>Only if they have no prejudice, and if he recognizes that he speaks\n>with a person without prejudice. But both requirements are very rarely\n>met. So he is right to be cautious. Indeed, we learn it from the\n>earliest age not to trust too early.\n\nWell, there is a distinction to be made between the role\nof a teacher and the role of a physicist debating matters\nwith another physicist. We expect our teachers to honestly\ntell us which things they are teaching are well established\nand which are their opinions. Perhaps not all teachers\nmeet this high standard, but I think it\'s important to\nkeep that standard in place.\n\nI would also think that, when approached by a non-expert\nwho has a relatively simple question to ask, the physicist\nwho answers implicitly adopts the role of a teacher.\n\n>> As another example, if somebody asks "Is the Riemann hypothesis true?",\n>> most knowledgeable people would reply that it isn\'t known whether\n>> or not it is true, although it is widely believed that it is.\n>> Somebody who simply says "Yes, it\'s true," would be being honest\n>> by your criteria,\n\n>Only if he really thinks it is true, according to the standards\n>of mathematics. For example, I think that Louis de Branges\n>can say it with honesty.\n>http://www.math.columbia.edu/~woit/blog/archives/000035.html\n\nI await the results of the scrutiny of his proof with interest.\n\nDo you, incidentally, think that mathematicians should hold\nthemselves to higher standards than physicists when telling\nothers that a particular statement is true?\n\n>>>It is ridiculous to require a percentage of people in a field\n>>>to agree with you before you utter a statement without adding\n>>>a qualification like \'I believe\' or \'Some physisicts believe\'.\n>>>There would never be an agreement on the percentage required\n>>>to do so.\n>>\n>> I agree. I never suggested that one should require a\n>> specific percentage of physicists to agree with one before\n>> saying something.\n\n>You suggested that one should require 50% in the mail which\n>caused my three question marks.\n\nI gave an example of 50% as a figure that would indicate\ncontroversy. I would not and do not suggest that one\nshould ever go to the bother of checking whether it\nis 49% or 51% of physicists who agree with an opinion.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>rof@maths.tcd.ie wrote:
>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>
>>>rof@maths.tcd.ie wrote:
>>
>>>You seem to be projecting _your_ anger onto me.
>>
>> Perhaps it seems that way to you; I assure you that I'm not.
>Then it must have been an artifact of the medium usenet.
>It seems to make statements to look more emotional than they
>are meant, which occasionally (and in unmoderated groups often)
>leads to an involuntary rise in aggression.
Indeed; this happens far too often. In diplomacy, people
have developed formalized rules to avoid involuntary
rises in aggression like this, and refer to it as
protocol. Usenet hasn't got anything similar yet, excapt
for the vague rule that one shold be polite.
>>>And when I say that state reduction is a
>>>physical process, I both state my belief and happen to coincide with
>>>famous physicists like von Neumann and many others, and this is good
>>>enough to make this statement honestly.
>>
>> Well, von Neumann was actually of the opinion that state reduction
>> wasn't a physical process, as far as I can determine from reading
>> his papers. In your post, you also said (more or less) that it
>> wasn't a physical process, so I presume you left out a "not"
>> above.
>No. I meant ''state reduction is a physical process'' since this is
>what I said and what physicists observe.
Perhaps you are using the word "physical" in a way with which I'm
not familiar. You referred, in your original post to collapse
as "an artifact of the description of a quantum system by
a limited number of observables". To me, that sounds very
much like saying that collapse isn't a physical process.
>See
> A. Neumaier,
> Collapse challenge for interpretations of quantum mechanics
> http://www.arxiv.org/abs/quant-ph/0505172
> (see also http://www.mat.univie.ac.at/~neum/collapse.html).
The latter link appears to be broken. Your treatment of the Copenhagen
interpretation in the article claims that the "unresolved
quantum-classical interface issue (including the missing definition
of which situations constitute a measurement) is a serious defect
of the Copenhagen interpretation when viewed as a fundamental
interpretation of quantum mechanics."
This is slightly unfair to the Copenhagen interpretation, in
which the wavefunction is understood to represent knowledge
about the system, rather than the system itself. A definition
of measurement isn't missing because measurement is the
acquisition of new knowledge. State vector reduction happens
because the observer acquires new knowledge and then updates
the mathematical representation of his knowledge to reflect
the new knowledge that he has.
It is only if we ignore this, and suppose that the Copenhagen
interpretation asserts the opposite, namely that the wavefunction
doesn't represent knowledge, but represents the state of the
system, that the discontinuous change in the wavefunction
looks problematic, since that would mean that the system
itself changes discontinuously.
>Von Neumann takes the collapse as an axiom, hence also testifies to its
>reality.
He uses it as an axiom, but that doesn't mean that he claimed that
the wavefunction didn't represent knowledge.
>I'd appreciate getting a clear reference where he states
>the contrary (if he does so).
He is less clear about it than Bohr or Heisenberg, but, for
example, in his 1938 paper with Birkhoff, "The Logic of
Quantum Mechanics", for example, he expresses the view
that the formalism of quantum mechanics is the way it
is because the algebra of Hilbert-space subspaces is
that of a non-distributive orthomodular lattice, which
matches the structure of the collection of experimentally
verifiable propositions about a system. This seems to
me to be an indication that he considered rays of Hilbert
space to be associated with propositions (knowledge), rather
than with the actual configuration of the system.
More concretely, in chapter 4 of his "Mathematical
Foundations of Quantum Mechanics", he says:
"Let us assume that we do not know the state of a
system, S, but that we have made certain measurements
about the state of S and know their results. In reality,
it always happens this way, because we can learn something
about the state of S only from the results of measurements.
More precisely, the states are only a theoretical construction,
only the results of measurements are actually available, and
the problem of physics is to furnish relationships between
the results of past and future measurements." p. 337
In addition, he credits Bohr on page 420 with the insight
that quantum mechanics can only be understood in terms
of the relationship between the physical and the psychical,
which seems to me to be a direct indication that he
understood and agreed with the idea that the mathematical
representations that quantum mechanics uses refer to
knowledge about the system and not to the system itself.
He devotes chapter 6 to explaining that it doesn't
matter where the boundary between the system and
the observer is placed, whether at the pointer
on the measuring device or at the eye of the
observer. The reason that he does this is that, as
he says, "the danger lies in the fact that the
principle of psycho-physical parallelism is
violated, so long as it is not shown that the
boundary between the observed system and the observer
can be displaced arbitrarily..." (p. 421).
Now, the principle of psycho-physical parallelism is
understood by Von Neumann to be "that it must
be possible to describe the subjective experience
as if it were in reality in the physical world", and
that "that [the] boundary can be pushed arbitrarily
into the body of the actual observer is the content
of the principle of psycho-physical parallelism" (p. 420).
What this means (as I understand it) is, firstly,
that the ray of the Hilbert space in quantum
mechanics represents knowledge, and the question
"Knowledge about what?" can be given many answers,
such as "knowledge about the position of the
instrument pointer", "knowledge about the momentum
of the particle", or "knowledge about the conditions
inside of my body." The principle of psycho-physical
parallelism tells us that, whatever we claim to know
about the physical world, what we actually know about
is what's going on inside our body, and Von Neumann
is observing that pushing the boundary between the
observer and the observed inside the body of the
observer works just fine with quantum mechanics.
I'd be interested to hear any conflicting interpretations
of the above quotes regarding psycho-physical parallelism
and pushing the boundary inside the body of the observer.
You might also want to read the paper by Lon Becker:
"That von Neumann Did Not Believe in a Physical Collapse",
http://bjps.oupjournals.org/cgi/content/abstract/55/1/121
>> You may very well say that this is a harsh lesson that he needs to
>> learn. I would say that it would be better if people clearly
>> distinguished between what was merely their opinion and
>> what is well-established, and then those who ask questions
>> would be able to trust the answers that physicists give them.
>Only if they have no prejudice, and if he recognizes that he speaks
>with a person without prejudice. But both requirements are very rarely
>met. So he is right to be cautious. Indeed, we learn it from the
>earliest age not to trust too early.
Well, there is a distinction to be made between the role
of a teacher and the role of a physicist debating matters
with another physicist. We expect our teachers to honestly
tell us which things they are teaching are well established
and which are their opinions. Perhaps not all teachers
meet this high standard, but I think it's important to
keep that standard in place.
I would also think that, when approached by a non-expert
who has a relatively simple question to ask, the physicist
who answers implicitly adopts the role of a teacher.
>> As another example, if somebody asks "Is the Riemann hypothesis true?",
>> most knowledgeable people would reply that it isn't known whether
>> or not it is true, although it is widely believed that it is.
>> Somebody who simply says "Yes, it's true," would be being honest
>> by your criteria,
>Only if he really thinks it is true, according to the standards
>of mathematics. For example, I think that Louis de Branges
>can say it with honesty.
>http://www.math.columbia.edu/~woit/blog/archives/000035.html
I await the results of the scrutiny of his proof with interest.
Do you, incidentally, think that mathematicians should hold
themselves to higher standards than physicists when telling
others that a particular statement is true?
>>>It is ridiculous to require a percentage of people in a field
>>>to agree with you before you utter a statement without adding
>>>a qualification like 'I believe' or 'Some physisicts believe'.
>>>There would never be an agreement on the percentage required
>>>to do so.
>>
>> I agree. I never suggested that one should require a
>> specific percentage of physicists to agree with one before
>> saying something.
>You suggested that one should require 50% in the mail which
>caused my three question marks.
I gave an example of 50% as a figure that would indicate
controversy. I would not and do not suggest that one
should ever go to the bother of checking whether it
is 49% or 51% of physicists who agree with an opinion.
R.
Arnold Neumaier
May30-05, 11:49 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>rof@maths.tcd.ie wrote:\n>\n>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>>\n>>No. I meant \'\'state reduction is a physical process\'\' since this is\n>>what I said and what physicists observe.\n>\n> Perhaps you are using the word "physical" in a way with which I\'m\n> not familiar. You referred, in your original post to collapse\n> as "an artifact of the description of a quantum system by\n> a limited number of observables". To me, that sounds very\n> much like saying that collapse isn\'t a physical process.\n\nIt _is_ an observable (hence physical) process since all our\ndescriptions useful for prediction and quantitative analysis\nare necesarily reduced, for example already since only part of the\nuniverse is accessible to our observations.\n\nUnder the usual handwaving inherent in Markov approximations,\nthe collapse is also deducible from the unitary evolution of\nthe universe as a whole, though a rigorous mathematical basis\nis missing.\n\n\n\n>\n>\n>>See\n>> A. Neumaier,\n>> Collapse challenge for interpretations of quantum mechanics\n>> quant-ph/0505172\n>> (see also http://www.mat.univie.ac.at/~neum/collapse.html).\n>\n>\n> The latter link appears to be broken.\n\nWe had a server failure on the weekend. Things are repaired now,\nand I checked that the link works.\n\n\n> Your treatment of the Copenhagen\n> interpretation in the article claims that the "unresolved\n> quantum-classical interface issue (including the missing definition\n> of which situations constitute a measurement) is a serious defect\n> of the Copenhagen interpretation when viewed as a fundamental\n> interpretation of quantum mechanics."\n>\n> This is slightly unfair to the Copenhagen interpretation, in\n> which the wavefunction is understood to represent knowledge\n> about the system, rather than the system itself.\n\nNo. As far as I can tell, the first mention of the claim that\n\'\'the wavefunction is understood to represent knowledge\'\' is by\nJaynes in the 1950ies, long after the establishment of the\nCopenhagen interpretation.\n\n\n> A definition\n> of measurement isn\'t missing because measurement is the\n> acquisition of new knowledge.\n\nThis is not a good definition since it is never specified what\nconstitutes acquisition of knowledge. The theory of knowledge\nacquisition is a branch of psychology, not of physics.\n\n\n> State vector reduction happens\n> because the observer acquires new knowledge and then updates\n> the mathematical representation of his knowledge to reflect\n> the new knowledge that he has.\n\nI doubt whether any observer updates his or her knowledge according\nto Bayesian reasoning. Field studies probably show large deviations\nfrom this supposedly universal behavior.\n\nFurthermore, knowledge depends on subjective decisions to trust\na measurement. If we discard one as an artifact, there is no\ncollapse. How can the collapse depend on such subjective issues?\n\nAt the time of Bohr, von neumann and Wigner, the collapse meant\nsomething objective, though it might have been related to the mind\nin some unspecified way.\n\n\n\n>>Von Neumann takes the collapse as an axiom, hence also testifies to its\n>>reality.\n>\n> He uses it as an axiom, but that doesn\'t mean that he claimed that\n> the wavefunction didn\'t represent knowledge.\n\nBut he certainly didn\'t claim that the wavefunction does represent\nknowledge.\n\n\n\n> in his 1938 paper with Birkhoff, "The Logic of\n> Quantum Mechanics", for example, he expresses the view\n> that the formalism of quantum mechanics is the way it\n> is because the algebra of Hilbert-space subspaces is\n> that of a non-distributive orthomodular lattice, which\n> matches the structure of the collection of experimentally\n> verifiable propositions about a system. This seems to\n> me to be an indication that he considered rays of Hilbert\n> space to be associated with propositions (knowledge), rather\n> than with the actual configuration of the system.\n\nNo. A proposition is a statement that is true or false,\nor undecidable. It has nothing to do with whether or not\nanyone knows (or claims to know) its truth or falsehood.\n\n\n> "Let us assume that we do not know the state of a\n> system, S,\n\nThis assumption already shows that the state of the system\nmust exist independent of our knowledge.\n\n\n> but that we have made certain measurements\n> about the state of S and know their results. In reality,\n> it always happens this way, because we can learn something\n> about the state of S only from the results of measurements.\n> More precisely, the states are only a theoretical construction,\n> only the results of measurements are actually available, and\n> the problem of physics is to furnish relationships between\n> the results of past and future measurements." p. 337\n\n\n> The principle of psycho-physical\n> parallelism tells us that, whatever we claim to know\n> about the physical world, what we actually know about\n> is what\'s going on inside our body,\n\nI don\'t buy this. What we know is some platonic extract\nextrapolated from sense data. And much of it is mistaken\nin detail, but still we think we know and act accordingly.\nIt has nothing to do with physics as understood pragmatically.\n\n\n> You might also want to read the paper by Lon Becker:\n> "That von Neumann Did Not Believe in a Physical Collapse",\n> http://bjps.oupjournals.org/cgi/content/abstract/55/1/121\n\nI\'ll readf it and comment later, if I have more to say than\nwhat I said already.\n\n\n> Well, there is a distinction to be made between the role\n> of a teacher and the role of a physicist debating matters\n> with another physicist. We expect our teachers to honestly\n\nyes, but expectations are not always born out in practice.\nThe hallmark of a good scientist ist his or her scepticism.\n\n\n> tell us which things they are teaching are well established\n> and which are their opinions. Perhaps not all teachers\n> meet this high standard, but I think it\'s important to\n> keep that standard in place.\n\nI agree that this is important. But equally important is\nto teach students not to take their teachers for infallible,\nbut to check for themselves whatever they find dubious.\n\n\n\n>>Only if he really thinks it is true, according to the standards\n>>of mathematics. For example, I think that Louis de Branges\n>>can say it with honesty.\n>>http://www.math.columbia.edu/~woit/blog/archives/000035.html\n>\n>\n> I await the results of the scrutiny of his proof with interest.\n\nOf course. But our discussion was about honesty, not truth.\n\n\n> Do you, incidentally, think that mathematicians should hold\n> themselves to higher standards than physicists when telling\n> others that a particular statement is true?\n\nWhen they discuss mathematical results (only), and upon request\n(only), yes. For ordinary conversations (such as\nthose on the usenet), the ordinary level of honesty is enough.\n\nBut their standard of truth is higher that that of physicists\nsince their subject matter is completely standardized and\nsubject to logic rather than experiment.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>rof@maths.tcd.ie wrote:
>
>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>>
>>No. I meant ''state reduction is a physical process'' since this is
>>what I said and what physicists observe.
>
> Perhaps you are using the word "physical" in a way with which I'm
> not familiar. You referred, in your original post to collapse
> as "an artifact of the description of a quantum system by
> a limited number of observables". To me, that sounds very
> much like saying that collapse isn't a physical process.
It _is_ an observable (hence physical) process since all our
descriptions useful for prediction and quantitative analysis
are necesarily reduced, for example already since only part of the
universe is accessible to our observations.
Under the usual handwaving inherent in Markov approximations,
the collapse is also deducible from the unitary evolution of
the universe as a whole, though a rigorous mathematical basis
is missing.
>
>
>>See
>> A. Neumaier,
>> Collapse challenge for interpretations of quantum mechanics
>> http://www.arxiv.org/abs/quant-ph/0505172
>> (see also http://www.mat.univie.ac.at/~neum/collapse.html).
>
>
> The latter link appears to be broken.
We had a server failure on the weekend. Things are repaired now,
and I checked that the link works.
> Your treatment of the Copenhagen
> interpretation in the article claims that the "unresolved
> quantum-classical interface issue (including the missing definition
> of which situations constitute a measurement) is a serious defect
> of the Copenhagen interpretation when viewed as a fundamental
> interpretation of quantum mechanics."
>
> This is slightly unfair to the Copenhagen interpretation, in
> which the wavefunction is understood to represent knowledge
> about the system, rather than the system itself.
No. As far as I can tell, the first mention of the claim that
''the wavefunction is understood to represent knowledge'' is by
Jaynes in the 1950ies, long after the establishment of the
Copenhagen interpretation.
> A definition
> of measurement isn't missing because measurement is the
> acquisition of new knowledge.
This is not a good definition since it is never specified what
constitutes acquisition of knowledge. The theory of knowledge
acquisition is a branch of psychology, not of physics.
> State vector reduction happens
> because the observer acquires new knowledge and then updates
> the mathematical representation of his knowledge to reflect
> the new knowledge that he has.
I doubt whether any observer updates his or her knowledge according
to Bayesian reasoning. Field studies probably show large deviations
from this supposedly universal behavior.
Furthermore, knowledge depends on subjective decisions to trust
a measurement. If we discard one as an artifact, there is no
collapse. How can the collapse depend on such subjective issues?
At the time of Bohr, von neumann and Wigner, the collapse meant
something objective, though it might have been related to the mind
in some unspecified way.
>>Von Neumann takes the collapse as an axiom, hence also testifies to its
>>reality.
>
> He uses it as an axiom, but that doesn't mean that he claimed that
> the wavefunction didn't represent knowledge.
But he certainly didn't claim that the wavefunction does represent
knowledge.
> in his 1938 paper with Birkhoff, "The Logic of
> Quantum Mechanics", for example, he expresses the view
> that the formalism of quantum mechanics is the way it
> is because the algebra of Hilbert-space subspaces is
> that of a non-distributive orthomodular lattice, which
> matches the structure of the collection of experimentally
> verifiable propositions about a system. This seems to
> me to be an indication that he considered rays of Hilbert
> space to be associated with propositions (knowledge), rather
> than with the actual configuration of the system.
No. A proposition is a statement that is true or false,
or undecidable. It has nothing to do with whether or not
anyone knows (or claims to know) its truth or falsehood.
> "Let us assume that we do not know the state of a
> system, S,
This assumption already shows that the state of the system
must exist independent of our knowledge.
> but that we have made certain measurements
> about the state of S and know their results. In reality,
> it always happens this way, because we can learn something
> about the state of S only from the results of measurements.
> More precisely, the states are only a theoretical construction,
> only the results of measurements are actually available, and
> the problem of physics is to furnish relationships between
> the results of past and future measurements." p. 337
> The principle of psycho-physical
> parallelism tells us that, whatever we claim to know
> about the physical world, what we actually know about
> is what's going on inside our body,
I don't buy this. What we know is some platonic extract
extrapolated from sense data. And much of it is mistaken
in detail, but still we think we know and act accordingly.
It has nothing to do with physics as understood pragmatically.
> You might also want to read the paper by Lon Becker:
> "That von Neumann Did Not Believe in a Physical Collapse",
> http://bjps.oupjournals.org/cgi/content/abstract/55/1/121
I'll readf it and comment later, if I have more to say than
what I said already.
> Well, there is a distinction to be made between the role
> of a teacher and the role of a physicist debating matters
> with another physicist. We expect our teachers to honestly
yes, but expectations are not always born out in practice.
The hallmark of a good scientist ist his or her scepticism.
> tell us which things they are teaching are well established
> and which are their opinions. Perhaps not all teachers
> meet this high standard, but I think it's important to
> keep that standard in place.
I agree that this is important. But equally important is
to teach students not to take their teachers for infallible,
but to check for themselves whatever they find dubious.
>>Only if he really thinks it is true, according to the standards
>>of mathematics. For example, I think that Louis de Branges
>>can say it with honesty.
>>http://www.math.columbia.edu/~woit/blog/archives/000035.html
>
>
> I await the results of the scrutiny of his proof with interest.
Of course. But our discussion was about honesty, not truth.
> Do you, incidentally, think that mathematicians should hold
> themselves to higher standards than physicists when telling
> others that a particular statement is true?
When they discuss mathematical results (only), and upon request
(only), yes. For ordinary conversations (such as
those on the usenet), the ordinary level of honesty is enough.
But their standard of truth is higher that that of physicists
since their subject matter is completely standardized and
subject to logic rather than experiment.
Arnold Neumaier
Seratend
May30-05, 11:49 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier a écrit :\n> Seratend wrote:\n>\n> > QM deals only with statistics of outcomes\n> > and, in my opinion, outcomes are the "classical world" (what we "see").\n>\n> In my opinion, the "classical world" (what we "see") is the world\n> as seen after irreversible effects have set in, i.e., the world\n> as described by nonequilibrium thermodynamics (including hydromechanics\n> and kinetic theory).\n\nInteresting.\nYou seem to view the measurement results exclusively through the mean\nvalue filter in my point of view (like the interference pattern: single\nphoton screen impact event versus multiple independent photons\ninterference pattern event).\nHow do you explain the observed state of a single photon event? (I\nunderstand you can explain the mean value of the measurement apparatus\nthat is almost equal to the outcome with the good hypotheses, but not\nthe one of photon or electron object).\n\nWhat do you intend by irreversible effects?\n\n> Everything in thermodynamics and kinetic theory\n> is real, objective, without any of the dubiosities that characterize\n> the traditional interpretations of the quantum world.\n>\n\nFrankly, I have a real problem to see reality behind pressure, volume\nand energy/temperature. All are macroscopic random variables through\nthe mean value filter (or the law of large numbers if you prefer) and\nthis seems to be a restrictive choice on what can be observed,\nespecially when we consider the observation of a microscopic phenomenon\nthrough a macroscopic one: most of the usual quantum cases measuring\nsingle particles.\n\n>\n> > Therefore, it is relatively difficult for me to understand people who\n> > want to demonstrate that there is a physical collapse leading to the\n> > outcomes.\n>\n> The quest is to show that the interaction of a quantum system with\n> a macroscopic detector describable by thermodynamics (and hence,\n> through statistical mechanics, by quantum theory)\n\nStatistical classical mechanics?\n\n> gives rise to\n> macroscopic, observable effects in the detector that can be regarded\n> as the physical equivalent of an objective record of measurements.\n>\n\nI am not sure I understand what you say. In the QM description, I just\nhave statistics of outcomes. I have for a macroscopic detetector, a\nmacroscopic observable A= sum_i Ai where Ai are the microscopic\nobservables of the apparatus (huge number). The result of the\nmeasurement will be for example the value of this observable that is\nhighly degenerated at the limit. Except for the preferred basis\nproblem, I do not understand what you are looking for.\n\n> I gave a concise formulation of a specific case of this quest in\n> my recent paper quant-ph/0505172.\n>\nI have read quickly you paper. I have not found the original thread. So\nI have some questions:\na) what is the initial state of the photon (assuming a wave packet) :\n|psi>= |path1>+|path2> with <path1|path2>=0?\nb) if yes, |path1> and |path2> are for example 2 parallel paths, where\n|path1> is 100% stopped by the first screen and |path2> 100% not?\nc) what do you want to say?\n\nI mean, I have a system that is well described through unitary\nevolution (superposition of states). At the end, I must apply the born\nrules to get the statistics (what I see in the experiment). QM does not\nexplain the preferred basis (here the paths of the particles), neither\nwhy we have a particular outcome, the physical collapse?, in a given\ntrial.\n\nAre you just searching for a predictive description of a particular\noutcome in a given QM experiment?\n\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier a écrit :
> Seratend wrote:
>
> > QM deals only with statistics of outcomes
> > and, in my opinion, outcomes are the "classical world" (what we "see").
>
> In my opinion, the "classical world" (what we "see") is the world
> as seen after irreversible effects have set in, i.e., the world
> as described by nonequilibrium thermodynamics (including hydromechanics
> and kinetic theory).
Interesting.
You seem to view the measurement results exclusively through the mean
value filter in my point of view (like the interference pattern: single
photon screen impact event versus multiple independent photons
interference pattern event).
How do you explain the observed state of a single photon event? (I
understand you can explain the mean value of the measurement apparatus
that is almost equal to the outcome with the good hypotheses, but not
the one of photon or electron object).
What do you intend by irreversible effects?
> Everything in thermodynamics and kinetic theory
> is real, objective, without any of the dubiosities that characterize
> the traditional interpretations of the quantum world.
>
Frankly, I have a real problem to see reality behind pressure, volume
and energy/temperature. All are macroscopic random variables through
the mean value filter (or the law of large numbers if you prefer) and
this seems to be a restrictive choice on what can be observed,
especially when we consider the observation of a microscopic phenomenon
through a macroscopic one: most of the usual quantum cases measuring
single particles.
>
> > Therefore, it is relatively difficult for me to understand people who
> > want to demonstrate that there is a physical collapse leading to the
> > outcomes.
>
> The quest is to show that the interaction of a quantum system with
> a macroscopic detector describable by thermodynamics (and hence,
> through statistical mechanics, by quantum theory)
Statistical classical mechanics?
> gives rise to
> macroscopic, observable effects in the detector that can be regarded
> as the physical equivalent of an objective record of measurements.
>
I am not sure I understand what you say. In the QM description, I just
have statistics of outcomes. I have for a macroscopic detetector, a
macroscopic observable A= sum_i Ai where Ai are the microscopic
observables of the apparatus (huge number). The result of the
measurement will be for example the value of this observable that is
highly degenerated at the limit. Except for the preferred basis
problem, I do not understand what you are looking for.
> I gave a concise formulation of a specific case of this quest in
> my recent paper http://www.arxiv.org/abs/quant-ph/0505172.
>
I have read quickly you paper. I have not found the original thread. So
I have some questions:
a) what is the initial state of the photon (assuming a wave packet) :
|\psi>= |path1>+|path2> with <path1|path2>=0?
b) if yes, |path1> and |path2> are for example 2 parallel paths, where
|path1> is 100% stopped by the first screen and |path2> 100% not?
c) what do you want to say?
I mean, I have a system that is well described through unitary
evolution (superposition of states). At the end, I must apply the born
rules to get the statistics (what I see in the experiment). QM does not
explain the preferred basis (here the paths of the particles), neither
why we have a particular outcome, the physical collapse?, in a given
trial.
Are you just searching for a predictive description of a particular
outcome in a given QM experiment?
Seratend.
Arnold Neumaier
May31-05, 01:34 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier a =E9crit :\n>\n>>Seratend wrote:\n>>\n>>>QM deals only with statistics of outcomes\n>>>and, in my opinion, outcomes are the "classical world" (what we "see").\n>>\n>>In my opinion, the "classical world" (what we "see") is the world\n>>as seen after irreversible effects have set in, i.e., the world\n>>as described by nonequilibrium thermodynamics (including hydromechanics\n>>and kinetic theory).\n>\n> Interesting.\n> You seem to view the measurement results exclusively through the mean\n> value filter\n\nYes. Mean values of thermodynamic origin are the raw observables\nin all experiments; everything else is derived from these by theory\nor speculation.\n\nI call this the \'consistent experiment interpretation\', following\nfirst steps in this direction taken in Section 10 of\nquant-ph/0303047 =3D Int. J. Mod. Phys. B 17 (2003), 2937-2980.\nSince I wrote this, my view has considerably gained in strength.\nIf you read German, you can find much more about it at\nhttp://www.mat.univie.ac.at/~neum/physik-faq.tex\nI am working on a paper describing everything more formally\nand in English, expecting (because of other work to do)\nto have it finished by the end of the summer. In the mean time,\nI am happy to feed the main qualitative arguments into this\ndiscussion, if you are interested.\n\n\n> in my point of view (like the interference pattern: single\n> photon screen impact event versus multiple independent photons\n> interference pattern event).\n> How do you explain the observed state of a single photon event?\n\nIt is only a sloppy way of speaking, not a real physical event.\nWhat actually happens is the following:\n\nThe light ray of a laser is an electromagnetic field localized in a\nsmall region along the ray that begins in the laser and ends at the\nphotodetector. A ray of intensity I is described by a coherent state\n|I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...\nIf I is tiny then, from time to time, an electron responds (in some\nloose way of speaking that itself would need correction) to the\nenergy continuously transmitted by the ray by going into an excited\nstate, an event which is magnified in the detector and recorded.\nThese occasional events form a Poisson process, with a rate proportional\nto the intensity I. This, no more and no less, is the experimental\nobservation. It is precisely what is predicted by quantum mechanics.\n\nThe traditional sloppy way of picturing this in an intuitive way is to\nsay that, from time to time, a photon arrives at the screen and kicks\nan electron out of its orbit. This is a nice piccture, especially for\nthe newcomer or the lay man, but it cannot be taken any more seriously\nthan Bohr\'s picture of an atom, in which electrons orbit a nucleus in\ncertain quantum orbits. For nothing of this can be checked by experiment\n- it is empty talk intended to serve intuition, but in fact causing more\ndamange than understanding.\n\nAnother way to see that is that the photo effect also happens for\nfermionic matter in a classical external field. (See, e.g., the\nquantum optics book by mandel and Wolf.) Thus the observed\nPoisson process cannot be a consequence of quantized light, but\nrather is an indication of quantized detectors.\n\n\n\n> What do you intend by irreversible effects?\n\nDissipation, introduced by the Markov approximation necessary to get\na sensible dynamics of a system smaller than the whole universe.\n\n\n>>Everything in thermodynamics and kinetic theory\n>>is real, objective, without any of the dubiosities that characterize\n>>the traditional interpretations of the quantum world.\n>>\n> Frankly, I have a real problem to see reality behind pressure, volume\n> and energy/temperature.\n\nAsk any engineer. They know what is real. I understand reality in the\nengineering sense. They can determine the pressure, to within the\naccuracy allowed by statistical mechanics. A single measurement on a\nsingle large quantum system (such as a cup of tee) is usually sufficient\nto get a reasonable objective value.\n\nIf this is not real, there is no reality at all, and we are all dreaming.\n\n\n> All are macroscopic random variables through\n> the mean value filter (or the law of large numbers if you prefer) and\n> this seems to be a restrictive choice on what can be observed,\n> especially when we consider the observation of a microscopic phenomenon\n> through a macroscopic one: most of the usual quantum cases measuring\n> single particles.\n\nHow can you measure a microscopic object without measuring something\nmacroscopic. You need the macroscopic, thermodynamic state of something\nto assert that indeed some definite, objective event happened.\nTake away objectivity and you lose all of physics.\n\n\n>>>Therefore, it is relatively difficult for me to understand people who\n>>>want to demonstrate that there is a physical collapse leading to the\n>>>outcomes.\n>>\n>>The quest is to show that the interaction of a quantum system with\n>>a macroscopic detector describable by thermodynamics (and hence,\n>>through statistical mechanics, by quantum theory)\n>\n> Statistical classical mechanics?\n\nNo. Statistical mechanics as taught in textbooks. Which includes\n(and on the deepest level is only) quantum mechanics.\n\n\n>>gives rise to\n>>macroscopic, observable effects in the detector that can be regarded\n>>as the physical equivalent of an objective record of measurements.\n>>\n> I am not sure I understand what you say. In the QM description, I just\n> have statistics of outcomes. I have for a macroscopic detetector, a\n> macroscopic observable A=3D sum_i Ai\n\nNo. This is not what statistical mechanics teaches. The gurus there say\nthat the quantities thermodynamics is about are expectations of\nmicroscopic operators, not their eigenvalues!\n\n\n> where Ai are the microscopic\n> observables of the apparatus (huge number). The result of the\n> measurement will be for example the value of this observable that is\n> highly degenerated at the limit. Except for the preferred basis\n> problem, I do not understand what you are looking for.\n>\n>\n>>I gave a concise formulation of a specific case of this quest in\n>>my recent paper quant-ph/0505172.\n>>\n> I have read quickly you paper. I have not found the original thread. So\n> I have some questions:\n\nMy time is up; will respond to these another time.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier a =E9crit :
>
>>Seratend wrote:
>>
>>>QM deals only with statistics of outcomes
>>>and, in my opinion, outcomes are the "classical world" (what we "see").
>>
>>In my opinion, the "classical world" (what we "see") is the world
>>as seen after irreversible effects have set in, i.e., the world
>>as described by nonequilibrium thermodynamics (including hydromechanics
>>and kinetic theory).
>
> Interesting.
> You seem to view the measurement results exclusively through the mean
> value filter
Yes. Mean values of thermodynamic origin are the raw observables
in all experiments; everything else is derived from these by theory
or speculation.
I call this the 'consistent experiment interpretation', following
first steps in this direction taken in Section 10 of
http://www.arxiv.org/abs/quant-ph/0303047 =3D \Int. J. Mod. Phys. B 17 (2003), 2937-2980.
Since I wrote this, my view has considerably gained in strength.
If you read German, you can find much more about it at
http://www.mat.univie.ac.at/~neum/physik-faq.tex
I am working on a paper describing everything more formally
and in English, expecting (because of other work to do)
to have it finished by the end of the summer. In the mean time,
I am happy to feed the main qualitative arguments into this
discussion, if you are interested.
> in my point of view (like the interference pattern: single
> photon screen impact event versus multiple independent photons
> interference pattern event).
> How do you explain the observed state of a single photon event?
It is only a sloppy way of speaking, not a real physical event.
What actually happens is the following:
The light ray of a laser is an electromagnetic field localized in a
small region along the ray that begins in the laser and ends at the
photodetector. A ray of intensity I is described by a coherent state
|I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...
If I is tiny then, from time to time, an electron responds (in some
loose way of speaking that itself would need correction) to the
energy continuously transmitted by the ray by going into an excited
state, an event which is magnified in the detector and recorded.
These occasional events form a Poisson process, with a rate proportional
to the intensity I. This, no more and no less, is the experimental
observation. It is precisely what is predicted by quantum mechanics.
The traditional sloppy way of picturing this in an intuitive way is to
say that, from time to time, a photon arrives at the screen and kicks
an electron out of its orbit. This is a nice piccture, especially for
the newcomer or the lay man, but it cannot be taken any more seriously
than Bohr's picture of an atom, in which electrons orbit a nucleus in
certain quantum orbits. For nothing of this can be checked by experiment
- it is empty talk intended to serve intuition, but in fact causing more
damange than understanding.
Another way to see that is that the photo effect also happens for
fermionic matter in a classical external field. (See, e.g., the
quantum optics book by mandel and Wolf.) Thus the observed
Poisson process cannot be a consequence of quantized light, but
rather is an indication of quantized detectors.
> What do you intend by irreversible effects?
Dissipation, introduced by the Markov approximation necessary to get
a sensible dynamics of a system smaller than the whole universe.
>>Everything in thermodynamics and kinetic theory
>>is real, objective, without any of the dubiosities that characterize
>>the traditional interpretations of the quantum world.
>>
> Frankly, I have a real problem to see reality behind pressure, volume
> and energy/temperature.
Ask any engineer. They know what is real. I understand reality in the
engineering sense. They can determine the pressure, to within the
accuracy allowed by statistical mechanics. A single measurement on a
single large quantum system (such as a cup of tee) is usually sufficient
to get a reasonable objective value.
If this is not real, there is no reality at all, and we are all dreaming.
> All are macroscopic random variables through
> the mean value filter (or the law of large numbers if you prefer) and
> this seems to be a restrictive choice on what can be observed,
> especially when we consider the observation of a microscopic phenomenon
> through a macroscopic one: most of the usual quantum cases measuring
> single particles.
How can you measure a microscopic object without measuring something
macroscopic. You need the macroscopic, thermodynamic state of something
to assert that indeed some definite, objective event happened.
Take away objectivity and you lose all of physics.
>>>Therefore, it is relatively difficult for me to understand people who
>>>want to demonstrate that there is a physical collapse leading to the
>>>outcomes.
>>
>>The quest is to show that the interaction of a quantum system with
>>a macroscopic detector describable by thermodynamics (and hence,
>>through statistical mechanics, by quantum theory)
>
> Statistical classical mechanics?
No. Statistical mechanics as taught in textbooks. Which includes
(and on the deepest level is only) quantum mechanics.
>>gives rise to
>>macroscopic, observable effects in the detector that can be regarded
>>as the physical equivalent of an objective record of measurements.
>>
> I am not sure I understand what you say. In the QM description, I just
> have statistics of outcomes. I have for a macroscopic detetector, a
> macroscopic observable A=3D sum_i Ai
No. This is not what statistical mechanics teaches. The gurus there say
that the quantities thermodynamics is about are expectations of
microscopic operators, not their eigenvalues!
> where Ai are the microscopic
> observables of the apparatus (huge number). The result of the
> measurement will be for example the value of this observable that is
> highly degenerated at the limit. Except for the preferred basis
> problem, I do not understand what you are looking for.
>
>
>>I gave a concise formulation of a specific case of this quest in
>>my recent paper http://www.arxiv.org/abs/quant-ph/0505172.
>>
> I have read quickly you paper. I have not found the original thread. So
> I have some questions:
My time is up; will respond to these another time.
Arnold Neumaier
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier\n> At the time of Bohr, von Neumann and Wigner, the collapse meant\n> something objective,[...].\n\nIt seems, perhaps, interesting to point out that the\nfirst definition was "reduction of probability packet",\nsometimes "reduction of wave packet."\n\nQuoting from "Electrons et Photons - Rapports et Discussions\ndu Cinquieme Conseil de Physique de l\'Institut International\nde Physique Solvay", [Paris, Gauthier-Villars, 1928, p. 250].\nM. Born talking: "[...] En d\'autres termes: comment le caractère\ncorpuscolaire du phénomène peut-il etre concilié ici avec\nla raprésentation par ondes? Pour le faire, on doit faire appel\nà la notion de \'réduction du paquet de probabilité\' développée\npar Heisenberg."\n\nActually Heisenberg gave a physical picture in 1930.\n"There is then a definite probability for finding the photon\neither in one part or in the other part of the divided wave packet.\nAfter a suffcient time the two parts will be separated by any\ndistance desired; now if an experiment yields the result that\nthe photon is, say, in the reflected part of the packet, then\nthe probability of finding the photon in the other part of the\npacket immediately becomes zero. The experiment at the position\nof the reflected packet thus exerts a kind of action (reduction\nof the wave packet) at the distant point occupied by the transmitted\npacket, and one sees that this action is propagated with a velocity\ngreater than that of light. However, it is also obvious that\nthis kind of action can never be utilized for the transmission\nof signals so that it is not in conflict with the postulates\nof the theory of relativity." (\'The Physical Principles of the\nQuantum Theory\', University of Chicago Press, Chicago, 1930).\n\n(Following the above reasoning we expect that, i.e., the\ninformation about the probability of a particle being at\na distance x comes to us with a signal velocity c.\nThus the |wavefunction(x,t - r/c)|^2 should represent\nthe probability that a particle is at x, as seen at\nthe origin. Or am I wrong?)\n\nUnfortunately H.Kragh ("Dirac: a Scientific Biography", Cambridge\nU.P., 1990) describes a (1927) discussion between Dirac, Heisenberg\nand Born, about what, actually, gives rise to a "collapse".\nDirac said that it is \'Nature\' that makes the choice (of the\nmeasurement outcome). Born agreed. Heisenberg however maintained that,\nbehind the collapse, and the choice of which \'branch\' the wavefunction\nwould be followed, there was "the free-will of the human observer".\n\nAnd later, in "Physics and Philosophy" (Harper and Row, 1958, New York)\nHeisenberg writes "The observation itself changes the probability\nfunction discontinuously; it selects of all possible events\nthe actual one that has taken place [...] The discontinuous change\nin the probability function, however, takes place with the act\nof registration, because it is the discontinuous change\nof our knowledge in the instant of registration that has its\nimage in the discontinuous change of the probability function."\n\nAccording to Jan Faye "Bohr accepted the Born statistical\ninterpretation because he believed that the psi-function\nhas only a symbolic meaning and does not represent anything real.\nIt makes sense to talk about a collapse of the wave function\nonly if, as Bohr put it, the psi-function can be given a pictorial\nrepresentation, something he strongly denied."\n\nIt is really not so easy to find a definition (of the \'reduction\')\nby Niels Bohr. In a letter to Pauli (March 2, 1955) he wrote "Thus,\nwhen speaking of the physical interpretation of the formalism,\nI consider such details of procedure like "reduction of the wave\npackets" as integral parts of a consistent scheme conforming\nwith the indivisibility of the phenomena and the essential\nirreversibility involved in the very concept of observation."\n(Niels Bohr Collected Works, vol. 10, Elsevier 1999, page 568).\n\nEven in Max Born it is possible to find many (very) different\ninterpretations of the \'reduction\' (and of the wave-funtion).\nIn example "The question of whether the waves are something\n"real" or a function to describe and predict phenomena in\na convenient way is a matter of taste. I personally like\nto regard a probability wave, even in 3N-dimensional space,\nas a real thing, certainly as more than a tool for mathematical\ncalculations ... Quite generally, how could we rely on\nprobability predictions if by this notion we do not refer\nto something real and objective?" [Max Born, Dover publ., 1964,\n"Natural Philosophy of Cause and Chance", p. 107.]\n\n-serafino\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier
> At the time of Bohr, von Neumann and Wigner, the collapse meant
> something objective,[...].
It seems, perhaps, interesting to point out that the
first definition was "reduction of probability packet",
sometimes "reduction of wave packet."
Quoting from "Electrons et Photons - Rapports et Discussions
du Cinquieme Conseil de Physique de l'Institut International
de Physique Solvay", [Paris, Gauthier-Villars, 1928, p. 250].
M. Born talking: "[...] En d'autres termes: comment le caractère
corpuscolaire du phénomène peut-il etre concilié ici avec
la raprésentation par ondes? Pour le faire, on doit faire appel
à la notion de 'réduction du paquet de probabilité' développée
par Heisenberg."
Actually Heisenberg gave a physical picture in 1930.
"There is then a definite probability for finding the photon
either in one part or in the other part of the divided wave packet.
After a suffcient time the two parts will be separated by any
distance desired; now if an experiment yields the result that
the photon is, say, in the reflected part of the packet, then
the probability of finding the photon in the other part of the
packet immediately becomes zero. The experiment at the position
of the reflected packet thus exerts a kind of action (reduction
of the wave packet) at the distant point occupied by the transmitted
packet, and one sees that this action is propagated with a velocity
greater than that of light. However, it is also obvious that
this kind of action can never be utilized for the transmission
of signals so that it is not in conflict with the postulates
of the theory of relativity." ('The Physical Principles of the
Quantum Theory', University of Chicago Press, Chicago, 1930).
(Following the above reasoning we expect that, i.e., the
information about the probability of a particle being at
a distance x comes to us with a signal velocity c.
Thus the |wavefunction(x,t - r/c)|^2 should represent
the probability that a particle is at x, as seen at
the origin. Or am I wrong?)
Unfortunately H.Kragh ("Dirac: a Scientific Biography", Cambridge
U.P., 1990) describes a (1927) discussion between Dirac, Heisenberg
and Born, about what, actually, gives rise to a "collapse".
Dirac said that it is 'Nature' that makes the choice (of the
measurement outcome). Born agreed. Heisenberg however maintained that,
behind the collapse, and the choice of which 'branch' the wavefunction
would be followed, there was "the free-will of the human observer".
And later, in "Physics and Philosophy" (Harper and Row, 1958, New York)
Heisenberg writes "The observation itself changes the probability
function discontinuously; it selects of all possible events
the actual one that has taken place [...] The discontinuous change
in the probability function, however, takes place with the act
of registration, because it is the discontinuous change
of our knowledge in the instant of registration that has its
image in the discontinuous change of the probability function."
According to Jan Faye "Bohr accepted the Born statistical
interpretation because he believed that the \psi-function
has only a symbolic meaning and does not represent anything real.
It makes sense to talk about a collapse of the wave function
only if, as Bohr put it, the \psi-function can be given a pictorial
representation, something he strongly denied."
It is really not so easy to find a definition (of the 'reduction')
by Niels Bohr. In a letter to Pauli (March 2, 1955) he wrote "Thus,
when speaking of the physical interpretation of the formalism,
I consider such details of procedure like "reduction of the wave
packets" as integral parts of a consistent scheme conforming
with the indivisibility of the phenomena and the essential
irreversibility involved in the very concept of observation."
(Niels Bohr Collected Works, vol. 10, Elsevier 1999, page 568).
Even in Max Born it is possible to find many (very) different
interpretations of the 'reduction' (and of the wave-funtion).
In example "The question of whether the waves are something
"real" or a function to describe and predict phenomena in
a convenient way is a matter of taste. I personally like
to regard a probability wave, even in 3N-dimensional space,
as a real thing, certainly as more than a tool for mathematical
calculations ... Quite generally, how could we rely on
probability predictions if by this notion we do not refer
to something real and objective?" [Max Born, Dover publ., 1964,
"Natural Philosophy of Cause and Chance", p. 107.]
-serafino
Seratend
May31-05, 01:37 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman a =E9crit :\n> In article <1117183732.077481.57630@z14g2000cwz.googlegroups. com>,\n>\n> Why do we observe outcomes with probability |<a|psi>|^2? QM has no\n> answer for this question.\n>\nThis is the born rules, a postulate of QM. I think we are at the centre\nof our minor problem of comprehension. QM formulation provides a very\nformal statistical description of the system as Classical statistical\nmechanics does. This is a formal choice: We describe the statistics of\noutcomes rather than the description of the evolution of individual\noutcomes.\n\nFor me at least this is clear. I am not sure if it is clear for you\ntoo. In my comprehension, your question is just a mathematical\nquestion: why the probability of an event (P(A=3Da)) is the frequency of\nindependent outcomes with identical probability (the statistics of\noutcomes). This is simply the law of large numbers. Formally, I may\nalways do such affirmation: the hypotheses of the experiment where I\nhave this equality. This is not different from the coin tossing\nexperiment. (You can always question the validity of the independence,\nbut this is the problem of the experiment realization and not the\nvalidity of the results).\nIn QM, we choose the observables (the set of outcomes is the\neigenvalues of the observable) and states (or generalized states) to\ndescribe, formally, a probability law of the outcomes of the observable\n(the random variable). The choice of observables and states to describe\nthe probability law is more related to the time evolution of the\nprobability law where we have a simple expression (e.g. the difference\nbetween the observable expression of QM and the random variable\nexpression in Bohmian mechanics).\n\n> > I can only understand this sentence as the quest for a deterministic\n> > (causal) description of outcomes compatible with the statistics of QM.\n>\n> QM is deterministic and causal. That\'s the problem.\n>\nI do not understand where the problem is. I have a deterministic time\nevolution of the probability law. I may also have a deterministic\nevolution of the set of eigenvalues (the Heisenberg representation).\nWhere is the problem?\n\n> > If this is the case, we already have such a description, bohmian\n> > mechanics for the position eigen basis (and equivelent formulations i=\nn\n> > different eigenbasis).\n>\n> Bohmian mechanics has no relativistic generalization that I know of.\n>\nI think you should rather say bohmian mechanics has not a simple\nrelativistic generalization (the mathematical expression becomes more\ndifficult has the particle number in not conserved).\nSee for example Trajectories and Particle Creation and Annihilation in\nQuantum Field Theory, quant-ph/0208072, 2002.\nWith bohmian mechanics, we must separate the equivalent formulation of\nQM with contextual random variables from the interpretation. As long as\nwe stay with mathematical expressions (and knowing their hypothesis of\nvalidity), there is no problem.\n\n\n> [...]\n>\n> > > I\'m not sure I understand what you\'re asking. Let me try to answer\n> > > something, then. The question of what why we observe what we observ=\ne is\n> > > completely unanswered by quantum mechanics.\n> >\n> > So you are saying that QM theory does not explain the preferred basis.\n>\n> You\'ll have to communicate to me better what you mean by \'preferred\n> basis\'.\n\nOk, I will try to explain what I mean. I have no problem with the\npreferred basis (the basis where I have the experiment outcomes). I\njust have a problem with the prediction of such a basis by QM. I mean,\nwhere in the QM theory do I have results inferring the preferred basis?\nUp to now, I just know the preferred basis after I have done the\nexperiments. For example the interference pattern of double slit\nexperiments observed on the screen. I know, from this experiment, if I\nplace a screen, I will do a position measurement. But I have not seen\nanywhere in QM, where the mathematics can predict such a basis as every\nbasis is possible from the theory point of view.\n\nI can live with such a result. However, I prefer if everybody can\nacknowledge such a result: the QM formulation does not predict the\nbasis of outcomes in an experiment (out of scope). It is important (at\nleast for me) to understand the scope of a physical theory (what it may\npredict and what it does not predict).\n\n> Given an experimental setup with a classical measuring device\n> (where classical means large numbers of microstates per macrostate), I\n> can describe to you a preferred basis in that setup.\n\nOk, let\'s play with a simple toy model and you will try to tell me\nthe proffered basis of this experimental setup.\nLet\'s take the double slit experiment with electrons (formally\nsimpler in the terms of interaction description at the slit plate, but\nwe can change and choose photons as outside the local interaction the\nfree propagator or the photon and electron is equivalent).\n\na) Let\'s assume that the plate with the slits is a reflective plate\nsuch that we can describe it through an interaction: Hint_plate:\n|plate><plate|(x) V(r)\nWhere |plate> is a state of the free plat hamiltonian (no interaction\nwith the environment: we neglect it during the period of observation).\nV(r) is null outside the plate and at the slits and infinite within the\nplate (hypothesis model of the energy conservation). We just model the\nplate with a quantum wall (with a non null thickness).\nb) At a distance of the plate (z direction), we place a screen. Let\'s\ndescribe this screen by another Hamiltonian: Hint_screen=3D\n|Screen><Screen|(x)Vdiff(x) where Vdiff is a scattering potential null\noutside the screen (such that photons or electrons arriving at the\nscreen are transferred into another direction: how we may see\nexternally the interference pattern from another direction). |Screen>\nis an eigenstate of the Hamiltonian.\n\nWe have for this system: H=3D Ho+Ho_screen+H_int_plate+H_int_screen\nWe also have [Ho_screen,Hint_plate]=3D [Hint_screen,Hint_plate]=3D\n[Ho_plate,Hint_plate]=3D0\n\nAssume that the intial state is |state(o)>=3D|psi(o)>|plate>|screen>\nwhere |psi(o)> is the state of the electron or photon. Before the\nplate, |psi(t)> may be described by a wave packet centered on a\nmomentum |p_z> parallel to the z axis (free propagator of the electron\nor the photon).\n\nWe may add or remove the properties we want to this toy model. The\nimportant fact is the ability, by thought, to decrease the interaction\nwith the environment and to check if we still are able to predict an\neigenbasis or if the shcmidt eigenbasis is always correct for this\nexperiment (depending on the different hypotheses).\n\nNow how can you deduce (from QM theory) the preferred basis and what we\n"really" measure in this experiment?\n\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman a =E9crit :
> In article <1117183732.077481.57630@z14g2000cwz.googlegroups.c om>,
>
> Why do we observe outcomes with probability |<a|\psi>|^2? QM has no
> answer for this question.
>
This is the born rules, a postulate of QM. I think we are at the centre
of our minor problem of comprehension. QM formulation provides a very
formal statistical description of the system as Classical statistical
mechanics does. This is a formal choice: We describe the statistics of
outcomes rather than the description of the evolution of individual
outcomes.
For me at least this is clear. I am not sure if it is clear for you
too. In my comprehension, your question is just a mathematical
question: why the probability of an event (P(A=3Da)) is the frequency of
independent outcomes with identical probability (the statistics of
outcomes). This is simply the law of large numbers. Formally, I may
always do such affirmation: the hypotheses of the experiment where I
have this equality. This is not different from the coin tossing
experiment. (You can always question the validity of the independence,
but this is the problem of the experiment realization and not the
validity of the results).
In QM, we choose the observables (the set of outcomes is the
eigenvalues of the observable) and states (or generalized states) to
describe, formally, a probability law of the outcomes of the observable
(the random variable). The choice of observables and states to describe
the probability law is more related to the time evolution of the
probability law where we have a simple expression (e.g. the difference
between the observable expression of QM and the random variable
expression in Bohmian mechanics).
> > I can only understand this sentence as the quest for a deterministic
> > (causal) description of outcomes compatible with the statistics of QM.
>
> QM is deterministic and causal. That's the problem.
>
I do not understand where the problem is. I have a deterministic time
evolution of the probability law. I may also have a deterministic
evolution of the set of eigenvalues (the Heisenberg representation).
Where is the problem?
> > If this is the case, we already have such a description, bohmian
> > mechanics for the position eigen basis (and equivelent formulations i=
n
> > different eigenbasis).
>
> Bohmian mechanics has no relativistic generalization that I know of.
>
I think you should rather say bohmian mechanics has not a simple
relativistic generalization (the mathematical expression becomes more
difficult has the particle number in not conserved).
See for example Trajectories and Particle Creation and Annihilation in
Quantum Field Theory, http://www.arxiv.org/abs/quant-ph/0208072, 2002.
With bohmian mechanics, we must separate the equivalent formulation of
QM with contextual random variables from the interpretation. As long as
we stay with mathematical expressions (and knowing their hypothesis of
validity), there is no problem.
> [...]
>
> > > I'm not sure I understand what you're asking. Let me try to answer
> > > something, then. The question of what why we observe what we observ=
e is
> > > completely unanswered by quantum mechanics.
> >
> > So you are saying that QM theory does not explain the preferred basis.
>
> You'll have to communicate to me better what you mean by 'preferred
> basis'.
Ok, I will try to explain what I mean. I have no problem with the
preferred basis (the basis where I have the experiment outcomes). I
just have a problem with the prediction of such a basis by QM. I mean,
where in the QM theory do I have results inferring the preferred basis?
Up to now, I just know the preferred basis after I have done the
experiments. For example the interference pattern of double slit
experiments observed on the screen. I know, from this experiment, if I
place a screen, I will do a position measurement. But I have not seen
anywhere in QM, where the mathematics can predict such a basis as every
basis is possible from the theory point of view.
I can live with such a result. However, I prefer if everybody can
acknowledge such a result: the QM formulation does not predict the
basis of outcomes in an experiment (out of scope). It is important (at
least for me) to understand the scope of a physical theory (what it may
predict and what it does not predict).
> Given an experimental setup with a classical measuring device
> (where classical means large numbers of microstates per macrostate), I
> can describe to you a preferred basis in that setup.
Ok, let's play with a simple toy model and you will try to tell me
the proffered basis of this experimental setup.
Let's take the double slit experiment with electrons (formally
simpler in the terms of interaction description at the slit plate, but
we can change and choose photons as outside the local interaction the
free propagator or the photon and electron is equivalent).
a) Let's assume that the plate with the slits is a reflective plate
such that we can describe it through an interaction: Hint_plate:
|plate><plate|(x) V(r)
Where |plate> is a state of the free plat hamiltonian (no interaction
with the environment: we neglect it during the period of observation).
V(r) is null outside the plate and at the slits and infinite within the
plate (hypothesis model of the energy conservation). We just model the
plate with a quantum wall (with a non null thickness).
b) At a distance of the plate (z direction), we place a screen. Let's
describe this screen by another Hamiltonian: Hint_screen=3D
|Screen><Screen|(x)Vdiff(x) where Vdiff is a scattering potential null
outside the screen (such that photons or electrons arriving at the
screen are transferred into another direction: how we may see
externally the interference pattern from another direction). |Screen>
is an eigenstate of the Hamiltonian.
We have for this system: H=3D Ho+Ho_screen+H_{int_plate}+H_{int_screen}
We also have [Ho_screen,Hint_plate]=3D [Hint_screen,Hint_plate]=3D[Ho_plate,Hint_plate]=3D0
Assume that the intial state is |state(o)>=3D|\psi(o)>|plate>|screen>
where |\psi(o)> is the state of the electron or photon. Before the
plate, |\psi(t)> may be described by a wave packet centered on a
momentum |p_z> parallel to the z axis (free propagator of the electron
or the photon).
We may add or remove the properties we want to this toy model. The
important fact is the ability, by thought, to decrease the interaction
with the environment and to check if we still are able to predict an
eigenbasis or if the shcmidt eigenbasis is always correct for this
experiment (depending on the different hypotheses).
Now how can you deduce (from QM theory) the preferred basis and what we
"really" measure in this experiment?
Seratend.
Aaron Bergman
May31-05, 04:39 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117448074.219697.96620@f14g2000cwb.googlegroups. com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman a =E9crit :\n> > In article <1117183732.077481.57630@z14g2000cwz.googlegroups. com>,\n> >\n> > Why do we observe outcomes with probability |<a|psi>|^2? QM has no\n> > answer for this question.\n> >\n> This is the born rules, a postulate of QM.\n\nNot so much. It works as a good effective description, but if it refers\nto an explicit nonunitary collapse process, it fails to give a\ndescription of it. If it does not refer to collapse, then it fails to\nexplain our perception of (one part of) the reduced density matrix\n(say), rather than the full coherent wavefunction.\n\n[...]\n\n> > > I can only understand this sentence as the quest for a deterministic\n> > > (causal) description of outcomes compatible with the statistics of QM.\n> >\n> > QM is deterministic and causal. That\'s the problem.\n> >\n> I do not understand where the problem is. I have a deterministic time\n> evolution of the probability law. I may also have a deterministic\n> evolution of the set of eigenvalues (the Heisenberg representation).\n> Where is the problem?\n\nYou\'ll get the wrong answer if you apply such a prescription. If you\napply the Born rules without nondeterministic state reduction you get\nnonsense. If you lack an explicit state reduction, you are forced to\nexplain why, as I said above, we only perceive on \'branch\' of the\nwavefunction (given that decoherence effectively shields us from\nmacroscopic interferences).\n\n> > > If this is the case, we already have such a description, bohmian\n> > > mechanics for the position eigen basis (and equivelent formulations i=\n> n\n> > > different eigenbasis).\n> >\n> > Bohmian mechanics has no relativistic generalization that I know of.\n>\n> I think you should rather say bohmian mechanics has not a simple\n> relativistic generalization (the mathematical expression becomes more\n> difficult has the particle number in not conserved).\n> See for example Trajectories and Particle Creation and Annihilation in\n> Quantum Field Theory, quant-ph/0208072, 2002.\n> With bohmian mechanics, we must separate the equivalent formulation of\n> QM with contextual random variables from the interpretation. As long as\n> we stay with mathematical expressions (and knowing their hypothesis of\n> validity), there is no problem.\n\nI hadn\'t known of this attempt at a relativistic generalization.\nNonetheless, I believe that Bohmian mechanics still has a problem with\nthe reproduction of classical trajectories (although perhaps decoherence\ncan go a long way towards solving that).\n\n> > [...]\n> >\n> > > > I\'m not sure I understand what you\'re asking. Let me try to answer\n> > > > something, then. The question of what why we observe what we observ=\n> e is\n> > > > completely unanswered by quantum mechanics.\n> > >\n> > > So you are saying that QM theory does not explain the preferred basis.\n> >\n> > You\'ll have to communicate to me better what you mean by \'preferred\n> > basis\'.\n>\n> Ok, I will try to explain what I mean. I have no problem with the\n> preferred basis (the basis where I have the experiment outcomes). I\n> just have a problem with the prediction of such a basis by QM. I mean,\n> where in the QM theory do I have results inferring the preferred basis?\n> Up to now, I just know the preferred basis after I have done the\n> experiments. For example the interference pattern of double slit\n> experiments observed on the screen. I know, from this experiment, if I\n> place a screen, I will do a position measurement. But I have not seen\n> anywhere in QM, where the mathematics can predict such a basis as every\n> basis is possible from the theory point of view.\n\nNo, you know ahead of time that, if you place the screen, you do a\nposition measurement. You in know way had to the experiment to figure\nthis out. Inherent in any experimental design, you know which\nmacroscopic observable you are entangling you system with and that\ndetermines, via decoherece, a preferred basis. (Up to technicalities, I\nsuppose, like overcompleteness and the like).\n\n[...snip experiment...]\n\n> We have for this system: H=3D Ho+Ho_screen+H_int_plate+H_int_screen\n> We also have [Ho_screen,Hint_plate]=3D [Hint_screen,Hint_plate]=3D\n> [Ho_plate,Hint_plate]=3D0\n>\n> Assume that the intial state is |state(o)>=3D|psi(o)>|plate>|screen>\n> where |psi(o)> is the state of the electron or photon. Before the\n> plate, |psi(t)> may be described by a wave packet centered on a\n> momentum |p_z> parallel to the z axis (free propagator of the electron\n> or the photon).\n>\n> We may add or remove the properties we want to this toy model. The\n> important fact is the ability, by thought, to decrease the interaction\n> with the environment and to check if we still are able to predict an\n> eigenbasis or if the shcmidt eigenbasis is always correct for this\n> experiment (depending on the different hypotheses).\n>\n> Now how can you deduce (from QM theory) the preferred basis and what we\n> "really" measure in this experiment?\n\nYou need to describe to me the macroscopic degrees of freedom in your\nexperiment, ie, the macrostates by which you are performing your\nobservation. With that, simlply wait a period equal to a couple times\nthe decoherence time and pick the basis in which the reduced density\nmatrix is diagonal. You don\'t have to worry about uniqueness of schmidt\nbases or whatever.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117448074.219697.96620@f14g2000cwb.googlegroups.c om>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman a =E9crit :
> > In article <1117183732.077481.57630@z14g2000cwz.googlegroups.c om>,
> >
> > Why do we observe outcomes with probability |<a|\psi>|^2? QM has no
> > answer for this question.
> >
> This is the born rules, a postulate of QM.
Not so much. It works as a good effective description, but if it refers
to an explicit nonunitary collapse process, it fails to give a
description of it. If it does not refer to collapse, then it fails to
explain our perception of (one part of) the reduced density matrix
(say), rather than the full coherent wavefunction.
[...]
> > > I can only understand this sentence as the quest for a deterministic
> > > (causal) description of outcomes compatible with the statistics of QM.
> >
> > QM is deterministic and causal. That's the problem.
> >
> I do not understand where the problem is. I have a deterministic time
> evolution of the probability law. I may also have a deterministic
> evolution of the set of eigenvalues (the Heisenberg representation).
> Where is the problem?
You'll get the wrong answer if you apply such a prescription. If you
apply the Born rules without nondeterministic state reduction you get
nonsense. If you lack an explicit state reduction, you are forced to
explain why, as I said above, we only perceive on 'branch' of the
wavefunction (given that decoherence effectively shields us from
macroscopic interferences).
> > > If this is the case, we already have such a description, bohmian
> > > mechanics for the position eigen basis (and equivelent formulations i=
> n
> > > different eigenbasis).
> >
> > Bohmian mechanics has no relativistic generalization that I know of.
>
> I think you should rather say bohmian mechanics has not a simple
> relativistic generalization (the mathematical expression becomes more
> difficult has the particle number in not conserved).
> See for example Trajectories and Particle Creation and Annihilation in
> Quantum Field Theory, http://www.arxiv.org/abs/quant-ph/0208072, 2002.
> With bohmian mechanics, we must separate the equivalent formulation of
> QM with contextual random variables from the interpretation. As long as
> we stay with mathematical expressions (and knowing their hypothesis of
> validity), there is no problem.
I hadn't known of this attempt at a relativistic generalization.
Nonetheless, I believe that Bohmian mechanics still has a problem with
the reproduction of classical trajectories (although perhaps decoherence
can go a long way towards solving that).
> > [...]
> >
> > > > I'm not sure I understand what you're asking. Let me try to answer
> > > > something, then. The question of what why we observe what we observ=
> e is
> > > > completely unanswered by quantum mechanics.
> > >
> > > So you are saying that QM theory does not explain the preferred basis.
> >
> > You'll have to communicate to me better what you mean by 'preferred
> > basis'.
>
> Ok, I will try to explain what I mean. I have no problem with the
> preferred basis (the basis where I have the experiment outcomes). I
> just have a problem with the prediction of such a basis by QM. I mean,
> where in the QM theory do I have results inferring the preferred basis?
> Up to now, I just know the preferred basis after I have done the
> experiments. For example the interference pattern of double slit
> experiments observed on the screen. I know, from this experiment, if I
> place a screen, I will do a position measurement. But I have not seen
> anywhere in QM, where the mathematics can predict such a basis as every
> basis is possible from the theory point of view.
No, you know ahead of time that, if you place the screen, you do a
position measurement. You in know way had to the experiment to figure
this out. Inherent in any experimental design, you know which
macroscopic observable you are entangling you system with and that
determines, via decoherece, a preferred basis. (Up to technicalities, I
suppose, like overcompleteness and the like).
[...snip experiment...]
> We have for this system: H=3D Ho+Ho_screen+H_{int_plate}+H_{int_screen}
> We also have [Ho_screen,Hint_plate]=3D [Hint_screen,Hint_plate]=3D
> [Ho_plate,Hint_plate]=3D0
>
> Assume that the intial state is |state(o)>=3D|\psi(o)>|plate>|screen>
> where |\psi(o)> is the state of the electron or photon. Before the
> plate, |\psi(t)> may be described by a wave packet centered on a
> momentum |p_z> parallel to the z axis (free propagator of the electron
> or the photon).
>
> We may add or remove the properties we want to this toy model. The
> important fact is the ability, by thought, to decrease the interaction
> with the environment and to check if we still are able to predict an
> eigenbasis or if the shcmidt eigenbasis is always correct for this
> experiment (depending on the different hypotheses).
>
> Now how can you deduce (from QM theory) the preferred basis and what we
> "really" measure in this experiment?
You need to describe to me the macroscopic degrees of freedom in your
experiment, ie, the macrostates by which you are performing your
observation. With that, simlply wait a period equal to a couple times
the decoherence time and pick the basis in which the reduced density
matrix is diagonal. You don't have to worry about uniqueness of schmidt
bases or whatever.
Aaron
Arnold Neumaier
May31-05, 11:07 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier a écrit :\n>\n>>Seratend wrote:\n>>\n>>>Therefore, it is relatively difficult for me to understand people who\n>>>want to demonstrate that there is a physical collapse leading to the\n>>>outcomes.\n>>\n>>The quest is to show that the interaction of a quantum system with\n>>a macroscopic detector describable by thermodynamics (and hence,\n>>through statistical mechanics, by quantum theory) gives rise to\n>>macroscopic, observable effects in the detector that can be regarded\n>>as the physical equivalent of an objective record of measurements.\n>>\n> I am not sure I understand what you say. In the QM description, I just\n> have statistics of outcomes. I have for a macroscopic detetector, a\n> macroscopic observable A= sum_i Ai where Ai are the microscopic\n> observables of the apparatus (huge number). The result of the\n> measurement will be for example the value of this observable that is\n> highly degenerated at the limit. Except for the preferred basis\n> problem, I do not understand what you are looking for.\n\nI am looking for an explanation why a particular detector coupled\nto a particular quantum system produces the observed erratic but\nobjective record of individual results that can be analyzed\nstatistically and quoted in a physics journal.\n\nIf you want to claim more than that these outcomes are just the\nresults of changes of belief (aka \'knowledge\') in an observer\'s mind\n- and I think physics does and should claim more than that -\nyou need to explain why the observed record is objective,\nfor each individual observation, before any statistical analysis\nis done.\n\n\n>>I gave a concise formulation of a specific case of this quest in\n>>my recent paper quant-ph/0505172.\n>>\n> I have read quickly you paper. I have not found the original thread.\n\nType "collapse challenge" into\nhttp://groups-beta.google.com/groups?q=%22collapse+challenge%22&qt_s=Search\n\n\n> So I have some questions:\n> a) what is the initial state of the photon (assuming a wave packet) :\n> |psi>= |path1>+|path2> with <path1|path2>=0?\n\nNot quite. Roughly,\n|psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>\nwith spatial coherent states |pathi(t)> (i=1,2) moving at the\nvelocity of light and monochromatic 1-Photon Fock states |1>, say.\nThe actual situation would be more complicated since single\nphoton states are electromagnetic waves (solutions of the free\nMaxwell equations) approximately localized along some direction.\nThe challenge allows, however, any specific setting (even\nidealized, or with massive particles, etc.) that matches the\ninformal description in a reasonable way.\n\n\n> b) if yes, |path1> and |path2> are for example 2 parallel paths, where\n> |path1> is 100% stopped by the first screen and |path2> 100% not?\n\nYes. This is an example that can be prepared by half-silvered mirrors.\n\n\n> c) what do you want to say?\n>\n> I mean, I have a system that is well described through unitary\n> evolution (superposition of states).\n\nAbsorption by a screen is an irreversible macroscopic process\naccompanied by a minute increase of temperature. The claim that\nit is described by unitary evolution requires proof, which,\nif successful, would be part of an answer of the challenge.\n\nIf there is unitary dynamics only then the final result is not\nthe state |0,1,1> or |0,0,1> as observed, but a superposition\nof the two. Invoking Born\'s rule is _assuming_ the collapse\nrather than explaining it.\n\nThat something remains to be explained even from the Copenhagen\npoint of view (some version of which you seem to adhere to)\nis discussed in Section 3.\n\n\n\n> At the end, I must apply the born\n> rules to get the statistics (what I see in the experiment).\n\nThis is the informal prescription that is used to apply single-particle\nreasoning to a complex multiparticle experiment. It successfully\navoids looking at the physics happening at the screen, replacing it\nby simply assuming the collapse, i.e., the emergence of an objective\nrecord according to the probabilities from the Born rule.\nWhile this is an acceptable attitude it is obviously not the whole\nstory.\n\nThe challenge is to _explain_ the emergence of the objective record\nas a multiparticle phenomenon.\n\n\n> Are you just searching for a predictive description of a particular\n> outcome in a given QM experiment?\n\nJust an explanation for how particular outcomes arise through\nmeasurement. Leaving something as complex as \'measurement\' as\nan uninterpreted, vague fundamental concept, while practical\nmeasurement is a whole science in itself seem to me too gross\na simplification to be tolerable, and one of the reasons why the\nfoundations of QM are in the poor present state.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier a écrit :
>
>>Seratend wrote:
>>
>>>Therefore, it is relatively difficult for me to understand people who
>>>want to demonstrate that there is a physical collapse leading to the
>>>outcomes.
>>
>>The quest is to show that the interaction of a quantum system with
>>a macroscopic detector describable by thermodynamics (and hence,
>>through statistical mechanics, by quantum theory) gives rise to
>>macroscopic, observable effects in the detector that can be regarded
>>as the physical equivalent of an objective record of measurements.
>>
> I am not sure I understand what you say. In the QM description, I just
> have statistics of outcomes. I have for a macroscopic detetector, a
> macroscopic observable A= sum_i Ai where Ai are the microscopic
> observables of the apparatus (huge number). The result of the
> measurement will be for example the value of this observable that is
> highly degenerated at the limit. Except for the preferred basis
> problem, I do not understand what you are looking for.
I am looking for an explanation why a particular detector coupled
to a particular quantum system produces the observed erratic but
objective record of individual results that can be analyzed
statistically and quoted in a physics journal.
If you want to claim more than that these outcomes are just the
results of changes of belief (aka 'knowledge') in an observer's mind
- and I think physics does and should claim more than that -
you need to explain why the observed record is objective,
for each individual observation, before any statistical analysis
is done.
>>I gave a concise formulation of a specific case of this quest in
>>my recent paper http://www.arxiv.org/abs/quant-ph/0505172.
>>
> I have read quickly you paper. I have not found the original thread.
Type "collapse challenge" into
http://groups-\beta.google.com/groups?q=%22collapse+challenge%22&qt_s=Search
> So I have some questions:
> a) what is the initial state of the photon (assuming a wave packet) :
> |\psi>= |path1>+|path2> with <path1|path2>=0?
Not quite. Roughly,
|\psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>
with spatial coherent states |pathi(t)> (i=1,2) moving at the
velocity of light and monochromatic 1-Photon Fock states |1>, say.
The actual situation would be more complicated since single
photon states are electromagnetic waves (solutions of the free
Maxwell equations) approximately localized along some direction.
The challenge allows, however, any specific setting (even
idealized, or with massive particles, etc.) that matches the
informal description in a reasonable way.
> b) if yes, |path1> and |path2> are for example 2 parallel paths, where
> |path1> is 100% stopped by the first screen and |path2> 100% not?
Yes. This is an example that can be prepared by half-silvered mirrors.
> c) what do you want to say?
>
> I mean, I have a system that is well described through unitary
> evolution (superposition of states).
Absorption by a screen is an irreversible macroscopic process
accompanied by a minute increase of temperature. The claim that
it is described by unitary evolution requires proof, which,
if successful, would be part of an answer of the challenge.
If there is unitary dynamics only then the final result is not
the state |0,1,1> or |0,0,1> as observed, but a superposition
of the two. Invoking Born's rule is _assuming_ the collapse
rather than explaining it.
That something remains to be explained even from the Copenhagen
point of view (some version of which you seem to adhere to)
is discussed in Section 3.
> At the end, I must apply the born
> rules to get the statistics (what I see in the experiment).
This is the informal prescription that is used to apply single-particle
reasoning to a complex multiparticle experiment. It successfully
avoids looking at the physics happening at the screen, replacing it
by simply assuming the collapse, i.e., the emergence of an objective
record according to the probabilities from the Born rule.
While this is an acceptable attitude it is obviously not the whole
story.
The challenge is to _explain_ the emergence of the objective record
as a multiparticle phenomenon.
> Are you just searching for a predictive description of a particular
> outcome in a given QM experiment?
Just an explanation for how particular outcomes arise through
measurement. Leaving something as complex as 'measurement' as
an uninterpreted, vague fundamental concept, while practical
measurement is a whole science in itself seem to me too gross
a simplification to be tolerable, and one of the reasons why the
foundations of QM are in the poor present state.
Arnold Neumaier
I.Vecchi
May31-05, 05:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1117448074.219697.96620@f14g2000cwb.googlegroups. com>,\n> "Seratend" <ser_monmail@yahoo.fr> wrote:\n...\n> > Now how can you deduce (from QM theory) the preferred basis and what we\n> > "really" measure in this experiment?\n>\n> You need to describe to me the macroscopic degrees of freedom in your\n> experiment, ie, the macrostates by which you are performing your\n> observation.\n\nIsn\'t this obviously circular? Aren\'t the "the macrostates by which you\nare performing your observation" precisely what decoherence is supposed\nto derive from a purely quantum description the process?\n\nIV\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1117448074.219697.96620@f14g2000cwb.googlegroups.c om>,
> "Seratend" <ser_monmail@yahoo.fr> wrote:
...
> > Now how can you deduce (from QM theory) the preferred basis and what we
> > "really" measure in this experiment?
>
> You need to describe to me the macroscopic degrees of freedom in your
> experiment, ie, the macrostates by which you are performing your
> observation.
Isn't this obviously circular? Aren't the "the macrostates by which you
are performing your observation" precisely what decoherence is supposed
to derive from a purely quantum description the process?
IV
Seratend
May31-05, 05:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1117448074.219697.96620@f14g2000cwb.googlegroups. com>,\n\n> > This is the born rules, a postulate of QM.\n>\n> Not so much. It works as a good effective description, but if it refers\n> to an explicit nonunitary collapse process, it fails to give a\n> description of it. If it does not refer to collapse, then it fails to\n> explain our perception of (one part of) the reduced density matrix\n> (say), rather than the full coherent wavefunction.\n>\nIn my opinion, I think you are trying to say more than QM theory says.\nYou seem to be a adept of the wave function reality hence you try to\ndefine something out of the scope of the current QM theory formulation\n(an explication of the collapse) while I simply take the born rules as\nstatistics of outcomes and the collapse postulate the property where a\ngiven outcome value of a system is true ("Outcome A=a" true).\nIf I compute the frequency of identical independent measurement\nresults, I get the probability law of the event. I do not explain how\nto find these identical independent systems (out of scope) as I do not\nexplain how I get a particle at the place and time (qo,to) in classical\nmechanics (the initial condition).\n\n> [...]\n>\n> > > > I can only understand this sentence as the quest for a deterministic\n> > > > (causal) description of outcomes compatible with the statistics of QM.\n> > >\n> > > QM is deterministic and causal. That\'s the problem.\n> > >\n> > I do not understand where the problem is. I have a deterministic time\n> > evolution of the probability law. I may also have a deterministic\n> > evolution of the set of eigenvalues (the Heisenberg representation).\n> > Where is the problem?\n>\n> You\'ll get the wrong answer if you apply such a prescription. If you\n> apply the Born rules without nondeterministic state reduction you get\n> nonsense. If you lack an explicit state reduction, you are forced to\n> explain why, as I said above, we only perceive on \'branch\' of the\n> wavefunction (given that decoherence effectively shields us from\n> macroscopic interferences).\n>\nNo I do not need to explain why I have a state reduction if I do not\nattach any reality to the state and the collapse. It is simply a formal\nview like Kolgomorov probability theory.\nIn this formal point of view, the collapse postulate is just the\nlogical assertion that a given property of a given system is true (e.g.\n"Outcome A=a at time t"). We use it to select the systems (what you\nmay call a \'branch\' of the global unitary evolution) where it is\ntrue. Note that there is no time signification on this formal property:\nit is either true or false once forever for a given system.\nIn practical experiments, we have a detector, when this detector\ntriggers we know that we have a system instance with a given property.\n\n>\n> I hadn\'t known of this attempt at a relativistic generalization.\n> Nonetheless, I believe that Bohmian mechanics still has a problem with\n> the reproduction of classical trajectories (although perhaps decoherence\n> can go a long way towards solving that).\n>\nPlease, do not try to mix the mathematic formulation of bohmian\nmechanics with its interpretation (the reality of the bohmian paths).\nThere is no problem with the mathematical formulation while the\ninterpretation of bohmian paths is subject to problems.\n\n> >\n> > Ok, I will try to explain what I mean. I have no problem with the\n> > preferred basis (the basis where I have the experiment outcomes). I\n> > just have a problem with the prediction of such a basis by QM. I mean,\n> > where in the QM theory do I have results inferring the preferred basis?\n> > Up to now, I just know the preferred basis after I have done the\n> > experiments. For example the interference pattern of double slit\n> > experiments observed on the screen. I know, from this experiment, if I\n> > place a screen, I will do a position measurement. But I have not seen\n> > anywhere in QM, where the mathematics can predict such a basis as every\n> > basis is possible from the theory point of view.\n>\n> No, you know ahead of time that, if you place the screen, you do a\n> position measurement.\n\nBecause I have already learn it in an experiment before: I see an\ninterference pattern when I place a screen, hence the position\nmeasurement.\n\n> Inherent in any experimental design, you know which\n> macroscopic observable you are entangling you system with and that\n> determines, via decoherece, a preferred basis. (Up to technicalities, I\n> suppose, like overcompleteness and the like).\n>\nTherefore, your view is equivalent to the one saying QM theory does not\npredict the preferred basis. In this case, decoherence just explains\nwhy we have stable outcome values for this basis.\n\n> [...snip experiment...]\n\n> > Now how can you deduce (from QM theory) the preferred basis and what we\n> > "really" measure in this experiment?\n>\n> You need to describe to me the macroscopic degrees of freedom in your\n> experiment, ie, the macrostates by which you are performing your\n> observation. With that, simlply wait a period equal to a couple times\n> the decoherence time and pick the basis in which the reduced density\n> matrix is diagonal. You don\'t have to worry about uniqueness of schmidt\n> bases or whatever.\n>\n> Aaron\n\nI have forgotten in the hamiltonian of the system the free hamiltonian\nof the slit plate in the previous post:\n\nH= Ho+ Ho_plate+Ho_screen+H_int_plate+H_int_screen\n\nHin t_plate: |plate><plate|(x) V(r)\nHint_screen=|Screen><Screen|(x)Vdiff(r)\n\nM y model supposes (see above) that the free Hamiltonian of the plate\nand the screen commutes with the different interaction Hamiltonian:\n\na) [Ho_screen,Hint_plate]=0,\nb) [Hint_screen,Hint_plate]=0\nc) [Ho_plate,Hint_plate]=0,\nb) [Hint_plate,Hint_plate]=0\n\nTherefore if I have at time 0:\n\n|state(o)>=|psi(o)>|plate>|screen>\n\nI will have at *any* time t (whatever the form of the local interaction\nV(r) and Vdiff(r) is):\n\n|state(t)>=|psi(t)>|plate>|screen>\n\n=> No entanglement occurs with the state of the photons |psi(t)> and\nthe states of the plate and screen.\n\n(|plate> and |screen> are the eigenvectors of the free Hamiltonians of\nthe plate and the screen)\n\nFor a sufficient time, the initial wave packet has been partly\nreflected by the slit plate and partly transmitted before it interacts\nwith the screen (due to the local interaction that does not entangled\nthe photon/electron state with the slit plate):\n\n|psi(t)>= |psi_reflected(t)>+ |psi_slit1(t)>+ |psi_slit2(t)>\n\nWhere |<x|(|psi_slit1(t)>+ |psi_slit2(t)>)|^2= interference pattern for\na sufficient time.\n\nThen the part |psi_slit1(t)>+ |psi_slit2(t)> is scattered later by the\nscreen interaction potential without entanglement with the screen\nstate.\n\nTherefore, where is the preferred basis as in this model there is no\nentanglement between the photons and the plate or the screen (the state\nof the plate and the screen are not changed during the experiment)?\n\nSeratend\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1117448074.219697.96620@f14g2000cwb.googlegroups.c om>,
> > This is the born rules, a postulate of QM.
>
> Not so much. It works as a good effective description, but if it refers
> to an explicit nonunitary collapse process, it fails to give a
> description of it. If it does not refer to collapse, then it fails to
> explain our perception of (one part of) the reduced density matrix
> (say), rather than the full coherent wavefunction.
>
In my opinion, I think you are trying to say more than QM theory says.
You seem to be a adept of the wave function reality hence you try to
define something out of the scope of the current QM theory formulation
(an explication of the collapse) while I simply take the born rules as
statistics of outcomes and the collapse postulate the property where a
given outcome value of a system is true ("Outcome A=a" true).
If I compute the frequency of identical independent measurement
results, I get the probability law of the event. I do not explain how
to find these identical independent systems (out of scope) as I do not
explain how I get a particle at the place and time (qo,to) in classical
mechanics (the initial condition).
> [...]
>
> > > > I can only understand this sentence as the quest for a deterministic
> > > > (causal) description of outcomes compatible with the statistics of QM.
> > >
> > > QM is deterministic and causal. That's the problem.
> > >
> > I do not understand where the problem is. I have a deterministic time
> > evolution of the probability law. I may also have a deterministic
> > evolution of the set of eigenvalues (the Heisenberg representation).
> > Where is the problem?
>
> You'll get the wrong answer if you apply such a prescription. If you
> apply the Born rules without nondeterministic state reduction you get
> nonsense. If you lack an explicit state reduction, you are forced to
> explain why, as I said above, we only perceive on 'branch' of the
> wavefunction (given that decoherence effectively shields us from
> macroscopic interferences).
>
No I do not need to explain why I have a state reduction if I do not
attach any reality to the state and the collapse. It is simply a formal
view like Kolgomorov probability theory.
In this formal point of view, the collapse postulate is just the
logical assertion that a given property of a given system is true (e.g.
"Outcome A=a at time t"). We use it to select the systems (what you
may call a 'branch' of the global unitary evolution) where it is
true. Note that there is no time signification on this formal property:
it is either true or false once forever for a given system.
In practical experiments, we have a detector, when this detector
triggers we know that we have a system instance with a given property.
>
> I hadn't known of this attempt at a relativistic generalization.
> Nonetheless, I believe that Bohmian mechanics still has a problem with
> the reproduction of classical trajectories (although perhaps decoherence
> can go a long way towards solving that).
>
Please, do not try to mix the mathematic formulation of bohmian
mechanics with its interpretation (the reality of the bohmian paths).
There is no problem with the mathematical formulation while the
interpretation of bohmian paths is subject to problems.
> >
> > Ok, I will try to explain what I mean. I have no problem with the
> > preferred basis (the basis where I have the experiment outcomes). I
> > just have a problem with the prediction of such a basis by QM. I mean,
> > where in the QM theory do I have results inferring the preferred basis?
> > Up to now, I just know the preferred basis after I have done the
> > experiments. For example the interference pattern of double slit
> > experiments observed on the screen. I know, from this experiment, if I
> > place a screen, I will do a position measurement. But I have not seen
> > anywhere in QM, where the mathematics can predict such a basis as every
> > basis is possible from the theory point of view.
>
> No, you know ahead of time that, if you place the screen, you do a
> position measurement.
Because I have already learn it in an experiment before: I see an
interference pattern when I place a screen, hence the position
measurement.
> Inherent in any experimental design, you know which
> macroscopic observable you are entangling you system with and that
> determines, via decoherece, a preferred basis. (Up to technicalities, I
> suppose, like overcompleteness and the like).
>
Therefore, your view is equivalent to the one saying QM theory does not
predict the preferred basis. In this case, decoherence just explains
why we have stable outcome values for this basis.
> [...snip experiment...]
> > Now how can you deduce (from QM theory) the preferred basis and what we
> > "really" measure in this experiment?
>
> You need to describe to me the macroscopic degrees of freedom in your
> experiment, ie, the macrostates by which you are performing your
> observation. With that, simlply wait a period equal to a couple times
> the decoherence time and pick the basis in which the reduced density
> matrix is diagonal. You don't have to worry about uniqueness of schmidt
> bases or whatever.
>
> Aaron
I have forgotten in the hamiltonian of the system the free hamiltonian
of the slit plate in the previous post:
H= Ho+ Ho_plate+Ho_screen+H_{int_plate}+H_{int_screen}Hin t_plate:[/itex] |plate><plate|(x) V(r)Hint_screen=|Screen><Screen|(x)Vdiff(r)
My model supposes (see above) that the free Hamiltonian of the plate
and the screen commutes with the different interaction Hamiltonian:
a) [Ho_screen,Hint_plate]=0,b) [Hint_screen,Hint_plate]=0c) [Ho_plate,Hint_plate]=0,b) [Hint_plate,Hint_plate]=0
Therefore if I have at time 0:
|state(o)>=|\psi(o)>|plate>|screen>
I will have at *any* time t (whatever the form of the local interaction
V(r) and Vdiff(r) is):
|state(t)>=|\psi(t)>|plate>|screen>=> No entanglement occurs with the state of the photons |\psi(t)> and
the states of the plate and screen.
(|plate> and |screen> are the eigenvectors of the free Hamiltonians of
the plate and the screen)
For a sufficient time, the initial wave packet has been partly
reflected by the slit plate and partly transmitted before it interacts
with the screen (due to the local interaction that does not entangled
the photon/electron state with the slit plate):
[itex]|\psi(t)>= |\psi_reflected(t)>+ |\psi_slit1(t)>+ |\psi_slit2(t)>
Where |<x|(|\psi_slit1(t)>+ |\psi_slit2(t)>)|^2= interference pattern for
a sufficient time.
Then the part |\psi_slit1(t)>+ |\psi_slit2(t)> is scattered later by the
screen interaction potential without entanglement with the screen
state.
Therefore, where is the preferred basis as in this model there is no
entanglement between the photons and the plate or the screen (the state
of the plate and the screen are not changed during the experiment)?
Seratend
Eugene Stefanovich
May31-05, 05:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nAaron Bergman wrote:\n\n> Why do we observe outcomes with probability |<a|psi>|^2? QM has no\n> answer for this question.\n\nLet me add my two cents to this debate.\n\n1. results of measurements performed on micro-systems are\ninherently statistical/unpredictable. If you prepare twice the same\nsystem in the same state, and measure the same observable,\nyou may get two different measurement results.\n\n2. Quantum mechanics does not explain the origin of these probabilities.\nAll QM can do is to calculate these probabilities.\nIn textbook QM, the formula |<a|psi>|^2 is a postulate, but this\nformula can be derived from a more fundamental "quantum logic" approach.\n(see chapter 4 in physics/0504062)\nIf you know the rules of quantum mechanics, you can describe the\nstate of your system by a vector |psi> in the Hilbert space,\nand the measurement by another vector |a>, and calculate/predict\nthe probability of finding value a in the state |psi> by using above\nformula.\n\n3. Quantum mechanics cannot "explain" why each time you measure\nobservable A in the state |psi> you obtain different values\na_1, a_2, a_3...\nQM cannot predict exactly which value will occur next.\nIt can only predict the probability for each possible outcome.\n\n4. The probabilistic behavior of micro-systems will be explained\nby a theory that goes beyond quantum mechanics (there is no\nsuch a theory, to the best of my knowledge) or, most likely,\nnot explained ever.\n\nEugene Stefanovich.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> Why do we observe outcomes with probability |<a|\psi>|^2? QM has no
> answer for this question.
Let me add my two cents to this debate.
1. results of measurements performed on micro-systems are
inherently statistical/unpredictable. If you prepare twice the same
system in the same state, and measure the same observable,
you may get two different measurement results.
2. Quantum mechanics does not explain the origin of these probabilities.
All QM can do is to calculate these probabilities.
In textbook QM, the formula |<a|\psi>|^2 is a postulate, but this
formula can be derived from a more fundamental "quantum logic" approach.
(see chapter 4 in http://www.arxiv.org/abs/physics/0504062)
If you know the rules of quantum mechanics, you can describe the
state of your system by a vector |\psi> in the Hilbert space,
and the measurement by another vector |a>, and calculate/predict
the probability of finding value a in the state |\psi> by using above
formula.
3. Quantum mechanics cannot "explain" why each time you measure
observable A in the state |\psi> you obtain different values
a_1, a_2, a_3...
QM cannot predict exactly which value will occur next.
It can only predict the probability for each possible outcome.
4. The probabilistic behavior of micro-systems will be explained
by a theory that goes beyond quantum mechanics (there is no
such a theory, to the best of my knowledge) or, most likely,
not explained ever.
Eugene Stefanovich.
rof@maths.tcd.ie
May31-05, 05:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n>rof@maths.tcd.ie wrote:\n\n>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>\n>> Your treatment of the Copenhagen\n>> interpretation in the article claims that the "unresolved\n>> quantum-classical interface issue (including the missing definition\n>> of which situations constitute a measurement) is a serious defect\n>> of the Copenhagen interpretation when viewed as a fundamental\n>> interpretation of quantum mechanics."\n>>\n>> This is slightly unfair to the Copenhagen interpretation, in\n>> which the wavefunction is understood to represent knowledge\n>> about the system, rather than the system itself.\n\n>No. As far as I can tell, the first mention of the claim that\n>\'\'the wavefunction is understood to represent knowledge\'\' is by\n>Jaynes in the 1950ies, long after the establishment of the\n>Copenhagen interpretation.\n\nI may have confused the official Copenhagen interpretation with\nwhat Bohr, Heisenberg, von Neumann and so on believed. As Scerir\npointed out in this thread, Heisenberg said "The discontinuous change\nin the probability function, however, takes place with the act\nof registration, because it is the discontinuous change\nof our knowledge in the instant of registration that has its\nimage in the discontinuous change of the probability function.",\nHiesenberg, "Physics and Philosophy", 1958\n\nIt may be that Heisenberg changed his interpretation of quantum\nmechanics before he wrote that. It\'s even possible that Jaynes\ninfluenced him for all I know. From what you have said about\nyour own interpretation, I take it that you claim that\nHeisenberg was completely wrong when he wrote the\nsentence quoted above.\n\nWith due respect, and I sincerely mean no offense, I believe\nthat you have been infected with the mental disease that I\nranted about in an earlier post:\nhttp://groups-beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source\nMy understanding is that this is why you react so negatively to the\nsuggestion that the wavefunction describes knowledge. There is\nnothing inherently absurd about that idea, but physicists and\nmathematicians who believe that their subject is "noble", and that\ninvestigation of the mind is "dirty" will reject it immediately and\nwithout very good arguments, although they will do a great deal of\nsneering and insulting to make up for the lack of good counter-arguments\n(this is not to suggest that you have done so, or that you should,\nbut it is the way people in general react when their mental diseases\nare attacked).\n\nThis idea of nobility is, quite frankly, medieval savagery, but\npeople in general are quite willing to adopt such an idea if it\nhelps their self-esteem. Everybody wants to be noble. Of course,\nthat doesn\'t mean that people are fully aware of what is happening.\nThe thought "I\'m superior to that other group of people over there?\nI like that idea," probably doesn\'t explicitly pass through their\nmind, but some low-level mental processing registers exactly that.\n\n>> A definition\n>> of measurement isn\'t missing because measurement is the\n>> acquisition of new knowledge.\n\n>This is not a good definition since it is never specified what\n>constitutes acquisition of knowledge.\n\nAcquisition of knowledge is what happens when you look at the\nmeasuring device and see where the pointer is pointing. That\'s\nperfectly precise for a normal person, but it seems insufficient\nto somebody who wants to know about "the real objective world".\n\n>The theory of knowledge\n>acquisition is a branch of psychology, not of physics.\n\nThe theory of knowledge acquisition is actually part of\nphilosophy, and is called epistemology. It is what metaphysics\nshould be, but unfortunately, in their rush to find out\nwhat "really exists", most people who think about metaphysics\nend up doing ontology instead. Ontology is a false hope -\nyou can never know "what really really exists"; we learn this\nif we study epistemology, which is the theory of knowledge\nacquistion, and which is qualified to address questions\nabout what we can know. Those who rush into ontology,\nhowever, never learn this. They take it for granted that\nthey can know the truth about what\'s real, and rush off\nin search of it. "I\'m not interested in knowledge," they\nsay, "I want to know what\'s real." When approached by\nan epistemologist who wants to help them understand\nthe situation, they react with scorn, declaring that\nthe theory of knowledge acquisition is a branch of\npsychology, implying that it is therefore unworthy\nof study, less noble than the quest for what\'s "real".\n\nOf course, if this is pointed out to them, they\ndeny it, saying "Why not at all - I am the most\nreasonable of fellows. I have carefully deliberated\nand decided that what I am doing is the most sensible\nthing to do. Let me refute your arguments," and then\nthey produce arguments which are unconvincing even to\nthemselves.\n\n>> State vector reduction happens\n>> because the observer acquires new knowledge and then updates\n>> the mathematical representation of his knowledge to reflect\n>> the new knowledge that he has.\n\n>I doubt whether any observer updates his or her knowledge according\n>to Bayesian reasoning. Field studies probably show large deviations\n>from this supposedly universal behavior.\n\nI have seen this kind of argument many times, and have never\nunderstood why anybody would think it was valid. The general\nform of the argument goes like this:\n\nA: X is the proper way to do task Y.\nB: That\'s wrong because X is not the way the average man on the street\nattempts to do task Y.\n\nNow, it seems to me abundantly clear that what the man on the\nstreet does is of little relevance to the question of whether\nX is the proper way to do task Y. The assertion that Bayesian\nreasoning is the correct way to proceed when one has incomplete\ninformation is not an assertion about how people behave, and\ncannot be disproved by field studies.\n\n>Furthermore, knowledge depends on subjective decisions to trust\n>a measurement. If we discard one as an artifact, there is no\n>collapse. How can the collapse depend on such subjective issues?\n\nIn the "wavefunction represents knowledge" interpretation, the\nwavefunction is not an objective thing, but different observers\nwill use different wavefunctions, depending on what knowledge they\nhave about the system. The "collapse" is what happens when the\nobserver receives new knowledge, and updates his mathematical\nrepresentation of his knowledge to reflect the new knowledge that\nhe has. This is a subjective thing, because a different observer,\nwho has not received any new knowledge, will continue to use his\noriginal wavefunction, and so the collapse is not objective. So\nthe answer to "How can the collapse depend on such subjective\nissues?" is that the collapse itself is subjective. This is evident\nfrom what Heisenberg said above about the "discontinuous change in\nour knowledge."\n\nRecall that subjective doesn\'t mean simply bad. It means that\nthe thing in question is particular to a single observer,\nand it not common to all observers.\n\n>At the time of Bohr, von neumann and Wigner, the collapse meant\n>something objective, though it might have been related to the mind\n>in some unspecified way.\n\nI have to disagree with that, although I do not mean it in an\nadversarial way. The relation to the mind was perfectly clear and\nvery specific for these people, at least by the \'50s. Also, since\nthey understood that the wavefunction represented knowledge, the\ncollapse wasn\'t an objective thing for them.\n\n>>>Von Neumann takes the collapse as an axiom, hence also testifies to its\n>>>reality.\n>>\n>> He uses it as an axiom, but that doesn\'t mean that he claimed that\n>> the wavefunction didn\'t represent knowledge.\n\n>But he certainly didn\'t claim that the wavefunction does represent\n>knowledge.\n\nAs I quoted before,\n\n"Let us assume that we do not know the state of a system, S, but\nthat we have made certain measurements about the state of S and\nknow their results. In reality, it always happens this way, because\nwe can learn something about the state of S only from the results\nof measurements. More precisely, the states are only a theoretical\nconstruction, only the results of measurements are actually available,\nand the problem of physics is to furnish relationships between the\nresults of past and future measurements." p. 337\n\nThis is exactly a claim that the wavefunction represents\nknowledge. "The states are a theoretical construction,\nonly the results of measurements are actually available" refers\nto the fact that the results of measurements are the knowledge\navailable, and that the states are a theoretical construction\nwhich encode that knowledge.\n\n>> in his 1938 paper with Birkhoff, "The Logic of\n>> Quantum Mechanics", for example, he expresses the view\n>> that the formalism of quantum mechanics is the way it\n>> is because the algebra of Hilbert-space subspaces is\n>> that of a non-distributive orthomodular lattice, which\n>> matches the structure of the collection of experimentally\n>> verifiable propositions about a system. This seems to\n>> me to be an indication that he considered rays of Hilbert\n>> space to be associated with propositions (knowledge), rather\n>> than with the actual configuration of the system.\n\n>No. A proposition is a statement that is true or false,\n>or undecidable. It has nothing to do with whether or not\n>anyone knows (or claims to know) its truth or falsehood.\n\nLogic, which includes the propositional calculus, is the formal\nscience of inference, and inference can only be done by the mind.\nAn inference is what allows one to derive new knowledge from\nknowledge that one already has. Knowledge is always of the\nform "I know that proposition X is true", so propositions\ncertainly have a lot to do with knowledge.\n\nWhat you have done is to suggest that I said that what\na proposition is depends on whether somebody knows or\nclaims to know its truth or falsehood. I never said\nthat, and I don\'t claim it now.\n\nThe desire to assert that logic has nothing to do with the mind is,\nI believe, rooted in the primitive notion of nobility, since logic\nis clearly part of the foundation of mathematics and therefore\nworthy of respect, while the mind is the province of philosophers\nand psychologists, who are not worthy of a physicist\'s respect. The\nassertion that logic has nothing to do with the mind, however, is\nevidently incorrect. My dictionary defines logic as "the science\nof reasoning, proof, thinking, or inference", which means that it\nis the science of certain mental acts.\n\nI have to anticipate how somebody could reject something as\nsimple as this. The only thing I can think of is that somebody\nmight claim that, since computers can be programmed to do\nsymbolic manipulation, logic has nothing to do with thinking.\n\nThe problem with this argument is that the fact that computers\ncan do the symbolic manipulation associated with formal logic\nindicates only that logic can be represented by symbolic\nmanipulations, but establishes nothing about what those\nsymbolic manipulations describe. Logic was established\nin its present form because those symbolic manipulations\ndescribe certain rules of correct thinking.\n\n>> "Let us assume that we do not know the state of a\n>> system, S,\n\n>This assumption already shows that the state of the system\n>must exist independent of our knowledge.\n\nNow, as far as you were aware when you read that, nobody\nhad claimed that the state of the system didn\'t exist.\n\nI was not asserting that the state of the system, considered as a\nseparate thing from our knowledge of it, doesn\'t exist. I was\nasserting that von Neumann was aware that we only know the results\nof measurements, and so these are what the mathematical symbols\nthat we write down represent. He goes on to say:\n\n"More precisely, the states are only a theoretical construction,\nonly the results of measurements are actually available, and the\nproblem of physics is to furnish relationships between the results\nof past and future measurements. To be sure, this is always\naccomplished through the introduction of the auxilliary concept\n"state", but the physical theory must then tell us on the one hand\nhow to make from past measurements inferences about the present\nstate, and on the other hand, how to go from the present state to\nthe results of future measurements." p. 337\n\nWhat he is saying is that, in quantum mechanics, what we call\na "state" is actually a theoretical construction which incorporates\ninformation about the results of past measurements on the system.\nThat is why the wavefunction represents knowledge. We are free,\nof course, to say that the actual system is in a state which\nis distinct from our knowledge of it, and that the measurements\ntell us information about the "real" state, but the "state"\nin quantum mechanics incorporates only whatever information\nis available from the results of past measurements, and the\nconcept of the "real" state is an auxilliary concept. To say\nthat it is an auxilliary concept does not denigrate it in\nany way, or insult its nobility, or deny the existence\nof an actual state of the system, but it means that the concept\ncarries with it no information which is relevant for predicting\nfuture measurement results based on past ones.\n\n>> The principle of psycho-physical\n>> parallelism tells us that, whatever we claim to know\n>> about the physical world, what we actually know about\n>> is what\'s going on inside our body,\n\n>I don\'t buy this. What we know is some platonic extract\n>extrapolated from sense data. And much of it is mistaken\n>in detail, but still we think we know and act accordingly.\n>It has nothing to do with physics as understood pragmatically.\n\nBasically, you are saying that knowledge is a dirty thing,\nnot worth investigating for a noble physicist. You are\nright that it has nothing to do with physics as understood\npragmatically, which means that it is not relevant for\nthe practical purposes of turning on the measuring device\nand pressing the buttons on it. On the other hand, it\nis relevant for a proper understanding of physics.\n\nLet me try to address your concern that knowledge is\nhuman and therefore fallible. It might be said that\ninference is human and therefore fallible. That is\nwhy we develop logic as a formal science - to\nrelieve us of the labour of making inferences ourselves.\nThe fallibility of humans doesn\'t mean that logic\nis somehow flawed; it means that people make mistakes in\ntheir application of it.\n\nWith knowledge, there is also a way to think and process\nknowledge without making mistakes, although people\nmight not always succeed in using it properly. That\nis why we look for a symbolic formalism; if we develop\none, mistakes will be easier to spot, as they are in\nlogic.\n\nAlso, when you say "I don\'t buy this," are you saying that\nyou don\'t believe that von Neumann held this opinion,\nnamely that the principle of psycho-physical parallelism\ntells us that we can consider what we are observing\nto be within our own bodies? Because he did:\n\n"We wish to measure a temperature. ... [we can] say: this\ntemperature is measured by the thermometer. ... we can\ncalculate the resultant length of the mercury column,\nand then say: this length is seen by the observer. Going\nstill further, and taking the light source into consideration ...\nwe would say: this image is registered by the retina of the\nobserver. And were our physiological knowledge more precise\nthan it is today, we could go still further, tracing the\nchemical reactions which produce the impression of this image on\nthe retina, in the optic nerve tract and in the brain, and then in\nthe end say: these chemical changes of his brain cells are\nperceived by the observer." p.419\n\n"That this boundary can be pushed arbitrarily into the interior\nof the body of the observer is the content of the principle\nof the psycho-physical parallelism." p.420\n\n>> You might also want to read the paper by Lon Becker:\n>> "That von Neumann Did Not Believe in a Physical Collapse",\n>> http://bjps.oupjournals.org/cgi/content/abstract/55/1/121\n\n>I\'ll read it and comment later, if I have more to say than\n>what I said already.\n\nLon seems to be trying to present the view that von Neumann\nbelieved in a relative-state interpretation, which is\npresumably his own favourite interpretation, and I further\npresume that he believed that he could garner support\nfor his interpretation by claiming that von Neumann\nbelieved it.\n\nSimilarly, you are trying to claim that von Neumann shared your\n"collapse is a physical process" interpretation, and I assert that\nhe believed the wavefunction represented knowledge.\n\nHe also didn\'t have the "subjective means bad" attitude of modern\nphysicists, and was aware that what we deal with in physics is\nnot "the real world", but rather with subjective observations:\n"Indeed experience only makes statements of this type: an observer\nhas made a certain (subjective) observation; and never any like\nthis: a physical quantity has a certain value." p.420\n\nFor him, the distinction between the observer and the observed\nwas of fundamental importance in quantum mechanics; this is\nthe so-called quantum/classical boundary:\n"That is, we must always divide the world into two parts,\nthe one being the observed system, the other the observer. ...\nThe boundary between the two is arbitrary to a large extent. ...\nbut this does not change the fact that in each method of description\nthe boundary must be placed somewhere, if the method is not to\nproceed vacuously, i.e., if a comparison with experiment is to be\npossible." p.420\n\nSo, from von Neumann\'s point of view, to use a "wavefunction of the\nuniverse" would be to proceed vacuously.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>rof@maths.tcd.ie wrote:
>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>
>> Your treatment of the Copenhagen
>> interpretation in the article claims that the "unresolved
>> quantum-classical interface issue (including the missing definition
>> of which situations constitute a measurement) is a serious defect
>> of the Copenhagen interpretation when viewed as a fundamental
>> interpretation of quantum mechanics."
>>
>> This is slightly unfair to the Copenhagen interpretation, in
>> which the wavefunction is understood to represent knowledge
>> about the system, rather than the system itself.
>No. As far as I can tell, the first mention of the claim that
>''the wavefunction is understood to represent knowledge'' is by
>Jaynes in the 1950ies, long after the establishment of the
>Copenhagen interpretation.
I may have confused the official Copenhagen interpretation with
what Bohr, Heisenberg, von Neumann and so on believed. As Scerir
pointed out in this thread, Heisenberg said "The discontinuous change
in the probability function, however, takes place with the act
of registration, because it is the discontinuous change
of our knowledge in the instant of registration that has its
image in the discontinuous change of the probability function.",
Hiesenberg, "Physics and Philosophy", 1958
It may be that Heisenberg changed his interpretation of quantum
mechanics before he wrote that. It's even possible that Jaynes
influenced him for all I know. From what you have said about
your own interpretation, I take it that you claim that
Heisenberg was completely wrong when he wrote the
sentence quoted above.
With due respect, and I sincerely mean no offense, I believe
that you have been infected with the mental disease that I
ranted about in an earlier post:
http://groups-\beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source
My understanding is that this is why you react so negatively to the
suggestion that the wavefunction describes knowledge. There is
nothing inherently absurd about that idea, but physicists and
mathematicians who believe that their subject is "noble", and that
investigation of the mind is "dirty" will reject it immediately and
without very good arguments, although they will do a great deal of
sneering and insulting to make up for the lack of good counter-arguments
(this is not to suggest that you have done so, or that you should,
but it is the way people in general react when their mental diseases
are attacked).
This idea of nobility is, quite frankly, medieval savagery, but
people in general are quite willing to adopt such an idea if it
helps their self-esteem. Everybody wants to be noble. Of course,
that doesn't mean that people are fully aware of what is happening.
The thought "I'm superior to that other group of people over there?
I like that idea," probably doesn't explicitly pass through their
mind, but some low-level mental processing registers exactly that.
>> A definition
>> of measurement isn't missing because measurement is the
>> acquisition of new knowledge.
>This is not a good definition since it is never specified what
>constitutes acquisition of knowledge.
Acquisition of knowledge is what happens when you look at the
measuring device and see where the pointer is pointing. That's
perfectly precise for a normal person, but it seems insufficient
to somebody who wants to know about "the real objective world".
>The theory of knowledge
>acquisition is a branch of psychology, not of physics.
The theory of knowledge acquisition is actually part of
philosophy, and is called epistemology. It is what metaphysics
should be, but unfortunately, in their rush to find out
what "really exists", most people who think about metaphysics
end up doing ontology instead. Ontology is a false hope -
you can never know "what really really exists"; we learn this
if we study epistemology, which is the theory of knowledge
acquistion, and which is qualified to address questions
about what we can know. Those who rush into ontology,
however, never learn this. They take it for granted that
they can know the truth about what's real, and rush off
in search of it. "I'm not interested in knowledge," they
say, "I want to know what's real." When approached by
an epistemologist who wants to help them understand
the situation, they react with scorn, declaring that
the theory of knowledge acquisition is a branch of
psychology, implying that it is therefore unworthy
of study, less noble than the quest for what's "real".
Of course, if this is pointed out to them, they
deny it, saying "Why not at all - I am the most
reasonable of fellows. I have carefully deliberated
and decided that what I am doing is the most sensible
thing to do. Let me refute your arguments," and then
they produce arguments which are unconvincing even to
themselves.
>> State vector reduction happens
>> because the observer acquires new knowledge and then updates
>> the mathematical representation of his knowledge to reflect
>> the new knowledge that he has.
>I doubt whether any observer updates his or her knowledge according
>to Bayesian reasoning. Field studies probably show large deviations
>from this supposedly universal behavior.
I have seen this kind of argument many times, and have never
understood why anybody would think it was valid. The general
form of the argument goes like this:
A: X is the proper way to do task Y.
B: That's wrong because X is not the way the average man on the street
attempts to do task Y.
Now, it seems to me abundantly clear that what the man on the
street does is of little relevance to the question of whether
X is the proper way to do task Y. The assertion that Bayesian
reasoning is the correct way to proceed when one has incomplete
information is not an assertion about how people behave, and
cannot be disproved by field studies.
>Furthermore, knowledge depends on subjective decisions to trust
>a measurement. If we discard one as an artifact, there is no
>collapse. How can the collapse depend on such subjective issues?
In the "wavefunction represents knowledge" interpretation, the
wavefunction is not an objective thing, but different observers
will use different wavefunctions, depending on what knowledge they
have about the system. The "collapse" is what happens when the
observer receives new knowledge, and updates his mathematical
representation of his knowledge to reflect the new knowledge that
he has. This is a subjective thing, because a different observer,
who has not received any new knowledge, will continue to use his
original wavefunction, and so the collapse is not objective. So
the answer to "How can the collapse depend on such subjective
issues?" is that the collapse itself is subjective. This is evident
from what Heisenberg said above about the "discontinuous change in
our knowledge."
Recall that subjective doesn't mean simply bad. It means that
the thing in question is particular to a single observer,
and it not common to all observers.
>At the time of Bohr, von neumann and Wigner, the collapse meant
>something objective, though it might have been related to the mind
>in some unspecified way.
I have to disagree with that, although I do not mean it in an
adversarial way. The relation to the mind was perfectly clear and
very specific for these people, at least by the '50s. Also, since
they understood that the wavefunction represented knowledge, the
collapse wasn't an objective thing for them.
>>>Von Neumann takes the collapse as an axiom, hence also testifies to its
>>>reality.
>>
>> He uses it as an axiom, but that doesn't mean that he claimed that
>> the wavefunction didn't represent knowledge.
>But he certainly didn't claim that the wavefunction does represent
>knowledge.
As I quoted before,
"Let us assume that we do not know the state of a system, S, but
that we have made certain measurements about the state of S and
know their results. In reality, it always happens this way, because
we can learn something about the state of S only from the results
of measurements. More precisely, the states are only a theoretical
construction, only the results of measurements are actually available,
and the problem of physics is to furnish relationships between the
results of past and future measurements." p. 337
This is exactly a claim that the wavefunction represents
knowledge. "The states are a theoretical construction,
only the results of measurements are actually available" refers
to the fact that the results of measurements are the knowledge
available, and that the states are a theoretical construction
which encode that knowledge.
>> in his 1938 paper with Birkhoff, "The Logic of
>> Quantum Mechanics", for example, he expresses the view
>> that the formalism of quantum mechanics is the way it
>> is because the algebra of Hilbert-space subspaces is
>> that of a non-distributive orthomodular lattice, which
>> matches the structure of the collection of experimentally
>> verifiable propositions about a system. This seems to
>> me to be an indication that he considered rays of Hilbert
>> space to be associated with propositions (knowledge), rather
>> than with the actual configuration of the system.
>No. A proposition is a statement that is true or false,
>or undecidable. It has nothing to do with whether or not
>anyone knows (or claims to know) its truth or falsehood.
Logic, which includes the propositional calculus, is the formal
science of inference, and inference can only be done by the mind.
An inference is what allows one to derive new knowledge from
knowledge that one already has. Knowledge is always of the
form "I know that proposition X is true", so propositions
certainly have a lot to do with knowledge.
What you have done is to suggest that I said that what
a proposition is depends on whether somebody knows or
claims to know its truth or falsehood. I never said
that, and I don't claim it now.
The desire to assert that logic has nothing to do with the mind is,
I believe, rooted in the primitive notion of nobility, since logic
is clearly part of the foundation of mathematics and therefore
worthy of respect, while the mind is the province of philosophers
and psychologists, who are not worthy of a physicist's respect. The
assertion that logic has nothing to do with the mind, however, is
evidently incorrect. My dictionary defines logic as "the science
of reasoning, proof, thinking, or inference", which means that it
is the science of certain mental acts.
I have to anticipate how somebody could reject something as
simple as this. The only thing I can think of is that somebody
might claim that, since computers can be programmed to do
symbolic manipulation, logic has nothing to do with thinking.
The problem with this argument is that the fact that computers
can do the symbolic manipulation associated with formal logic
indicates only that logic can be represented by symbolic
manipulations, but establishes nothing about what those
symbolic manipulations describe. Logic was established
in its present form because those symbolic manipulations
describe certain rules of correct thinking.
>> "Let us assume that we do not know the state of a
>> system, S,
>This assumption already shows that the state of the system
>must exist independent of our knowledge.
Now, as far as you were aware when you read that, nobody
had claimed that the state of the system didn't exist.
I was not asserting that the state of the system, considered as a
separate thing from our knowledge of it, doesn't exist. I was
asserting that von Neumann was aware that we only know the results
of measurements, and so these are what the mathematical symbols
that we write down represent. He goes on to say:
"More precisely, the states are only a theoretical construction,
only the results of measurements are actually available, and the
problem of physics is to furnish relationships between the results
of past and future measurements. To be sure, this is always
accomplished through the introduction of the auxilliary concept
"state", but the physical theory must then tell us on the one hand
how to make from past measurements inferences about the present
state, and on the other hand, how to go from the present state to
the results of future measurements." p. 337
What he is saying is that, in quantum mechanics, what we call
a "state" is actually a theoretical construction which incorporates
information about the results of past measurements on the system.
That is why the wavefunction represents knowledge. We are free,
of course, to say that the actual system is in a state which
is distinct from our knowledge of it, and that the measurements
tell us information about the "real" state, but the "state"
in quantum mechanics incorporates only whatever information
is available from the results of past measurements, and the
concept of the "real" state is an auxilliary concept. To say
that it is an auxilliary concept does not denigrate it in
any way, or insult its nobility, or deny the existence
of an actual state of the system, but it means that the concept
carries with it no information which is relevant for predicting
future measurement results based on past ones.
>> The principle of psycho-physical
>> parallelism tells us that, whatever we claim to know
>> about the physical world, what we actually know about
>> is what's going on inside our body,
>I don't buy this. What we know is some platonic extract
>extrapolated from sense data. And much of it is mistaken
>in detail, but still we think we know and act accordingly.
>It has nothing to do with physics as understood pragmatically.
Basically, you are saying that knowledge is a dirty thing,
not worth investigating for a noble physicist. You are
right that it has nothing to do with physics as understood
pragmatically, which means that it is not relevant for
the practical purposes of turning on the measuring device
and pressing the buttons on it. On the other hand, it
is relevant for a proper understanding of physics.
Let me try to address your concern that knowledge is
human and therefore fallible. It might be said that
inference is human and therefore fallible. That is
why we develop logic as a formal science - to
relieve us of the labour of making inferences ourselves.
The fallibility of humans doesn't mean that logic
is somehow flawed; it means that people make mistakes in
their application of it.
With knowledge, there is also a way to think and process
knowledge without making mistakes, although people
might not always succeed in using it properly. That
is why we look for a symbolic formalism; if we develop
one, mistakes will be easier to spot, as they are in
logic.
Also, when you say "I don't buy this," are you saying that
you don't believe that von Neumann held this opinion,
namely that the principle of psycho-physical parallelism
tells us that we can consider what we are observing
to be within our own bodies? Because he did:
"We wish to measure a temperature. ... [we can] say: this
temperature is measured by the thermometer. ... we can
calculate the resultant length of the mercury column,
and then say: this length is seen by the observer. Going
still further, and taking the light source into consideration ...
we would say: this image is registered by the retina of the
observer. And were our physiological knowledge more precise
than it is today, we could go still further, tracing the
chemical reactions which produce the impression of this image on
the retina, in the optic nerve tract and in the brain, and then in
the end say: these chemical changes of his brain cells are
perceived by the observer." p.419
"That this boundary can be pushed arbitrarily into the interior
of the body of the observer is the content of the principle
of the psycho-physical parallelism." p.420
>> You might also want to read the paper by Lon Becker:
>> "That von Neumann Did Not Believe in a Physical Collapse",
>> http://bjps.oupjournals.org/cgi/content/abstract/55/1/121
>I'll read it and comment later, if I have more to say than
>what I said already.
Lon seems to be trying to present the view that von Neumann
believed in a relative-state interpretation, which is
presumably his own favourite interpretation, and I further
presume that he believed that he could garner support
for his interpretation by claiming that von Neumann
believed it.
Similarly, you are trying to claim that von Neumann shared your
"collapse is a physical process" interpretation, and I assert that
he believed the wavefunction represented knowledge.
He also didn't have the "subjective means bad" attitude of modern
physicists, and was aware that what we deal with in physics is
not "the real world", but rather with subjective observations:
"Indeed experience only makes statements of this type: an observer
has made a certain (subjective) observation; and never any like
this: a physical quantity has a certain value." p.420
For him, the distinction between the observer and the observed
was of fundamental importance in quantum mechanics; this is
the so-called quantum/classical boundary:
"That is, we must always divide the world into two parts,
the one being the observed system, the other the observer. ...
The boundary between the two is arbitrary to a large extent. ...
but this does not change the fact that in each method of description
the boundary must be placed somewhere, if the method is not to
proceed vacuously, i.e., if a comparison with experiment is to be
possible." p.420
So, from von Neumann's point of view, to use a "wavefunction of the
universe" would be to proceed vacuously.
R.
Eugene Stefanovich
May31-05, 05:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nArnold Neumaier wrote:\n\n>\n> The light ray of a laser is an electromagnetic field localized in a\n> small region along the ray that begins in the laser and ends at the\n> photodetector. A ray of intensity I is described by a coherent state\n> |I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...\n> If I is tiny then, from time to time, an electron responds (in some\n> loose way of speaking that itself would need correction) to the\n> energy continuously transmitted by the ray by going into an excited\n> state, an event which is magnified in the detector and recorded.\n> These occasional events form a Poisson process, with a rate proportional\n> to the intensity I. This, no more and no less, is the experimental\n> observation. It is precisely what is predicted by quantum mechanics.\n>\n> The traditional sloppy way of picturing this in an intuitive way is to\n> say that, from time to time, a photon arrives at the screen and kicks\n> an electron out of its orbit. This is a nice piccture, especially for\n> the newcomer or the lay man, but it cannot be taken any more seriously\n> than Bohr\'s picture of an atom, in which electrons orbit a nucleus in\n> certain quantum orbits. For nothing of this can be checked by experiment\n> - it is empty talk intended to serve intuition, but in fact causing more\n> damange than understanding.\n\n\nLaser ray is a complex phenomenon involving a large number of photons.\nHow your coherent state/Poisson process picture describes the\ninteraction of a single photon with the screen or atom? I guess you\ndo not dispute the fact that single photons can be routinely prepared\nin a laboratory, and their "arrivals at the screen" can be observed.\n\nEugene Stefanovich.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
>
> The light ray of a laser is an electromagnetic field localized in a
> small region along the ray that begins in the laser and ends at the
> photodetector. A ray of intensity I is described by a coherent state
> |I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...
> If I is tiny then, from time to time, an electron responds (in some
> loose way of speaking that itself would need correction) to the
> energy continuously transmitted by the ray by going into an excited
> state, an event which is magnified in the detector and recorded.
> These occasional events form a Poisson process, with a rate proportional
> to the intensity I. This, no more and no less, is the experimental
> observation. It is precisely what is predicted by quantum mechanics.
>
> The traditional sloppy way of picturing this in an intuitive way is to
> say that, from time to time, a photon arrives at the screen and kicks
> an electron out of its orbit. This is a nice piccture, especially for
> the newcomer or the lay man, but it cannot be taken any more seriously
> than Bohr's picture of an atom, in which electrons orbit a nucleus in
> certain quantum orbits. For nothing of this can be checked by experiment
> - it is empty talk intended to serve intuition, but in fact causing more
> damange than understanding.
Laser ray is a complex phenomenon involving a large number of photons.
How your coherent state/Poisson process picture describes the
interaction of a single photon with the screen or atom? I guess you
do not dispute the fact that single photons can be routinely prepared
in a laboratory, and their "arrivals at the screen" can be observed.
Eugene Stefanovich.
Aaron Bergman
May31-05, 11:42 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117568337.945299.75400@g14g2000cwa.googlegroups. com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n> > In article <1117448074.219697.96620@f14g2000cwb.googlegroups. com>,\n>\n> > > This is the born rules, a postulate of QM.\n> >\n> > Not so much. It works as a good effective description, but if it refers\n> > to an explicit nonunitary collapse process, it fails to give a\n> > description of it. If it does not refer to collapse, then it fails to\n> > explain our perception of (one part of) the reduced density matrix\n> > (say), rather than the full coherent wavefunction.\n> >\n> In my opinion, I think you are trying to say more than QM theory says.\n\nFunny, I feel the same way.\n\n> You seem to be a adept of the wave function reality hence you try to\n> define something out of the scope of the current QM theory formulation\n> (an explication of the collapse) while I simply take the born rules as\n> statistics of outcomes and the collapse postulate the property where a\n> given outcome value of a system is true ("Outcome A=a" true).\n\nI don\'t consider the Born rule part of QM. QM is unitary evolution.\nEverything is else is what we do to make sense of the wavefunction. The\nBorn rules are a pragmatic procedure, but they lack a microscopic\nmechanism.\n\n[...]\n\n> > > > > I can only understand this sentence as the quest for a deterministic\n> > > > > (causal) description of outcomes compatible with the statistics of QM.\n> > > >\n> > > > QM is deterministic and causal. That\'s the problem.\n> > > >\n> > > I do not understand where the problem is. I have a deterministic time\n> > > evolution of the probability law. I may also have a deterministic\n> > > evolution of the set of eigenvalues (the Heisenberg representation).\n> > > Where is the problem?\n> >\n> > You\'ll get the wrong answer if you apply such a prescription. If you\n> > apply the Born rules without nondeterministic state reduction you get\n> > nonsense. If you lack an explicit state reduction, you are forced to\n> > explain why, as I said above, we only perceive on \'branch\' of the\n> > wavefunction (given that decoherence effectively shields us from\n> > macroscopic interferences).\n> >\n> No I do not need to explain why I have a state reduction if I do not\n> attach any reality to the state and the collapse. It is simply a formal\n> view like Kolgomorov probability theory.\n> In this formal point of view, the collapse postulate is just the\n> logical assertion that a given property of a given system is true (e.g.\n> "Outcome A=a at time t"). We use it to select the systems (what you\n> may call a \'branch\' of the global unitary evolution) where it is\n> true. Note that there is no time signification on this formal property:\n> it is either true or false once forever for a given system.\n> In practical experiments, we have a detector, when this detector\n> triggers we know that we have a system instance with a given property.\n\nAre you advocating a sort of consistent histories approach? That seems\nto me to be a language in which to describe quantum outcomes, but\nnothing like an interpretation. Regardless, when you make a real-world\nmeasurement, you better collapse the wavefunction, whether through\ndecoherence or some other manner, or you will get the wrong answer. For\nfuture measurements.\n\n[...]\n\n> > > Ok, I will try to explain what I mean. I have no problem with the\n> > > preferred basis (the basis where I have the experiment outcomes). I\n> > > just have a problem with the prediction of such a basis by QM. I mean,\n> > > where in the QM theory do I have results inferring the preferred basis?\n> > > Up to now, I just know the preferred basis after I have done the\n> > > experiments. For example the interference pattern of double slit\n> > > experiments observed on the screen. I know, from this experiment, if I\n> > > place a screen, I will do a position measurement. But I have not seen\n> > > anywhere in QM, where the mathematics can predict such a basis as every\n> > > basis is possible from the theory point of view.\n> >\n> > No, you know ahead of time that, if you place the screen, you do a\n> > position measurement.\n>\n> Because I have already learn it in an experiment before: I see an\n> interference pattern when I place a screen, hence the position\n> measurement.\n\nNo. You understand your measurement apparatus. It\'s not a mystery. There\nare macroscopic degrees of freedom -- work backwards from there and you\nknow what your \'preferred basis\' is.\n\n[snip to end]\n\nI\'m sorry, but I can\'t figure out what you\'re talking about in your\nexperiment.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117568337.945299.75400@g14g2000cwa.googlegroups.c om>,
Seratend <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> > In article <1117448074.219697.96620@f14g2000cwb.googlegroups.c om>,
>
> > > This is the born rules, a postulate of QM.
> >
> > Not so much. It works as a good effective description, but if it refers
> > to an explicit nonunitary collapse process, it fails to give a
> > description of it. If it does not refer to collapse, then it fails to
> > explain our perception of (one part of) the reduced density matrix
> > (say), rather than the full coherent wavefunction.
> >
> In my opinion, I think you are trying to say more than QM theory says.
Funny, I feel the same way.
> You seem to be a adept of the wave function reality hence you try to
> define something out of the scope of the current QM theory formulation
> (an explication of the collapse) while I simply take the born rules as
> statistics of outcomes and the collapse postulate the property where a
> given outcome value of a system is true ("Outcome A=a" true).
I don't consider the Born rule part of QM. QM is unitary evolution.
Everything is else is what we do to make sense of the wavefunction. The
Born rules are a pragmatic procedure, but they lack a microscopic
mechanism.
[...]
> > > > > I can only understand this sentence as the quest for a deterministic
> > > > > (causal) description of outcomes compatible with the statistics of QM.
> > > >
> > > > QM is deterministic and causal. That's the problem.
> > > >
> > > I do not understand where the problem is. I have a deterministic time
> > > evolution of the probability law. I may also have a deterministic
> > > evolution of the set of eigenvalues (the Heisenberg representation).
> > > Where is the problem?
> >
> > You'll get the wrong answer if you apply such a prescription. If you
> > apply the Born rules without nondeterministic state reduction you get
> > nonsense. If you lack an explicit state reduction, you are forced to
> > explain why, as I said above, we only perceive on 'branch' of the
> > wavefunction (given that decoherence effectively shields us from
> > macroscopic interferences).
> >
> No I do not need to explain why I have a state reduction if I do not
> attach any reality to the state and the collapse. It is simply a formal
> view like Kolgomorov probability theory.
> In this formal point of view, the collapse postulate is just the
> logical assertion that a given property of a given system is true (e.g.
> "Outcome A=a at time t"). We use it to select the systems (what you
> may call a 'branch' of the global unitary evolution) where it is
> true. Note that there is no time signification on this formal property:
> it is either true or false once forever for a given system.
> In practical experiments, we have a detector, when this detector
> triggers we know that we have a system instance with a given property.
Are you advocating a sort of consistent histories approach? That seems
to me to be a language in which to describe quantum outcomes, but
nothing like an interpretation. Regardless, when you make a real-world
measurement, you better collapse the wavefunction, whether through
decoherence or some other manner, or you will get the wrong answer. For
future measurements.
[...]
> > > Ok, I will try to explain what I mean. I have no problem with the
> > > preferred basis (the basis where I have the experiment outcomes). I
> > > just have a problem with the prediction of such a basis by QM. I mean,
> > > where in the QM theory do I have results inferring the preferred basis?
> > > Up to now, I just know the preferred basis after I have done the
> > > experiments. For example the interference pattern of double slit
> > > experiments observed on the screen. I know, from this experiment, if I
> > > place a screen, I will do a position measurement. But I have not seen
> > > anywhere in QM, where the mathematics can predict such a basis as every
> > > basis is possible from the theory point of view.
> >
> > No, you know ahead of time that, if you place the screen, you do a
> > position measurement.
>
> Because I have already learn it in an experiment before: I see an
> interference pattern when I place a screen, hence the position
> measurement.
No. You understand your measurement apparatus. It's not a mystery. There
are macroscopic degrees of freedom -- work backwards from there and you
know what your 'preferred basis' is.
[snip to end]
I'm sorry, but I can't figure out what you're talking about in your
experiment.
Aaron
Arnold Neumaier
Jun1-05, 08:27 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Eugene Stefanovich wrote:\n>\n> Arnold Neumaier wrote:\n>\n>> The light ray of a laser is an electromagnetic field localized in a\n>> small region along the ray that begins in the laser and ends at the\n>> photodetector. A ray of intensity I is described by a coherent state\n>> |I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...\n>> If I is tiny then, from time to time, an electron responds (in some\n>> loose way of speaking that itself would need correction) to the\n>> energy continuously transmitted by the ray by going into an excited\n>> state, an event which is magnified in the detector and recorded.\n>> These occasional events form a Poisson process, with a rate proportional\n>> to the intensity I. This, no more and no less, is the experimental\n>> observation. It is precisely what is predicted by quantum mechanics.\n>>\n>> The traditional sloppy way of picturing this in an intuitive way is to\n>> say that, from time to time, a photon arrives at the screen and kicks\n>> an electron out of its orbit. This is a nice piccture, especially for\n>> the newcomer or the lay man, but it cannot be taken any more seriously\n>> than Bohr\'s picture of an atom, in which electrons orbit a nucleus in\n>> certain quantum orbits. For nothing of this can be checked by experiment\n>> - it is empty talk intended to serve intuition, but in fact causing more\n>> damange than understanding.\n>\n> Laser ray is a complex phenomenon involving a large number of photons.\n\nNot complex in the typically used models.\nThe large number of photons are described by the single coherent state.\nI recommend that you read some thorough quantum optics books such as\nthe comprehensive\nL. Mandel and E. Wolf,\nOptical Coherence and Quantum Optics,\nCambridge University Press, 1995.\nor the lighter\nU. Leonhardt,\nMeasuring the Quantum State of Light,\nCambridge, 1997.\n\n\n> How your coherent state/Poisson process picture describes the\n> interaction of a single photon with the screen or atom?\n\nThis is described in the book by Mandel and Wolf just quoted.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Eugene Stefanovich wrote:
>
> Arnold Neumaier wrote:
>
>> The light ray of a laser is an electromagnetic field localized in a
>> small region along the ray that begins in the laser and ends at the
>> photodetector. A ray of intensity I is described by a coherent state
>> |I>> =3D |0> + I|1> + I^2/2|2> + I^3/6|3> + ...
>> If I is tiny then, from time to time, an electron responds (in some
>> loose way of speaking that itself would need correction) to the
>> energy continuously transmitted by the ray by going into an excited
>> state, an event which is magnified in the detector and recorded.
>> These occasional events form a Poisson process, with a rate proportional
>> to the intensity I. This, no more and no less, is the experimental
>> observation. It is precisely what is predicted by quantum mechanics.
>>
>> The traditional sloppy way of picturing this in an intuitive way is to
>> say that, from time to time, a photon arrives at the screen and kicks
>> an electron out of its orbit. This is a nice piccture, especially for
>> the newcomer or the lay man, but it cannot be taken any more seriously
>> than Bohr's picture of an atom, in which electrons orbit a nucleus in
>> certain quantum orbits. For nothing of this can be checked by experiment
>> - it is empty talk intended to serve intuition, but in fact causing more
>> damange than understanding.
>
> Laser ray is a complex phenomenon involving a large number of photons.
Not complex in the typically used models.
The large number of photons are described by the single coherent state.
I recommend that you read some thorough quantum optics books such as
the comprehensive
L. Mandel and E. Wolf,
Optical Coherence and Quantum Optics,
Cambridge University Press, 1995.
or the lighter
U. Leonhardt,
Measuring the Quantum State of Light,
Cambridge, 1997.
> How your coherent state/Poisson process picture describes the
> interaction of a single photon with the screen or atom?
This is described in the book by Mandel and Wolf just quoted.
Arnold Neumaier
Arnold Neumaier
Jun1-05, 08:27 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>rof@maths.tcd.ie wrote:\n>\n>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>>\n>>>Your treatment of the Copenhagen\n>>>interpretation in the article claims that the "unresolved\n>>>quantum-classical interface issue (including the missing definition\n>>>of which situations constitute a measurement) is a serious defect\n>>>of the Copenhagen interpretation when viewed as a fundamental\n>>>interpretation of quantum mechanics."\n>>>\n>>>This is slightly unfair to the Copenhagen interpretation, in\n>>>which the wavefunction is understood to represent knowledge\n>>>about the system, rather than the system itself.\n>\n>>No. As far as I can tell, the first mention of the claim that\n>>\'\'the wavefunction is understood to represent knowledge\'\' is by\n>>Jaynes in the 1950ies, long after the establishment of the\n>>Copenhagen interpretation.\n>\n> I may have confused the official Copenhagen interpretation with\n> what Bohr, Heisenberg, von Neumann and so on believed. As Scerir\n> pointed out in this thread, Heisenberg said "The discontinuous change\n> in the probability function, however, takes place with the act\n> of registration, because it is the discontinuous change\n> of our knowledge in the instant of registration that has its\n> image in the discontinuous change of the probability function.",\n> Hiesenberg, "Physics and Philosophy", 1958\n\nI commented that already. the \'acto of registration\' happens on the\nphotographic plate or in the eye, not in the mind, and is simply\nthe irreversible magnification due to dissipation by interaction with\na macroscopic detector. It is objective and has no connection to\nany \'knowledge\'.\n\n\n> It may be that Heisenberg changed his interpretation of quantum\n> mechanics before he wrote that. It\'s even possible that Jaynes\n> influenced him for all I know. From what you have said about\n> your own interpretation, I take it that you claim that\n> Heisenberg was completely wrong when he wrote the\n> sentence quoted above.\n\nNo; only that your interpretation of what he said in terms of\nknowledge is a postmodern interpretation, and either the\nCopenhagen interpretation nor Heisenberg\'s intention.\n\n\n> With due respect, and I sincerely mean no offense, I believe\n> that you have been infected\n\nWhatever I am infected with, I hope it is highly infectuous\nand incurable, so that it spreads and has a lasting effect.\n\n\n> with the mental disease that I\n> ranted about in an earlier post:\n> http://groups-beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source\n\nThis is a long post, I cannot recognize myself reflected in it.\nNeither do I recognize signs of a mental disease in my behavior.\n\n\n> My understanding is that this is why you react so negatively to the\n> suggestion that the wavefunction describes knowledge.\n\nI followed the historical development of the interpretations of QM\nquite closely, reading hundreds of papers, to be able to make up my\nown mind of how _I_ should interpret QM (and other physics).\nIn the discussions on s.p.r., I share my insights for those who might\nwish to learn from it. I simply think that phrasing objective\ndescriptions in a psychological language, making them dependent on\nmental processes, is neither necessary to understanding nor does it\nserve any useful purpose. There is nothing inherently absurd about\nthis assessment.\n\n\n> There is\n> nothing inherently absurd about that idea, but physicists and\n> mathematicians who believe that their subject is "noble", and that\n> investigation of the mind is "dirty" will reject it immediately and\n> without very good arguments,\n\nI considered lots of argumewnts of all sides of the discussion, and\nbelieve to have excellent arguments for my point of view, that can\ncompete well with other arguments. They have nothing to do with\nnobility, but with realism, intelligibility, easy visualitization.\nI believe that certain things really exist and can be described\nobjectively, and that even the subjective, observer-dependent\naspects can be described objectively. This makes for clear foundations,\nwhich is my supreme objective in my quest about physics.\n\n\n>>>A definition\n>>>of measurement isn\'t missing because measurement is the\n>>>acquisition of new knowledge.\n>\n>>This is not a good definition since it is never specified what\n>>constitutes acquisition of knowledge.\n>\n> Acquisition of knowledge is what happens when you look at the\n> measuring device and see where the pointer is pointing. That\'s\n> perfectly precise for a normal person, but it seems insufficient\n> to somebody who wants to know about "the real objective world".\n\nIt seems that it is sufficient for you. But it is insufficient for me.\n\nI want a mathematical model of reality within which one can clearly\nsay what exists, what is an experiment, an observer, a measurement,\na record, etc., in such a way that one can predict in principle which\nexperiments give outcomes with which accuracy.\nSuch arguments are common in qunatum mechanical foundations (e.g.\ndiscussions of the Heisenberg microscope) but currently based on\ninformal notions of experiment, observer, measurement, record\nonly.\n\nMy goal is to put the foundations of physics on a basis similarly to\nthe foundations of mathematics, where the whole logical process of\ncoherent deduction can be modelled on a metalevel and gives clarity\nto the foundations of mathematics that is missing in physics.\n\nAnd I think that such foundations are possible and will provide the\nsame clarity for physics.\n\n\n>>The theory of knowledge\n>>acquisition is a branch of psychology, not of physics.\n>\n> The theory of knowledge acquisition is actually part of\n> philosophy, and is called epistemology.\n\nPhiosophy can only discuss what should be, but not how knowledge\nacquisition actually happens. The latter is an experimental question,\nnot a purely deductive one, and hence belongs to psychology,\nnot to philosophy.\n\n\n> When approached by\n> an epistemologist who wants to help them understand\n> the situation, they react with scorn, declaring that\n> the theory of knowledge acquisition is a branch of\n> psychology, implying that it is therefore unworthy\n> of study, less noble than the quest for what\'s "real".\n\nNo. First, I didn\'t react with scorn (again you put guessed\nemotions of your choice into my statements), but simply observed\nwhat to me is a fact. Second, I don\'t think that psychology\nis not worth studying, quite on the contrary, it is a very\ninteresting science. I only assert that psychology is a poor\nfoundation for physics.\n\n\n> Of course, if this is pointed out to them, they\n> deny it, saying "Why not at all - I am the most\n> reasonable of fellows.\n\nEveryone who has a sensible point of view argues that way,\nincluding you. What I point out to you does not seem sensible\nto you, and conversely. This is the natural situation in\ntopics of controversy, and does not prove that you are right.\n\n\n>>>State vector reduction happens\n>>>because the observer acquires new knowledge and then updates\n>>>the mathematical representation of his knowledge to reflect\n>>>the new knowledge that he has.\n>\n>>I doubt whether any observer updates his or her knowledge according\n>>to Bayesian reasoning. Field studies probably show large deviations\n>>from this supposedly universal behavior.\n\n> The assertion that Bayesian\n> reasoning is the correct way to proceed when one has incomplete\n> information is not an assertion about how people behave, and\n> cannot be disproved by field studies.\n\nIf you assert that the wave function is about knowledge then knowledge\nresides somewhere - according to you in some mind. But the claimed\nbehavior of these minds is something that can be studied by field\nstudies.\n\nYour argument sounds as if you are not claiming that the wave function\ncollapse is about the change of real knowledge of real minds,\nbut about how knowledge should change if someone observes something\nand acts completely rational. But then it becomes a moral statement\ncompletely outside science.\n\nHowever, the collapse was formulated by the founders as a necessity to\nmake sense of quantum mechanics, and not as a postulate about moral\nstandards for maintaining knowledge in minds.\n\n\n>>Furthermore, knowledge depends on subjective decisions to trust\n>>a measurement. If we discard one as an artifact, there is no\n>>collapse. How can the collapse depend on such subjective issues?\n>\n> In the "wavefunction represents knowledge" interpretation, the\n> wavefunction is not an objective thing,\n\nHow then can a non-objective thing change in time in an objective way???\n(Please don\'t be offended by the three ?s!)\n\n\n> but different observers\n> will use different wavefunctions, depending on what knowledge they\n> have about the system.\n\nIf I know nothing about an experiemnt, which wave function should I use?\nShould I use instead of a pure state the microcanonical ensemble,\nsuggested by many statistical mechanics treatments as noninformative\nprior? Then I make observations and find that they are not in accordance\nwith the predictions of my ensemble since it is born of ignorance\nrather than knowledge...\n\n\n> The "collapse" is what happens when the\n> observer receives new knowledge, and updates his mathematical\n> representation of his knowledge to reflect the new knowledge that\n> he has.\n\nThis must be a ficticious observer invented to suit your interpretation.\n\nA real observer with a real mind has no wave function in his mind --\nthat changes unitarily according to a differential equation whose\nsolution requires a computing capacity much beyond the mind\'s power, and\nonce it sees a measurement (any look out of the window, or only a\ncareful look at the detector needle to be sure of the third decimal?)\nit computes the solution of the corresponding eigenvalue problem to\nfind out how the wave functions must be collapsed to be consistent.\n\nAt least you won\'t find that when interrogating the most competent\nexperimental physicists who know how they update their knowledge.\n\n\n> Recall that subjective doesn\'t mean simply bad.\n\nI never assumed that. But subjective means outside the realm of science,\nunless that subjectivity can be explained and predicted by models of how\nit arises from something objective, such as the subjective\nobserver-dependence in special and general relativity.\n\n\n>>At the time of Bohr, von Neumann and Wigner, the collapse meant\n>>something objective, though it might have been related to the mind\n>>in some unspecified way.\n>\n> I have to disagree with that, although I do not mean it in an\n> adversarial way. The relation to the mind was perfectly clear and\n> very specific for these people, at least by the \'50s. Also, since\n> they understood that the wavefunction represented knowledge, the\n> collapse wasn\'t an objective thing for them.\n\nPlease support your claims by solid evidence!\n\n\n>>>>Von Neumann takes the collapse as an axiom, hence also testifies to its\n>>>>reality.\n>>>\n>>>He uses it as an axiom, but that doesn\'t mean that he claimed that\n>>>the wavefunction didn\'t represent knowledge.\n>\n>>But he certainly didn\'t claim that the wavefunction does represent\n>>knowledge.\n>\n> As I quoted before,\n>\n> "Let us assume that we do not know the state of a system, S, but\n> that we have made certain measurements about the state of S and\n> know their results. In reality, it always happens this way, because\n> we can learn something about the state of S only from the results\n> of measurements. More precisely, the states are only a theoretical\n> construction, only the results of measurements are actually available,\n> and the problem of physics is to furnish relationships between the\n> results of past and future measurements." p. 337\n>\n> This is exactly a claim that the wavefunction represents\n> knowledge.\n\nI cannot understand how you can possibly arrive at this statement.\nIf your claim were true, what von Neumann actually said (first sentence)\nwould mean: \'\'Let us assume that we do not know what we know (the state\nof S)\'\', and then he deduces correctly from this (obviously false)\npremise everything he likes.\n\n\n> "The states are a theoretical construction,\n> only the results of measurements are actually available" refers\n> to the fact that the results of measurements are the knowledge\n> available, and that the states are a theoretical construction\n> which encode that knowledge.\n\nNo; it refers to the fact that the state is something that exists\n(since we can learn something about it) but we _don\'t_ know,\nhence must infer by a theoretical construction, while we _do_ know\nthe results of the measurements, and can infer from them partial\ninformation about the state.\n\nThis is a much more coherent interpretation of his statement,\nand conforms quite well with the form of knowledge experimenters\nactually have, and with the practice of state estimation in\nhigh quality quantum experiments.\n\n\n>>No. A proposition is a statement that is true or false,\n>>or undecidable. It has nothing to do with whether or not\n>>anyone knows (or claims to know) its truth or falsehood.\n>\n> Logic, which includes the propositional calculus, is the formal\n> science of inference, and inference can only be done by the mind.\n\nNo. It is routinely (and more reliably) done by computers.\n\nWe accept (usually without doubt) the inferences that a\nsystem like Mathematica performs upon our requests.\nAnd if we doubt, we usually doubt first _our_ abilities to\nmake the right requests (resulting in a process called \'debugging\')\nrather than the inference abilities of the computer.\n\n\n> An inference is what allows one to derive new knowledge from\n> knowledge that one already has. Knowledge is always of the\n> form "I know that proposition X is true", so propositions\n> certainly have a lot to do with knowledge.\n\nOf course knowledge is about propositions, but propositions\nare not about knowledge.\n\nPeople discuss the consequences of the proposition\n\'The Riemann hypothesis is true\' in the absence\nof any knowledge about the truth of this statement.\nThe same happens routinely in proofs by contradiction,\nwhere we assume some proposition although we know (and want\nto demonstrate to someone else) that it is _not_ true.\n\n\n> The desire to assert that logic has nothing to do with the mind is,\n> I believe, rooted in the primitive notion of nobility,\n\nNo. For example, it can be rooted in the fact that logic can\nbe performed by microchips, which have little to do with mind as\ncommonly understood.\n\n\n\n> I was\n> asserting that von Neumann was aware that we only know the results\n> of measurements,\n\nI agree with this assertion. It is in flat contradiction with your claim\nthat the wave function represents our knowledge. For a wave function\nneeds infinitely many bits to specify, while the results of measurements\n(according to what you just stated, the _only_ thing we know about the\nsystem) can be coded in the finite number of bits making up a protocol.\n\n\n\n> "More precisely, the states are only a theoretical construction,\n> only the results of measurements are actually available, and the\n> problem of physics is to furnish relationships between the results\n> of past and future measurements. To be sure, this is always\n> accomplished through the introduction of the auxilliary concept\n> "state", but the physical theory must then tell us on the one hand\n> how to make from past measurements inferences about the present\n> state, and on the other hand, how to go from the present state to\n> the results of future measurements." p. 337\n>\n> What he is saying is that, in quantum mechanics, what we call\n> a "state" is actually a theoretical construction\n\nbut with the same objective status as mass, temperature, momentum,\ncharge distribution, etc. of an object. These are also theoretical\nconstructs used to organize our observations.\n\nAnd with the same objective status as the galaxy as an assembly of\nmyriads of hot and heavy stars, a theoretical construction used to\norganize the information we can gather about certain light dots in\nthe sky.\n\nAll of physics is theoretical construction based on past measurements.\nEven the measurement results (\'the spin of this particle was up\')\nthemselves are theoretical constructions, indirectly derived from\nthe raw observations.\n\n\n\n> which incorporates\n> information about the results of past measurements on the system.\n\njust as we infer the temperature field in a room from\ninformation about the results of past measurements of a thermometer.\n\n\n> That is why the wavefunction represents knowledge.\n\nIn this sense, it is a tautology. But this is not what von Neumann\ncould have had in mind.\n\n\n\n>>>The principle of psycho-physical\n>>>parallelism tells us that, whatever we claim to know\n>>>about the physical world, what we actually know about\n>>>is what\'s going on inside our body,\n>\n>>I don\'t buy this. What we know is some platonic extract\n>>extrapolated from sense data. And much of it is mistaken\n>>in detail, but still we think we know and act accordingly.\n>>It has nothing to do with physics as understood pragmatically.\n>\n> Basically, you are saying that knowledge is a dirty thing,\n\nNo. You read this into my statements. Knowledge has nothing to\ndo with cleanliness. Dirty things can be washed; I wouldn\'t know\nhow to wash knowledge.\n\n\nKnowledge is what we (think we) know. This may be a number of\nexperimental results to within some accuracy, an approximate\ndescription of a quantum mechanical state, the rough\ntemperature distribution in a room, the behavior of a piece of\nequipment according to the manufacturer\'s manual (perhaps\ncorrected by our own calibration experiments), the weight,\nlength and age of the persons working in a room, etc.\nIt is (in some idealization) something describable in a finite\nstring of symbols.\n\nOn the other hand, fundamental physics is about the mathematical\nmodel of Nature resulting from such information. This model\n(von Neumann\'s \'\'theoretical construction\'\') is inferred from\nobservations and contains more accurate parts, less accurate parts,\nprobably a few mistaken parts, and completely unknown parts -\nit is like a 17th century world map, but instead for the\nphysical phenomenon under study. The objective state of the\nsystem is one of the polethora of states compatible with the\nasvailable information - which one, we don\'t know. But if we know\nsufficiently much, all compatible states are approximately the same,\nso working with any particular of them will give good predicitions.\n\nNothing here prevents one of taking the system to be the whole universe.\nThe state of the universe must simply be compatible with all details\nwe observed in the parts of the universe accessible to our experiments.\n\n\n> Also, when you say "I don\'t buy this," are you saying that\n> you don\'t believe that von Neumann held this opinion,\n> namely that the principle of psycho-physical parallelism\n> tells us that we can consider what we are observing\n> to be within our own bodies? Because he did:\n>\n> "We wish to measure a temperature. ... [we can] say: this\n> temperature is measured by the thermometer. ... we can\n> calculate the resultant length of the mercury column,\n> and then say: this length is seen by the observer. Going\n> still further, and taking the light source into consideration ...\n> we would say: this image is registered by the retina of the\n> observer. And were our physiological knowledge more precise\n> than it is today, we could go still further, tracing the\n> chemical reactions which produce the impression of this image on\n> the retina, in the optic nerve tract and in the brain, and then in\n> the end say: these chemical changes of his brain cells are\n> perceived by the observer." p.419\n>\n> "That this boundary can be pushed arbitrarily into the interior\n> of the body of the observer is the content of the principle\n> of the psycho-physical parallelism." p.420\n\nVon Neumann says that collapse happens in each particular physical\nsystem (defined by its boundary), but that consistency requires that\nif we regard a particular system as part of a bigger system then\nthe collapse of the larger system must give, for the smaller system,\nresults compatible with the collapse of the smaller system considered\nby itself. This is nothing more than an obvious compatibility\ncondition. It has nothing to do with the nature of the two systems,\nYou might care to notice that von Neumann carefully avoids to invoke\neither the \'mind\' or the observer\'s \'knowledge\'.\n\nVon Neumann simply argues that the collapse is consistent with the\npsycho-physical parallelism (to the extent that one can define the\nlatter by the assertion that the \'\'boundary can be pushed arbitrarily\ninto the interior of the body of the observer\'\'). But his general\nargument does not require a body or a brain; it is true wherever\nthe boundary is placed, for example when the boundary is placed\nbetween the exposed photographic plate and the process developing\nthe plate to see the picture.\n\nThus the psycho-physical parallelism is completely inessential for\nthe interpretation of the collapse.\n\n\n>>>You might also want to read the paper by Lon Becker:\n>>>"That von Neumann Did Not Believe in a Physical Collapse",\n>>>http://bjps.oupjournals.org/cgi/content/abstract/55/1/121\n>\n>>I\'ll read it and comment later, if I have more to say than\n>>what I said already.\n\nI read it and found it wanting. It projects a particular\nprejudice into his statements.\n\n\n> He also didn\'t have the "subjective means bad" attitude of modern\n> physicists, and was aware that what we deal with in physics is\n> not "the real world", but rather with subjective observations:\n> "Indeed experience only makes statements of this type: an observer\n> has made a certain (subjective) observation; and never any like\n> this: a physical quantity has a certain value." p.420\n\nVon Neumann is more careful in his use of language than you in your\ninterpretation of his words.\n\nThere is a difference between \'experience\' and \'experiment\'.\nThe former is a psychological concept; the latter is a concept\nof physics.\n\nAn experience produces subjective sensory perceptions;\nan experiment produces recorded values of physical quantities.\n\n\n> For him, the distinction between the observer and the observed\n> was of fundamental importance in quantum mechanics; this is\n> the so-called quantum/classical boundary:\n> "That is, we must always divide the world into two parts,\n> the one being the observed system, the other the observer. ...\n> The boundary between the two is arbitrary to a large extent. ...\n\n... to such an extent that his observer can be an inanimate object\nlike a camera or a thermometer.\n\n\n> but this does not change the fact that in each method of description\n> the boundary must be placed somewhere, if the method is not to\n> proceed vacuously, i.e., if a comparison with experiment is to be\n> possible." p.420\n>\n> So, from von Neumann\'s point of view, to use a "wavefunction of the\n> universe" would be to proceed vacuously.\n\nOnly in this last statement I agree with your interpretation of\nhis position.\n\nAt this point my view of quantum mechanics differs from his.\nAnd with good grounds.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>rof@maths.tcd.ie wrote:
>
>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>>
>>>Your treatment of the Copenhagen
>>>interpretation in the article claims that the "unresolved
>>>quantum-classical interface issue (including the missing definition
>>>of which situations constitute a measurement) is a serious defect
>>>of the Copenhagen interpretation when viewed as a fundamental
>>>interpretation of quantum mechanics."
>>>
>>>This is slightly unfair to the Copenhagen interpretation, in
>>>which the wavefunction is understood to represent knowledge
>>>about the system, rather than the system itself.
>
>>No. As far as I can tell, the first mention of the claim that
>>''the wavefunction is understood to represent knowledge'' is by
>>Jaynes in the 1950ies, long after the establishment of the
>>Copenhagen interpretation.
>
> I may have confused the official Copenhagen interpretation with
> what Bohr, Heisenberg, von Neumann and so on believed. As Scerir
> pointed out in this thread, Heisenberg said "The discontinuous change
> in the probability function, however, takes place with the act
> of registration, because it is the discontinuous change
> of our knowledge in the instant of registration that has its
> image in the discontinuous change of the probability function.",
> Hiesenberg, "Physics and Philosophy", 1958
I commented that already. the 'acto of registration' happens on the
photographic plate or in the eye, not in the mind, and is simply
the irreversible magnification due to dissipation by interaction with
a macroscopic detector. It is objective and has no connection to
any 'knowledge'.
> It may be that Heisenberg changed his interpretation of quantum
> mechanics before he wrote that. It's even possible that Jaynes
> influenced him for all I know. From what you have said about
> your own interpretation, I take it that you claim that
> Heisenberg was completely wrong when he wrote the
> sentence quoted above.
No; only that your interpretation of what he said in terms of
knowledge is a postmodern interpretation, and either the
Copenhagen interpretation nor Heisenberg's intention.
> With due respect, and I sincerely mean no offense, I believe
> that you have been infected
Whatever I am infected with, I hope it is highly infectuous
and incurable, so that it spreads and has a lasting effect.
> with the mental disease that I
> ranted about in an earlier post:
> http://groups-\beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source
This is a long post, I cannot recognize myself reflected in it.
Neither do I recognize signs of a mental disease in my behavior.
> My understanding is that this is why you react so negatively to the
> suggestion that the wavefunction describes knowledge.
I followed the historical development of the interpretations of QM
quite closely, reading hundreds of papers, to be able to make up my
own mind of how _I_ should interpret QM (and other physics).
In the discussions on s.p.r., I share my insights for those who might
wish to learn from it. I simply think that phrasing objective
descriptions in a psychological language, making them dependent on
mental processes, is neither necessary to understanding nor does it
serve any useful purpose. There is nothing inherently absurd about
this assessment.
> There is
> nothing inherently absurd about that idea, but physicists and
> mathematicians who believe that their subject is "noble", and that
> investigation of the mind is "dirty" will reject it immediately and
> without very good arguments,
I considered lots of argumewnts of all sides of the discussion, and
believe to have excellent arguments for my point of view, that can
compete well with other arguments. They have nothing to do with
nobility, but with realism, intelligibility, easy visualitization.
I believe that certain things really exist and can be described
objectively, and that even the subjective, observer-dependent
aspects can be described objectively. This makes for clear foundations,
which is my supreme objective in my quest about physics.
>>>A definition
>>>of measurement isn't missing because measurement is the
>>>acquisition of new knowledge.
>
>>This is not a good definition since it is never specified what
>>constitutes acquisition of knowledge.
>
> Acquisition of knowledge is what happens when you look at the
> measuring device and see where the pointer is pointing. That's
> perfectly precise for a normal person, but it seems insufficient
> to somebody who wants to know about "the real objective world".
It seems that it is sufficient for you. But it is insufficient for me.
I want a mathematical model of reality within which one can clearly
say what exists, what is an experiment, an observer, a measurement,
a record, etc., in such a way that one can predict in principle which
experiments give outcomes with which accuracy.
Such arguments are common in qunatum mechanical foundations (e.g.
discussions of the Heisenberg microscope) but currently based on
informal notions of experiment, observer, measurement, record
only.
My goal is to put the foundations of physics on a basis similarly to
the foundations of mathematics, where the whole logical process of
coherent deduction can be modelled on a metalevel and gives clarity
to the foundations of mathematics that is missing in physics.
And I think that such foundations are possible and will provide the
same clarity for physics.
>>The theory of knowledge
>>acquisition is a branch of psychology, not of physics.
>
> The theory of knowledge acquisition is actually part of
> philosophy, and is called epistemology.
Phiosophy can only discuss what should be, but not how knowledge
acquisition actually happens. The latter is an experimental question,
not a purely deductive one, and hence belongs to psychology,
not to philosophy.
> When approached by
> an epistemologist who wants to help them understand
> the situation, they react with scorn, declaring that
> the theory of knowledge acquisition is a branch of
> psychology, implying that it is therefore unworthy
> of study, less noble than the quest for what's "real".
No. First, I didn't react with scorn (again you put guessed
emotions of your choice into my statements), but simply observed
what to me is a fact. Second, I don't think that psychology
is not worth studying, quite on the contrary, it is a very
interesting science. I only assert that psychology is a poor
foundation for physics.
> Of course, if this is pointed out to them, they
> deny it, saying "Why not at all - I am the most
> reasonable of fellows.
Everyone who has a sensible point of view argues that way,
including you. What I point out to you does not seem sensible
to you, and conversely. This is the natural situation in
topics of controversy, and does not prove that you are right.
>>>State vector reduction happens
>>>because the observer acquires new knowledge and then updates
>>>the mathematical representation of his knowledge to reflect
>>>the new knowledge that he has.
>
>>I doubt whether any observer updates his or her knowledge according
>>to Bayesian reasoning. Field studies probably show large deviations
>>from this supposedly universal behavior.
> The assertion that Bayesian
> reasoning is the correct way to proceed when one has incomplete
> information is not an assertion about how people behave, and
> cannot be disproved by field studies.
If you assert that the wave function is about knowledge then knowledge
resides somewhere - according to you in some mind. But the claimed
behavior of these minds is something that can be studied by field
studies.
Your argument sounds as if you are not claiming that the wave function
collapse is about the change of real knowledge of real minds,
but about how knowledge should change if someone observes something
and acts completely rational. But then it becomes a moral statement
completely outside science.
However, the collapse was formulated by the founders as a necessity to
make sense of quantum mechanics, and not as a postulate about moral
standards for maintaining knowledge in minds.
>>Furthermore, knowledge depends on subjective decisions to trust
>>a measurement. If we discard one as an artifact, there is no
>>collapse. How can the collapse depend on such subjective issues?
>
> In the "wavefunction represents knowledge" interpretation, the
> wavefunction is not an objective thing,
How then can a non-objective thing change in time in an objective way???
(Please don't be offended by the three ?s!)
> but different observers
> will use different wavefunctions, depending on what knowledge they
> have about the system.
If I know nothing about an experiemnt, which wave function should I use?
Should I use instead of a pure state the microcanonical ensemble,
suggested by many statistical mechanics treatments as noninformative
prior? Then I make observations and find that they are not in accordance
with the predictions of my ensemble since it is born of ignorance
rather than knowledge...
> The "collapse" is what happens when the
> observer receives new knowledge, and updates his mathematical
> representation of his knowledge to reflect the new knowledge that
> he has.
This must be a ficticious observer invented to suit your interpretation.
A real observer with a real mind has no wave function in his mind --
that changes unitarily according to a differential equation whose
solution requires a computing capacity much beyond the mind's power, and
once it sees a measurement (any look out of the window, or only a
careful look at the detector needle to be sure of the third decimal?)
it computes the solution of the corresponding eigenvalue problem to
find out how the wave functions must be collapsed to be consistent.
At least you won't find that when interrogating the most competent
experimental physicists who know how they update their knowledge.
> Recall that subjective doesn't mean simply bad.
I never assumed that. But subjective means outside the realm of science,
unless that subjectivity can be explained and predicted by models of how
it arises from something objective, such as the subjective
observer-dependence in special and general relativity.
>>At the time of Bohr, von Neumann and Wigner, the collapse meant
>>something objective, though it might have been related to the mind
>>in some unspecified way.
>
> I have to disagree with that, although I do not mean it in an
> adversarial way. The relation to the mind was perfectly clear and
> very specific for these people, at least by the '50s. Also, since
> they understood that the wavefunction represented knowledge, the
> collapse wasn't an objective thing for them.
Please support your claims by solid evidence!
>>>>Von Neumann takes the collapse as an axiom, hence also testifies to its
>>>>reality.
>>>
>>>He uses it as an axiom, but that doesn't mean that he claimed that
>>>the wavefunction didn't represent knowledge.
>
>>But he certainly didn't claim that the wavefunction does represent
>>knowledge.
>
> As I quoted before,
>
> "Let us assume that we do not know the state of a system, S, but
> that we have made certain measurements about the state of S and
> know their results. In reality, it always happens this way, because
> we can learn something about the state of S only from the results
> of measurements. More precisely, the states are only a theoretical
> construction, only the results of measurements are actually available,
> and the problem of physics is to furnish relationships between the
> results of past and future measurements." p. 337
>
> This is exactly a claim that the wavefunction represents
> knowledge.
I cannot understand how you can possibly arrive at this statement.
If your claim were true, what von Neumann actually said (first sentence)
would mean: ''Let us assume that we do not know what we know (the state
of S)'', and then he deduces correctly from this (obviously false)
premise everything he likes.
> "The states are a theoretical construction,
> only the results of measurements are actually available" refers
> to the fact that the results of measurements are the knowledge
> available, and that the states are a theoretical construction
> which encode that knowledge.
No; it refers to the fact that the state is something that exists
(since we can learn something about it) but we _don't_ know,
hence must infer by a theoretical construction, while we _do_ know
the results of the measurements, and can infer from them partial
information about the state.
This is a much more coherent interpretation of his statement,
and conforms quite well with the form of knowledge experimenters
actually have, and with the practice of state estimation in
high quality quantum experiments.
>>No. A proposition is a statement that is true or false,
>>or undecidable. It has nothing to do with whether or not
>>anyone knows (or claims to know) its truth or falsehood.
>
> Logic, which includes the propositional calculus, is the formal
> science of inference, and inference can only be done by the mind.
No. It is routinely (and more reliably) done by computers.
We accept (usually without doubt) the inferences that a
system like Mathematica performs upon our requests.
And if we doubt, we usually doubt first _our_ abilities to
make the right requests (resulting in a process called 'debugging')
rather than the inference abilities of the computer.
> An inference is what allows one to derive new knowledge from
> knowledge that one already has. Knowledge is always of the
> form "I know that proposition X is true", so propositions
> certainly have a lot to do with knowledge.
Of course knowledge is about propositions, but propositions
are not about knowledge.
People discuss the consequences of the proposition
'The Riemann hypothesis is true' in the absence
of any knowledge about the truth of this statement.
The same happens routinely in proofs by contradiction,
where we assume some proposition although we know (and want
to demonstrate to someone else) that it is _not_ true.
> The desire to assert that logic has nothing to do with the mind is,
> I believe, rooted in the primitive notion of nobility,
No. For example, it can be rooted in the fact that logic can
be performed by microchips, which have little to do with mind as
commonly understood.
> I was
> asserting that von Neumann was aware that we only know the results
> of measurements,
I agree with this assertion. It is in flat contradiction with your claim
that the wave function represents our knowledge. For a wave function
needs infinitely many bits to specify, while the results of measurements
(according to what you just stated, the _only_ thing we know about the
system) can be coded in the finite number of bits making up a protocol.
> "More precisely, the states are only a theoretical construction,
> only the results of measurements are actually available, and the
> problem of physics is to furnish relationships between the results
> of past and future measurements. To be sure, this is always
> accomplished through the introduction of the auxilliary concept
> "state", but the physical theory must then tell us on the one hand
> how to make from past measurements inferences about the present
> state, and on the other hand, how to go from the present state to
> the results of future measurements." p. 337
>
> What he is saying is that, in quantum mechanics, what we call
> a "state" is actually a theoretical construction
but with the same objective status as mass, temperature, momentum,
charge distribution, etc. of an object. These are also theoretical
constructs used to organize our observations.
And with the same objective status as the galaxy as an assembly of
myriads of hot and heavy stars, a theoretical construction used to
organize the information we can gather about certain light dots in
the sky.
All of physics is theoretical construction based on past measurements.
Even the measurement results ('the spin of this particle was up')
themselves are theoretical constructions, indirectly derived from
the raw observations.
> which incorporates
> information about the results of past measurements on the system.
just as we infer the temperature field in a room from
information about the results of past measurements of a thermometer.
> That is why the wavefunction represents knowledge.
In this sense, it is a tautology. But this is not what von Neumann
could have had in mind.
>>>The principle of psycho-physical
>>>parallelism tells us that, whatever we claim to know
>>>about the physical world, what we actually know about
>>>is what's going on inside our body,
>
>>I don't buy this. What we know is some platonic extract
>>extrapolated from sense data. And much of it is mistaken
>>in detail, but still we think we know and act accordingly.
>>It has nothing to do with physics as understood pragmatically.
>
> Basically, you are saying that knowledge is a dirty thing,
No. You read this into my statements. Knowledge has nothing to
do with cleanliness. Dirty things can be washed; I wouldn't know
how to wash knowledge.
Knowledge is what we (think we) know. This may be a number of
experimental results to within some accuracy, an approximate
description of a quantum mechanical state, the rough
temperature distribution in a room, the behavior of a piece of
equipment according to the manufacturer's manual (perhaps
corrected by our own calibration experiments), the weight,
length and age of the persons working in a room, etc.
It is (in some idealization) something describable in a finite
string of symbols.
On the other hand, fundamental physics is about the mathematical
model of Nature resulting from such information. This model
(von Neumann's ''theoretical construction'') is inferred from
observations and contains more accurate parts, less accurate parts,
probably a few mistaken parts, and completely unknown parts -
it is like a 17th century world map, but instead for the
physical phenomenon under study. The objective state of the
system is one of the polethora of states compatible with the
asvailable information - which one, we don't know. But if we know
sufficiently much, all compatible states are approximately the same,
so working with any particular of them will give good predicitions.
Nothing here prevents one of taking the system to be the whole universe.
The state of the universe must simply be compatible with all details
we observed in the parts of the universe accessible to our experiments.
> Also, when you say "I don't buy this," are you saying that
> you don't believe that von Neumann held this opinion,
> namely that the principle of psycho-physical parallelism
> tells us that we can consider what we are observing
> to be within our own bodies? Because he did:
>
> "We wish to measure a temperature. ... [we can] say: this
> temperature is measured by the thermometer. ... we can
> calculate the resultant length of the mercury column,
> and then say: this length is seen by the observer. Going
> still further, and taking the light source into consideration ...
> we would say: this image is registered by the retina of the
> observer. And were our physiological knowledge more precise
> than it is today, we could go still further, tracing the
> chemical reactions which produce the impression of this image on
> the retina, in the optic nerve tract and in the brain, and then in
> the end say: these chemical changes of his brain cells are
> perceived by the observer." p.419
>
> "That this boundary can be pushed arbitrarily into the interior
> of the body of the observer is the content of the principle
> of the psycho-physical parallelism." p.420
Von Neumann says that collapse happens in each particular physical
system (defined by its boundary), but that consistency requires that
if we regard a particular system as part of a bigger system then
the collapse of the larger system must give, for the smaller system,
results compatible with the collapse of the smaller system considered
by itself. This is nothing more than an obvious compatibility
condition. It has nothing to do with the nature of the two systems,
You might care to notice that von Neumann carefully avoids to invoke
either the 'mind' or the observer's 'knowledge'.
Von Neumann simply argues that the collapse is consistent with the
psycho-physical parallelism (to the extent that one can define the
latter by the assertion that the ''boundary can be pushed arbitrarily
into the interior of the body of the observer''). But his general
argument does not require a body or a brain; it is true wherever
the boundary is placed, for example when the boundary is placed
between the exposed photographic plate and the process developing
the plate to see the picture.
Thus the psycho-physical parallelism is completely inessential for
the interpretation of the collapse.
>>>You might also want to read the paper by Lon Becker:
>>>"That von Neumann Did Not Believe in a Physical Collapse",
>>>http://bjps.oupjournals.org/cgi/content/abstract/55/1/121
>
>>I'll read it and comment later, if I have more to say than
>>what I said already.
I read it and found it wanting. It projects a particular
prejudice into his statements.
> He also didn't have the "subjective means bad" attitude of modern
> physicists, and was aware that what we deal with in physics is
> not "the real world", but rather with subjective observations:
> "Indeed experience only makes statements of this type: an observer
> has made a certain (subjective) observation; and never any like
> this: a physical quantity has a certain value." p.420
Von Neumann is more careful in his use of language than you in your
interpretation of his words.
There is a difference between 'experience' and 'experiment'.
The former is a psychological concept; the latter is a concept
of physics.
An experience produces subjective sensory perceptions;
an experiment produces recorded values of physical quantities.
> For him, the distinction between the observer and the observed
> was of fundamental importance in quantum mechanics; this is
> the so-called quantum/classical boundary:
> "That is, we must always divide the world into two parts,
> the one being the observed system, the other the observer. ...
> The boundary between the two is arbitrary to a large extent. ...
... to such an extent that his observer can be an inanimate object
like a camera or a thermometer.
> but this does not change the fact that in each method of description
> the boundary must be placed somewhere, if the method is not to
> proceed vacuously, i.e., if a comparison with experiment is to be
> possible." p.420
>
> So, from von Neumann's point of view, to use a "wavefunction of the
> universe" would be to proceed vacuously.
Only in this last statement I agree with your interpretation of
his position.
At this point my view of quantum mechanics differs from his.
And with good grounds.
Arnold Neumaier
Arnold Neumaier
Jun2-05, 12:28 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>scerir wrote:\n\n> Arnold Neumaier\n>\n>>At the time of Bohr, von Neumann and Wigner, the collapse meant\n>>something objective,[...].\n>\n> It seems, perhaps, interesting to point out that the\n> first definition was "reduction of probability packet",\n> sometimes "reduction of wave packet."\n\nYes. This is generally taken as synonymous with the collapse.\n\n\n> Actually Heisenberg gave a physical picture in 1930.\n> "There is then a definite probability for finding the photon\n> either in one part or in the other part of the divided wave packet.\n> After a sufficient time the two parts will be separated by any\n> distance desired; now if an experiment yields the result that\n> the photon is, say, in the reflected part of the packet, then\n> the probability of finding the photon in the other part of the\n> packet immediately becomes zero. The experiment at the position\n> of the reflected packet thus exerts a kind of action (reduction\n> of the wave packet) at the distant point occupied by the transmitted\n> packet, and one sees that this action is propagated with a velocity\n> greater than that of light. However, it is also obvious that\n> this kind of action can never be utilized for the transmission\n> of signals so that it is not in conflict with the postulates\n> of the theory of relativity." (\'The Physical Principles of the\n> Quantum Theory\', University of Chicago Press, Chicago, 1930).\n\nHere (\'\'The experiment at the position of the reflected packet\nthus exerts a kind of action\'\') the collapse is described as\nan objective event, unrelated to an \'observer\', but related to\nan \'experiment\'.\n\n\n> (Following the above reasoning we expect that, i.e., the\n> information about the probability of a particle being at\n> a distance x comes to us with a signal velocity c.\n> Thus the |wavefunction(x,t - r/c)|^2 should represent\n> the probability that a particle is at x, as seen at\n> the origin. Or am I wrong?)\n\nIn nonrelativistic QM (an there was no consistent relativistic QM\nbefore around 1947), superluminal signals would be nothing to worry\nabout. But the collapse is not a signal, so there is even less to worry.\n\n\n> Unfortunately H.Kragh ("Dirac: a Scientific Biography", Cambridge\n> U.P., 1990) describes a (1927) discussion between Dirac, Heisenberg\n> and Born, about what, actually, gives rise to a "collapse".\n> Dirac said that it is \'Nature\' that makes the choice (of the\n> measurement outcome). Born agreed. Heisenberg however maintained that,\n> behind the collapse, and the choice of which \'branch\' the wavefunction\n> would be followed, there was "the free-will of the human observer".\n\nInteresting but not conclusive. The free will of the observer\njust means the freedom to arrange a certain experiment (and hence to\nselect the preferred basis with respect to which the collapse happens),\nbut not the freedom to choose the branch of the wave function.\n\nIn any case, in a typical experiment at CERN, it is clearly Nature that\nmakes the choice about which particles to produce in a wire chamber\nexperiment.\n\n\n> And later, in "Physics and Philosophy" (Harper and Row, 1958, New York)\n> Heisenberg writes "The observation itself changes the probability\n> function discontinuously; it selects of all possible events\n> the actual one that has taken place [...] The discontinuous change\n> in the probability function, however, takes place with the act\n> of registration, because it is the discontinuous change\n> of our knowledge in the instant of registration that has its\n> image in the discontinuous change of the probability function."\n\nAgain, the act of registration has nothing to do with the mind but\nwith the photographic plate, the bubble chamber, the Geiger counter,\nor whatever detector is being used to register the phenomenon.\n\n\n> According to Jan Faye "Bohr accepted the Born statistical\n> interpretation because he believed that the psi-function\n> has only a symbolic meaning and does not represent anything real.\n> It makes sense to talk about a collapse of the wave function\n> only if, as Bohr put it, the psi-function can be given a pictorial\n> representation, something he strongly denied."\n>\n> It is really not so easy to find a definition (of the \'reduction\')\n> by Niels Bohr. In a letter to Pauli (March 2, 1955) he wrote "Thus,\n> when speaking of the physical interpretation of the formalism,\n> I consider such details of procedure like "reduction of the wave\n> packets" as integral parts of a consistent scheme conforming\n> with the indivisibility of the phenomena and the essential\n> irreversibility involved in the very concept of observation."\n> (Niels Bohr Collected Works, vol. 10, Elsevier 1999, page 568).\n\nThus the collapse is an integral part of the description of\nan experiment, accounting for the irreversibility (i.e. nonunitarity)\nof the system considered (since it is not isolated, but coupled to\nthe detector), and not a process of the mind.\n\nWithout irreversibility no experimental record, hence no measurement,\nhence no collapse. Experimental records are therefore intimately tied\nto irreversibility, hence to thermodynamics. Ultimately, the second\nlaw is responsible for the observability of Nature.\n\n\n> Even in Max Born it is possible to find many (very) different\n> interpretations of the \'reduction\' (and of the wave-funtion).\n> In example "The question of whether the waves are something\n> "real" or a function to describe and predict phenomena in\n> a convenient way is a matter of taste. I personally like\n> to regard a probability wave, even in 3N-dimensional space,\n> as a real thing, certainly as more than a tool for mathematical\n> calculations ... Quite generally, how could we rely on\n> probability predictions if by this notion we do not refer\n> to something real and objective?" [Max Born, Dover publ., 1964,\n> "Natural Philosophy of Cause and Chance", p. 107.]\n\nI share this assesment of Born.\n\nThanks for the quotes!\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>scerir wrote:
> Arnold Neumaier
>
>>At the time of Bohr, von Neumann and Wigner, the collapse meant
>>something objective,[...].
>
> It seems, perhaps, interesting to point out that the
> first definition was "reduction of probability packet",
> sometimes "reduction of wave packet."
Yes. This is generally taken as synonymous with the collapse.
> Actually Heisenberg gave a physical picture in 1930.
> "There is then a definite probability for finding the photon
> either in one part or in the other part of the divided wave packet.
> After a sufficient time the two parts will be separated by any
> distance desired; now if an experiment yields the result that
> the photon is, say, in the reflected part of the packet, then
> the probability of finding the photon in the other part of the
> packet immediately becomes zero. The experiment at the position
> of the reflected packet thus exerts a kind of action (reduction
> of the wave packet) at the distant point occupied by the transmitted
> packet, and one sees that this action is propagated with a velocity
> greater than that of light. However, it is also obvious that
> this kind of action can never be utilized for the transmission
> of signals so that it is not in conflict with the postulates
> of the theory of relativity." ('The Physical Principles of the
> Quantum Theory', University of Chicago Press, Chicago, 1930).
Here (''The experiment at the position of the reflected packet
thus exerts a kind of action'') the collapse is described as
an objective event, unrelated to an 'observer', but related to
an 'experiment'.
> (Following the above reasoning we expect that, i.e., the
> information about the probability of a particle being at
> a distance x comes to us with a signal velocity c.
> Thus the |wavefunction(x,t - r/c)|^2 should represent
> the probability that a particle is at x, as seen at
> the origin. Or am I wrong?)
In nonrelativistic QM (an there was no consistent relativistic QM
before around 1947), superluminal signals would be nothing to worry
about. But the collapse is not a signal, so there is even less to worry.
> Unfortunately H.Kragh ("Dirac: a Scientific Biography", Cambridge
> U.P., 1990) describes a (1927) discussion between Dirac, Heisenberg
> and Born, about what, actually, gives rise to a "collapse".
> Dirac said that it is 'Nature' that makes the choice (of the
> measurement outcome). Born agreed. Heisenberg however maintained that,
> behind the collapse, and the choice of which 'branch' the wavefunction
> would be followed, there was "the free-will of the human observer".
Interesting but not conclusive. The free will of the observer
just means the freedom to arrange a certain experiment (and hence to
select the preferred basis with respect to which the collapse happens),
but not the freedom to choose the branch of the wave function.
In any case, in a typical experiment at CERN, it is clearly Nature that
makes the choice about which particles to produce in a wire chamber
experiment.
> And later, in "Physics and Philosophy" (Harper and Row, 1958, New York)
> Heisenberg writes "The observation itself changes the probability
> function discontinuously; it selects of all possible events
> the actual one that has taken place [...] The discontinuous change
> in the probability function, however, takes place with the act
> of registration, because it is the discontinuous change
> of our knowledge in the instant of registration that has its
> image in the discontinuous change of the probability function."
Again, the act of registration has nothing to do with the mind but
with the photographic plate, the bubble chamber, the Geiger counter,
or whatever detector is being used to register the phenomenon.
> According to Jan Faye "Bohr accepted the Born statistical
> interpretation because he believed that the \psi-function
> has only a symbolic meaning and does not represent anything real.
> It makes sense to talk about a collapse of the wave function
> only if, as Bohr put it, the \psi-function can be given a pictorial
> representation, something he strongly denied."
>
> It is really not so easy to find a definition (of the 'reduction')
> by Niels Bohr. In a letter to Pauli (March 2, 1955) he wrote "Thus,
> when speaking of the physical interpretation of the formalism,
> I consider such details of procedure like "reduction of the wave
> packets" as integral parts of a consistent scheme conforming
> with the indivisibility of the phenomena and the essential
> irreversibility involved in the very concept of observation."
> (Niels Bohr Collected Works, vol. 10, Elsevier 1999, page 568).
Thus the collapse is an integral part of the description of
an experiment, accounting for the irreversibility (i.e. nonunitarity)
of the system considered (since it is not isolated, but coupled to
the detector), and not a process of the mind.
Without irreversibility no experimental record, hence no measurement,
hence no collapse. Experimental records are therefore intimately tied
to irreversibility, hence to thermodynamics. Ultimately, the second
law is responsible for the observability of Nature.
> Even in Max Born it is possible to find many (very) different
> interpretations of the 'reduction' (and of the wave-funtion).
> In example "The question of whether the waves are something
> "real" or a function to describe and predict phenomena in
> a convenient way is a matter of taste. I personally like
> to regard a probability wave, even in 3N-dimensional space,
> as a real thing, certainly as more than a tool for mathematical
> calculations ... Quite generally, how could we rely on
> probability predictions if by this notion we do not refer
> to something real and objective?" [Max Born, Dover publ., 1964,
> "Natural Philosophy of Cause and Chance", p. 107.]
I share this assesment of Born.
Thanks for the quotes!
Arnold Neumaier
Aaron Bergman
Jun2-05, 12:38 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <429CC172.3010801@synopsys.com>,\nEugene Stefanovich <eugenev@synopsys.com> wrote:\n\n> 2. Quantum mechanics does not explain the origin of these probabilities.\n> All QM can do is to calculate these probabilities.\n> In textbook QM, the formula |<a|psi>|^2 is a postulate, but this\n> formula can be derived from a more fundamental "quantum logic" approach.\n> (see chapter 4 in physics/0504062)\n> If you know the rules of quantum mechanics, you can describe the\n> state of your system by a vector |psi> in the Hilbert space,\n> and the measurement by another vector |a>, and calculate/predict\n> the probability of finding value a in the state |psi> by using above\n> formula.\n\nOutside of this \'envariance\' stuff that I don\'t really understand, I\nknow of no way to derive the probability rules from QM -- in particular,\nthe use of the reduced density matrix really already assumes the Born\nrule. Even envariance assumes, a priori, that these probabilities exist\nwhich seems to be avoiding the central question to me.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <429CC172.3010801@synopsys.com>,
Eugene Stefanovich <eugenev@synopsys.com> wrote:
> 2. Quantum mechanics does not explain the origin of these probabilities.
> All QM can do is to calculate these probabilities.
> In textbook QM, the formula |<a|\psi>|^2 is a postulate, but this
> formula can be derived from a more fundamental "quantum logic" approach.
> (see chapter 4 in http://www.arxiv.org/abs/physics/0504062)
> If you know the rules of quantum mechanics, you can describe the
> state of your system by a vector |\psi> in the Hilbert space,
> and the measurement by another vector |a>, and calculate/predict
> the probability of finding value a in the state |\psi> by using above
> formula.
Outside of this 'envariance' stuff that I don't really understand, I
know of no way to derive the probability rules from QM -- in particular,
the use of the reduced density matrix really already assumes the Born
rule. Even envariance assumes, a priori, that these probabilities exist
which seems to be avoiding the central question to me.
Aaron
Aaron Bergman
Jun2-05, 12:38 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117557478.880943.122100@g14g2000cwa.googlegroups .com>,\n"I.Vecchi" <vecchi@weirdtech.com> wrote:\n\n> Aaron Bergman wrote:\n> > In article <1117448074.219697.96620@f14g2000cwb.googlegroups. com>,\n> > "Seratend" <ser_monmail@yahoo.fr> wrote:\n> ..\n> > > Now how can you deduce (from QM theory) the preferred basis and what we\n> > > "really" measure in this experiment?\n> >\n> > You need to describe to me the macroscopic degrees of freedom in your\n> > experiment, ie, the macrostates by which you are performing your\n> > observation.\n>\n> Isn\'t this obviously circular? Aren\'t the "the macrostates by which you\n> are performing your observation" precisely what decoherence is supposed\n> to derive from a purely quantum description the process?\n\nI don\'t think see how. The macrostates are your pointer states.\nDecoherence is the process wherein the zillions of degrees of freedom in\nyour pointer conspire to diagonalize the reduced density matrix in the\npointer basis.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117557478.880943.122100@g14g2000cwa.googlegroups. com>,
"I.Vecchi" <vecchi@weirdtech.com> wrote:
> Aaron Bergman wrote:
> > In article <1117448074.219697.96620@f14g2000cwb.googlegroups.c om>,
> > "Seratend" <ser_monmail@yahoo.fr> wrote:
> ..
> > > Now how can you deduce (from QM theory) the preferred basis and what we
> > > "really" measure in this experiment?
> >
> > You need to describe to me the macroscopic degrees of freedom in your
> > experiment, ie, the macrostates by which you are performing your
> > observation.
>
> Isn't this obviously circular? Aren't the "the macrostates by which you
> are performing your observation" precisely what decoherence is supposed
> to derive from a purely quantum description the process?
I don't think see how. The macrostates are your pointer states.
Decoherence is the process wherein the zillions of degrees of freedom in
your pointer conspire to diagonalize the reduced density matrix in the
pointer basis.
Aaron
Seratend
Jun2-05, 12:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Seratend wrote:\n>\n> > Arnold Neumaier wrote:\n> >\n> >>Seratend wrote:\n> >>\n> >>>QM deals only with statistics of outcomes\n> >>>and, in my opinion, outcomes are the "classical world" (what we "see").\n> >>\n> >>In my opinion, the "classical world" (what we "see") is the world\n> >>as seen after irreversible effects have set in, i.e., the world\n> >>as described by nonequilibrium thermodynamics (including hydromechanics\n> >>and kinetic theory).\n> >\n> > Interesting.\n> > You seem to view the measurement results exclusively through the mean\n> > value filter\n>\n> Yes. Mean values of thermodynamic origin are the raw observables\n> in all experiments; everything else is derived from these by theory\n> or speculation.\n> I call this the \'consistent experiment interpretation\', following\n> first steps in this direction taken in Section 10 of\n> quant-ph/0303047 =3D Int. J. Mod. Phys. B 17 (2003), 2937-2980.\n> Since I wrote this, my view has considerably gained in strength.\n> If you read German, you can find much more about it at\n> http://www.mat.univie.ac.at/~neum/physik-faq.tex\n\nUnfortunately, I do not read German (and I regret it today : ).\nHowever, I am greatly interested by the mean value filter and hope that\nyou will be able to post soon the English version.\nI have also looked at your paper, section 10, but it not easy to\nunderstand the section alone (as the document is consistent : ) and\nmore precisely what do you intend by consistent experiment. Currently,\nI would like to understand what part of thermodynamics you want to use\nto derive some results.\n> In the mean time,\n> I am happy to feed the main qualitative arguments into this\n> discussion, if you are interested.\n>\nPlease do, I will be also very happy to understand your point of view.\n>\n> > in my point of view (like the interference pattern: single\n> > photon screen impact event versus multiple independent photons\n> > interference pattern event).\n> > How do you explain the observed state of a single photon event?\n>\n> It is only a sloppy way of speaking, not a real physical event.\n> What actually happens is the following:\n>\n> The light ray of a laser is an electromagnetic field localized in a\n> small region along the ray that begins in the laser and ends at the\n> photodetector. A ray of intensity I is described by a coherent state\n> |I>> = |0> + I|1> + I^2/2|2> + I^3/6|3> + ...\n> If I is tiny then, from time to time, an electron responds (in some\n> loose way of speaking that itself would need correction) to the\n> energy continuously transmitted by the ray by going into an excited\n> state, an event which is magnified in the detector and recorded.\n> These occasional events form a Poisson process, with a rate proportional\n> to the intensity I. This, no more and no less, is the experimental\n> observation. It is precisely what is predicted by quantum mechanics.\n>\nYes, but we have 2 possible observations for this experiment assuming\nthe independence of the triggering events of the detectors (e.g. CCD to\ncover the space of the interference pattern): Single events or the\ncomplete set of events (the complete interference pattern).\nBy single events, I mean an experiment where the intensity is so weak\nas we just have one click for one experiment trial (the electron case).\n\nFor the second experiment trial, there is sufficient intensity to\ntrigger the whole pattern (multiple independent electron case in time).\n\n> The traditional sloppy way of picturing this in an intuitive way is to\n> say that, from time to time, a photon arrives at the screen and kicks\n> an electron out of its orbit. This is a nice picture, especially for\n> the newcomer or the lay man, but it cannot be taken any more seriously\n> than Bohr\'s picture of an atom, in which electrons orbit a nucleus in\n> certain quantum orbits. For nothing of this can be checked by experiment\n> - it is empty talk intended to serve intuition, but in fact causing more\n> damange than understanding.\n>\nI agree, I do not care about the reality of the photon. I just want\nthat the generic mathematical model may be applied to every experiment\nand in some experiments, this model may be compatible with the particle\nview.\n\n> Another way to see that is that the photo effect also happens for\n> fermionic matter in a classical external field. (See, e.g., the\n> quantum optics book by mandel and Wolf.) Thus the observed\n> Poisson process cannot be a consequence of quantized light, but\n> rather is an indication of quantized detectors.\n>\nYes. However, in the case of single events (of the detector), we are\njust able to apply the mean value statistics to the detector (huge set\nof random variables/observables). In this case, I think the mean value\nfilter does not apply to the "particle" but only to the single\ntriggered detector: we may explain its "deterministic" triggering\nvalue but not the cause of its triggering (except for the peculiar case\nwhere the triggering value is equal to the photon state).\n>\n>\n> > What do you intend by irreversible effects?\n>\n> Dissipation, introduced by the Markov approximation necessary to get\n> a sensible dynamics of a system smaller than the whole universe.\n>\nDissipation means energy exchange or does it also includes other types\nof exchange (such as momentum, assuming energy conservation)?\n\n>\n> >>Everything in thermodynamics and kinetic theory\n> >>is real, objective, without any of the dubiosities that characterize\n> >>the traditional interpretations of the quantum world.\n> >>\n> > Frankly, I have a real problem to see reality behind pressure, volume\n> > and energy/temperature.\n>\n> Ask any engineer. They know what is real. I understand reality in the\n> engineering sense. They can determine the pressure, to within the\n> accuracy allowed by statistical mechanics. A single measurement on a\n> single large quantum system (such as a cup of tee) is usually sufficient\n> to get a reasonable objective value.\n> If this is not real, there is no reality at all, and we are all dreaming.\n>\nOk, I begin to understand better what you may mean when you use the\nworld reality. You are close to the epistemic view of physics, aren\'t\nyou? (the engineering sense).\nIf this is the case, it ok for me: you are not trying to say more that\nit is: what "we" can "see".\n\n>\n> How can you measure a microscopic object without measuring something\n> macroscopic. You need the macroscopic, thermodynamic state of something\n> to assert that indeed some definite, objective event happened.\n> Take away objectivity and you lose all of physics.\n>\nOk, for the macroscopic interface. See my previous answer with the\nphotons as I think there is a misunderstanding. I just question how you\ncan describe the trigger of such a macroscopic device by a single\nparticle event (e.g. an electron in a given quantum state).\nIf you only describe it through statistics (hence requires multiple\noutcomes), Is your description able to predict a preferred basis of the\nquantum state of the particle?\n\n>\n> >>>Therefore, it is relatively difficult for me to understand people who\n> >>>want to demonstrate that there is a physical collapse leading to the\n> >>>outcomes.\n> >>\n> >>The quest is to show that the interaction of a quantum system with\n> >>a macroscopic detector describable by thermodynamics (and hence,\n> >>through statistical mechanics, by quantum theory)\n> >\n> > Statistical classical mechanics?\n>\n> No. Statistical mechanics as taught in textbooks. Which includes\n> (and on the deepest level is only) quantum mechanics.\n>\n(you mean modern statistical mechanics, thus bases on QM and not the\nold gibbs statistical mechanics based on classical mechanics. I always\ntry to separate them as I seem to be an old-fashioned man : ).\n\nOk, I think I begin to understand what you are trying to say (tell me\nIf I am wrong).\nYou are using the mean value filter to try to get deterministic results\nof macroscopic systems (on a given basis of this system: e.g. pressure,\nenergy, position, volume, etc ...). If this is correct, all these\nmacroscopic observables will commute between themselves (simultaneous\nmeasurement possible). If you have a theorem stating that all the\nobservables of a macroscopic system (at the infinite number limit)\ncommute, you solve the preferred basis problem of the measurement.\n\nTherefore, once we define the quantum interaction between the quantum\nparticle and the macroscopic system, we are able to know the states of\nthe quantum particle through the values of the commuting observables of\nthe macroscopic system (e.g. pressure, energy, position, volume, etc\n...) if the decoherence results apply.\n\nVery interesting. May you confirm? (and develop)\nAnd the extra question, do you know such a theorem?\n\nHowever, now, I think if such a theorem is true (exists) for a\nmacroscopic observable, I think we are only be able to infer the local\nstate of the quantum particle associated to the measurement macroscopic\nvalue (local state= partial projection of the global state/density on\nthe highly degenerated basis of the macroscopic system associated to\nthe macroscopic value). While the global state for the given\nmacroscopic value (projection postulate) is the completely entangled\nstate of the quantum particle with the degenerated basis of the\nmacroscopic measurement value => no preferred basis of the particle in\nthe global state (only in the local projected state).\nWe seem to recover no preferred basis property of the collapse\npostulate required to verify the coherence with this hypothetic\ntheorem. Very interesting as I have not considered this aspect before.\n\n> >>\n> > I am not sure I understand what you say. In the QM description, I just\n> > have statistics of outcomes. I have for a macroscopic detetector, a\n> > macroscopic observable A=3D sum_i Ai\n>\n> No. This is not what statistical mechanics teaches. The gurus there say\n> that the quantities thermodynamics is about are expectations of\n> microscopic operators, not their eigenvalues!\n>\nOk, this seems to be the partial trace results. See my comment above. I\nthink if you have such a theorem about the commutation of macroscopic\nobservables of a macroscopic system, we are able to find easily this\nresult (entanglement with the degenerated basis of the macroscopic\nobservable and partial trace). And I think most of my questions may be\nanswered concerning the measurement by macroscopic systems : ).\n\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Seratend wrote:
>
> > Arnold Neumaier wrote:
> >
> >>Seratend wrote:
> >>
> >>>QM deals only with statistics of outcomes
> >>>and, in my opinion, outcomes are the "classical world" (what we "see").
> >>
> >>In my opinion, the "classical world" (what we "see") is the world
> >>as seen after irreversible effects have set in, i.e., the world
> >>as described by nonequilibrium thermodynamics (including hydromechanics
> >>and kinetic theory).
> >
> > Interesting.
> > You seem to view the measurement results exclusively through the mean
> > value filter
>
> Yes. Mean values of thermodynamic origin are the raw observables
> in all experiments; everything else is derived from these by theory
> or speculation.
> I call this the 'consistent experiment interpretation', following
> first steps in this direction taken in Section 10 of
> http://www.arxiv.org/abs/quant-ph/0303047 =3D \Int. J. Mod. Phys. B 17 (2003), 2937-2980.
> Since I wrote this, my view has considerably gained in strength.
> If you read German, you can find much more about it at
> http://www.mat.univie.ac.at/~neum/physik-faq.tex
Unfortunately, I do not read German (and I regret it today : ).
However, I am greatly interested by the mean value filter and hope that
you will be able to post soon the English version.
I have also looked at your paper, section 10, but it not easy to
understand the section alone (as the document is consistent : ) and
more precisely what do you intend by consistent experiment. Currently,
I would like to understand what part of thermodynamics you want to use
to derive some results.
> In the mean time,
> I am happy to feed the main qualitative arguments into this
> discussion, if you are interested.
>
Please do, I will be also very happy to understand your point of view.
>
> > in my point of view (like the interference pattern: single
> > photon screen impact event versus multiple independent photons
> > interference pattern event).
> > How do you explain the observed state of a single photon event?
>
> It is only a sloppy way of speaking, not a real physical event.
> What actually happens is the following:
>
> The light ray of a laser is an electromagnetic field localized in a
> small region along the ray that begins in the laser and ends at the
> photodetector. A ray of intensity I is described by a coherent state
> |I>> = |0> + I|1> + I^2/2|2> + I^3/6|3> + ...
> If I is tiny then, from time to time, an electron responds (in some
> loose way of speaking that itself would need correction) to the
> energy continuously transmitted by the ray by going into an excited
> state, an event which is magnified in the detector and recorded.
> These occasional events form a Poisson process, with a rate proportional
> to the intensity I. This, no more and no less, is the experimental
> observation. It is precisely what is predicted by quantum mechanics.
>
Yes, but we have 2 possible observations for this experiment assuming
the independence of the triggering events of the detectors (e.g. CCD to
cover the space of the interference pattern): Single events or the
complete set of events (the complete interference pattern).
By single events, I mean an experiment where the intensity is so weak
as we just have one click for one experiment trial (the electron case).
For the second experiment trial, there is sufficient intensity to
trigger the whole pattern (multiple independent electron case in time).
> The traditional sloppy way of picturing this in an intuitive way is to
> say that, from time to time, a photon arrives at the screen and kicks
> an electron out of its orbit. This is a nice picture, especially for
> the newcomer or the lay man, but it cannot be taken any more seriously
> than Bohr's picture of an atom, in which electrons orbit a nucleus in
> certain quantum orbits. For nothing of this can be checked by experiment
> - it is empty talk intended to serve intuition, but in fact causing more
> damange than understanding.
>
I agree, I do not care about the reality of the photon. I just want
that the generic mathematical model may be applied to every experiment
and in some experiments, this model may be compatible with the particle
view.
> Another way to see that is that the photo effect also happens for
> fermionic matter in a classical external field. (See, e.g., the
> quantum optics book by mandel and Wolf.) Thus the observed
> Poisson process cannot be a consequence of quantized light, but
> rather is an indication of quantized detectors.
>
Yes. However, in the case of single events (of the detector), we are
just able to apply the mean value statistics to the detector (huge set
of random variables/observables). In this case, I think the mean value
filter does not apply to the "particle" but only to the single
triggered detector: we may explain its "deterministic" triggering
value but not the cause of its triggering (except for the peculiar case
where the triggering value is equal to the photon state).
>
>
> > What do you intend by irreversible effects?
>
> Dissipation, introduced by the Markov approximation necessary to get
> a sensible dynamics of a system smaller than the whole universe.
>
Dissipation means energy exchange or does it also includes other types
of exchange (such as momentum, assuming energy conservation)?
>
> >>Everything in thermodynamics and kinetic theory
> >>is real, objective, without any of the dubiosities that characterize
> >>the traditional interpretations of the quantum world.
> >>
> > Frankly, I have a real problem to see reality behind pressure, volume
> > and energy/temperature.
>
> Ask any engineer. They know what is real. I understand reality in the
> engineering sense. They can determine the pressure, to within the
> accuracy allowed by statistical mechanics. A single measurement on a
> single large quantum system (such as a cup of tee) is usually sufficient
> to get a reasonable objective value.
> If this is not real, there is no reality at all, and we are all dreaming.
>
Ok, I begin to understand better what you may mean when you use the
world reality. You are close to the epistemic view of physics, aren't
you? (the engineering sense).
If this is the case, it ok for me: you are not trying to say more that
it is: what "we" can "see".
>
> How can you measure a microscopic object without measuring something
> macroscopic. You need the macroscopic, thermodynamic state of something
> to assert that indeed some definite, objective event happened.
> Take away objectivity and you lose all of physics.
>
Ok, for the macroscopic interface. See my previous answer with the
photons as I think there is a misunderstanding. I just question how you
can describe the trigger of such a macroscopic device by a single
particle event (e.g. an electron in a given quantum state).
If you only describe it through statistics (hence requires multiple
outcomes), Is your description able to predict a preferred basis of the
quantum state of the particle?
>
> >>>Therefore, it is relatively difficult for me to understand people who
> >>>want to demonstrate that there is a physical collapse leading to the
> >>>outcomes.
> >>
> >>The quest is to show that the interaction of a quantum system with
> >>a macroscopic detector describable by thermodynamics (and hence,
> >>through statistical mechanics, by quantum theory)
> >
> > Statistical classical mechanics?
>
> No. Statistical mechanics as taught in textbooks. Which includes
> (and on the deepest level is only) quantum mechanics.
>
(you mean modern statistical mechanics, thus bases on QM and not the
old gibbs statistical mechanics based on classical mechanics. I always
try to separate them as I seem to be an old-fashioned man : ).
Ok, I think I begin to understand what you are trying to say (tell me
If I am wrong).
You are using the mean value filter to try to get deterministic results
of macroscopic systems (on a given basis of this system: e.g. pressure,
energy, position, volume, etc ...). If this is correct, all these
macroscopic observables will commute between themselves (simultaneous
measurement possible). If you have a theorem stating that all the
observables of a macroscopic system (at the infinite number limit)
commute, you solve the preferred basis problem of the measurement.
Therefore, once we define the quantum interaction between the quantum
particle and the macroscopic system, we are able to know the states of
the quantum particle through the values of the commuting observables of
the macroscopic system (e.g. pressure, energy, position, volume, etc
...) if the decoherence results apply.
Very interesting. May you confirm? (and develop)
And the extra question, do you know such a theorem?
However, now, I think if such a theorem is true (exists) for a
macroscopic observable, I think we are only be able to infer the local
state of the quantum particle associated to the measurement macroscopic
value (local state= partial projection of the global state/density on
the highly degenerated basis of the macroscopic system associated to
the macroscopic value). While the global state for the given
macroscopic value (projection postulate) is the completely entangled
state of the quantum particle with the degenerated basis of the
macroscopic measurement value => no preferred basis of the particle in
the global state (only in the local projected state).
We seem to recover no preferred basis property of the collapse
postulate required to verify the coherence with this hypothetic
theorem. Very interesting as I have not considered this aspect before.
> >>
> > I am not sure I understand what you say. In the QM description, I just
> > have statistics of outcomes. I have for a macroscopic detetector, a
> > macroscopic observable A=3D sum_i Ai
>
> No. This is not what statistical mechanics teaches. The gurus there say
> that the quantities thermodynamics is about are expectations of
> microscopic operators, not their eigenvalues!
>
Ok, this seems to be the partial trace results. See my comment above. I
think if you have such a theorem about the commutation of macroscopic
observables of a macroscopic system, we are able to find easily this
result (entanglement with the degenerated basis of the macroscopic
observable and partial trace). And I think most of my questions may be
answered concerning the measurement by macroscopic systems : ).
Seratend.
Seratend
Jun2-05, 12:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n\n> I am looking for an explanation why a particular detector coupled\n> to a particular quantum system produces the observed erratic but\n> objective record of individual results that can be analyzed\n> statistically and quoted in a physics journal.\n>\nMe too. I just consider mathematics and experiment results to build\nlogical deductions.\n\n> If you want to claim more than that these outcomes are just the\n> results of changes of belief (aka \'knowledge\') in an observer\'s mind\n> - and I think physics does and should claim more than that -\n\nI agree. I prefer to have a logical view (mathematics) of what we\ndescribe: the only thing I know. In my sentences, the "we see" may\nbe anybody: a machine, a particle etc ... (very weak signification)\nand should not considered as a mind or everything else out of the\nsubject.\nThere are no minds just logical propositions or properties if you\nprefer that are true in each considered case (logical view). Everything\nelse is interpretation. We have to map these properties to the\n"reality" to verify the results, that\'s all (what you may call\nthe objective record in some cases). (like the mathematical circle\nobject and the drawing of a circle). The mapping may be falsified by\nthe experiments not the mathematical theory (supposed to be\nconsistent).\nHence, I may choose to describe a system by statistical or\ndeterministic tools. For quantum systems, I have not simple results in\nthe deterministic tools (e.g. bohmian mechanics as it requires the\ncreation of a specific un-measurable object, the path of the bohmian\nparticle) while the statistical results are simpler.\n>\n>\n> >>I gave a concise formulation of a specific case of this quest in\n> >>my recent paper quant-ph/0505172.\n> >>\n> > I have read quickly you paper. I have not found the original thread.\n>\n> Type "collapse challenge" into\n> http://groups-beta.google.com/groups?q=%22collapse+challenge%22&qt_s=Search\n>\n>\n> > So I have some questions:\n> > a) what is the initial state of the photon (assuming a wave packet) :\n> > |psi>= |path1>+|path2> with <path1|path2>=0?\n>\n> Not quite. Roughly,\n> |psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>\n> with spatial coherent states |pathi(t)> (i=1,2) moving at the\n> velocity of light and monochromatic 1-Photon Fock states |1>, say.\n\nOk, usually when I write a state |path1>, this state may be the tensor\nproduct of whatever we want (we may expand it when it is required).\nTherefore, you seem to require the detail of this state:\n\n|psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?\n\nWhere <x|path1(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given\ntransversal area we may call it A\nAnd <x|path2(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given\ntransversal area we may call it B\n\nSuch that {A} intersection {B} is empty.\n\n> The actual situation would be more complicated since single\n> photon states are electromagnetic waves (solutions of the free\n> Maxwell equations) approximately localized along some direction.\n\nOk, we may approximate these states as free moving wave packets outside\nthe are of interactions of the screens.\n\n> The challenge allows, however, any specific setting (even\n> idealized, or with massive particles, etc.) that matches the\n> informal description in a reasonable way.\n>\nIn other words we are free to choose the interactions and the\nHamiltonians as I have done it in another post in this thread for the\ninterference toy model.\n>\n> > b) if yes, |path1> and |path2> are for example 2 parallel paths, where\n> > |path1> is 100% stopped by the first screen and |path2> 100% not?\n>\n> Yes. This is an example that can be prepared by half-silvered mirrors.\n>\n>\n> > c) what do you want to say?\n> >\n> > I mean, I have a system that is well described through unitary\n> > evolution (superposition of states).\n>\n> Absorption by a screen is an irreversible macroscopic process\n> accompanied by a minute increase of temperature. The claim that\n> it is described by unitary evolution requires proof, which,\n> if successful, would be part of an answer of the challenge.\n>\nSee my description of the interference pattern toy model. I have\nchoosen Hamiltonians and interactions such that we have no entanglement\nbetween the photons and the screens (formal choice): H_screen=\n|screen><screen|(x)V(r)\nI usually prefer to replace photons by electrons, whenever it does not\nchange the global result as the free propagator of photons and\nelectrons are the same. In the case of photons, V(r) is the effective\npotential giving the source of the reflection or the transmission.\nThis model supposes the energy conservation between photons and the\nscreens (choice) and it is easy to see that everything evolves unitary,\njust by taking the wave packet.\n\nI may expand my explanation if required.\n\n> If there is unitary dynamics only then the final result is not\n> the state |0,1,1> or |0,0,1> as observed, but a superposition\n> of the two. Invoking Born\'s rule is _assuming_ the collapse\n> rather than explaining it.\n>\nI like this toy model where we force no entanglement between the\nphotons states and the screens and where we have the simple unitary\nevolution of the initial state. It reflects perfectly what we do on an\nexperiment that reflects this unitary evolution:\na) we have to choose between all the photons, the one with the initial\nstate (hence an initial measurement result)\nb) we simultaneously measure the reflected photons by either the first\nscreen or the second one outside the area of the local interaction of\nthe screens (here I suppose the plane of the reflecting screens are not\northogonal to the beam direction in order to put the "real"\ndetector outside the incoming beam. We have only a single detector that\nclicks at a time assuming the good energy trigger level on a restricted\narea.\n\nWe can put the detectors or not, they do not change the result of the\ntransformation of the wave function by the two screens before it is\ndetected by the detectors (we assume a local interaction of the\ndetectors: a choice). If we develop more, we see that the projector of\nthe detectors (the spatial location) commutes with the interaction of\nthe screens.\n\nAssuming this, we can say (interpretation) that the screens do not\ncollapse the wave function if we have no detectors, while if we put the\ndetectors we can say that the screen collapses the wave function.\n=> the collapse is only an acknowledgement of the results (a property\nof the system is true). Or if you prefer a view of a particular branch\nof the unitary evolution of all possible states.\n\nThe only possibility to get coherent results is to assume that a\ncollapse is the acknowledge of a given property on a given system. This\nis only mathematics: we have a set of experimental trials object where\n2 properties are true: the initial measurement to prepare the initial\nstate and the final measurement result. If you prefer, we can see it as\ncontextual random variables outcomes.\n\n\n> That something remains to be explained even from the Copenhagen\n> point of view (some version of which you seem to adhere to)\n> is discussed in Section 3.\n>\nCopenhagen interpretation does not assume the "reality" of the\nwavefunction. What it says is very analogue to what I say. There is\nmost of the time, with CI, in my opinion, a misunderstanding on the\nmeaning of "before" or "after" the measurement. Just replace\nthe word "before" by "there is no measurement" and "after"\nby "there is a measurement". Therefore, each instance of a system\nhas a single property: either there is a measurement or not (with its\nassociated definite single results).\nThere is no system where we have no measurement before and "after"\na measurement appears from nowhere. We have a measured system (of a\ngiven value) or not (no time reference).\n>\n>\n> > At the end, I must apply the born\n> > rules to get the statistics (what I see in the experiment).\n>\n> This is the informal prescription that is used to apply single-particle\n> reasoning to a complex multiparticle experiment. It successfully\n> avoids looking at the physics happening at the screen, replacing it\n> by simply assuming the collapse, i.e., the emergence of an objective\n> record according to the probabilities from the Born rule.\n> While this is an acceptable attitude it is obviously not the whole\n> story.\n>\nThis is what I call the statistical description of the physical\nphenomena (we do not explain the outcomes, we just measure their\nfrequency and their evolution in the space time).\nThe description of the outcomes production is the deterministic view.\nIt thus requires a description compatible with the statistical one. I\nwill say why not to use the bohmian mechanics?\n\n>\n> > Are you just searching for a predictive description of a particular\n> > outcome in a given QM experiment?\n>\n> Just an explanation for how particular outcomes arise through\n> measurement. Leaving something as complex as \'measurement\' as\n> an uninterpreted, vague fundamental concept, while practical\n> measurement is a whole science in itself seem to me too gross\n> a simplification to be tolerable, and one of the reasons why the\n> foundations of QM are in the poor present state.\n>\nDo you reject the deterministic bohmian formulation (at least in the\nnon relativistic case where it is the best achieved)?\n(I mean the mathematical formulation connection predicting the outcomes\nand not the interpretations).\n\nSeratend\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> I am looking for an explanation why a particular detector coupled
> to a particular quantum system produces the observed erratic but
> objective record of individual results that can be analyzed
> statistically and quoted in a physics journal.
>
Me too. I just consider mathematics and experiment results to build
logical deductions.
> If you want to claim more than that these outcomes are just the
> results of changes of belief (aka 'knowledge') in an observer's mind
> - and I think physics does and should claim more than that -
I agree. I prefer to have a logical view (mathematics) of what we
describe: the only thing I know. In my sentences, the "we see" may
be anybody: a machine, a particle etc ... (very weak signification)
and should not considered as a mind or everything else out of the
subject.
There are no minds just logical propositions or properties if you
prefer that are true in each considered case (logical view). Everything
else is interpretation. We have to map these properties to the
"reality" to verify the results, that's all (what you may call
the objective record in some cases). (like the mathematical circle
object and the drawing of a circle). The mapping may be falsified by
the experiments not the mathematical theory (supposed to be
consistent).
Hence, I may choose to describe a system by statistical or
deterministic tools. For quantum systems, I have not simple results in
the deterministic tools (e.g. bohmian mechanics as it requires the
creation of a specific un-measurable object, the path of the bohmian
particle) while the statistical results are simpler.
>
>
> >>I gave a concise formulation of a specific case of this quest in
> >>my recent paper http://www.arxiv.org/abs/quant-ph/0505172.
> >>
> > I have read quickly you paper. I have not found the original thread.
>
> Type "collapse challenge" into
> http://groups-\beta.google.com/groups?q=%22collapse+challenge%22&qt_s=Search
>
>
> > So I have some questions:
> > a) what is the initial state of the photon (assuming a wave packet) :
> > |\psi>= |path1>+|path2> with <path1|path2>=0?
>
> Not quite. Roughly,
> |\psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>
> with spatial coherent states |pathi(t)> (i=1,2) moving at the
> velocity of light and monochromatic 1-Photon Fock states |1>, say.
Ok, usually when I write a state |path1>, this state may be the tensor
product of whatever we want (we may expand it when it is required).
Therefore, you seem to require the detail of this state:
|\psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?
Where <x|path1(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given
transversal area we may call it A
And <x|path2(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given
transversal area we may call it B
Such that {A} intersection {B} is empty.
> The actual situation would be more complicated since single
> photon states are electromagnetic waves (solutions of the free
> Maxwell equations) approximately localized along some direction.
Ok, we may approximate these states as free moving wave packets outside
the are of interactions of the screens.
> The challenge allows, however, any specific setting (even
> idealized, or with massive particles, etc.) that matches the
> informal description in a reasonable way.
>
In other words we are free to choose the interactions and the
Hamiltonians as I have done it in another post in this thread for the
interference toy model.
>
> > b) if yes, |path1> and |path2> are for example 2 parallel paths, where
> > |path1> is 100% stopped by the first screen and |path2> 100% not?
>
> Yes. This is an example that can be prepared by half-silvered mirrors.
>
>
> > c) what do you want to say?
> >
> > I mean, I have a system that is well described through unitary
> > evolution (superposition of states).
>
> Absorption by a screen is an irreversible macroscopic process
> accompanied by a minute increase of temperature. The claim that
> it is described by unitary evolution requires proof, which,
> if successful, would be part of an answer of the challenge.
>
See my description of the interference pattern toy model. I have
choosen Hamiltonians and interactions such that we have no entanglement
between the photons and the screens (formal choice): H_{screen}=
|screen><screen|(x)V(r)
I usually prefer to replace photons by electrons, whenever it does not
change the global result as the free propagator of photons and
electrons are the same. In the case of photons, V(r) is the effective
potential giving the source of the reflection or the transmission.
This model supposes the energy conservation between photons and the
screens (choice) and it is easy to see that everything evolves unitary,
just by taking the wave packet.
I may expand my explanation if required.
> If there is unitary dynamics only then the final result is not
> the state |0,1,1> or |0,0,1> as observed, but a superposition
> of the two. Invoking Born's rule is _assuming_ the collapse
> rather than explaining it.
>
I like this toy model where we force no entanglement between the
photons states and the screens and where we have the simple unitary
evolution of the initial state. It reflects perfectly what we do on an
experiment that reflects this unitary evolution:
a) we have to choose between all the photons, the one with the initial
state (hence an initial measurement result)
b) we simultaneously measure the reflected photons by either the first
screen or the second one outside the area of the local interaction of
the screens (here I suppose the plane of the reflecting screens are not
orthogonal to the beam direction in order to put the "real"
detector outside the incoming beam. We have only a single detector that
clicks at a time assuming the good energy trigger level on a restricted
area.
We can put the detectors or not, they do not change the result of the
transformation of the wave function by the two screens before it is
detected by the detectors (we assume a local interaction of the
detectors: a choice). If we develop more, we see that the projector of
the detectors (the spatial location) commutes with the interaction of
the screens.
Assuming this, we can say (interpretation) that the screens do not
collapse the wave function if we have no detectors, while if we put the
detectors we can say that the screen collapses the wave function.
=> the collapse is only an acknowledgement of the results (a property
of the system is true). Or if you prefer a view of a particular branch
of the unitary evolution of all possible states.
The only possibility to get coherent results is to assume that a
collapse is the acknowledge of a given property on a given system. This
is only mathematics: we have a set of experimental trials object where
2 properties are true: the initial measurement to prepare the initial
state and the final measurement result. If you prefer, we can see it as
contextual random variables outcomes.
> That something remains to be explained even from the Copenhagen
> point of view (some version of which you seem to adhere to)
> is discussed in Section 3.
>
Copenhagen interpretation does not assume the "reality" of the
wavefunction. What it says is very analogue to what I say. There is
most of the time, with CI, in my opinion, a misunderstanding on the
meaning of "before" or "after" the measurement. Just replace
the word "before" by "there is no measurement" and "after"
by "there is a measurement". Therefore, each instance of a system
has a single property: either there is a measurement or not (with its
associated definite single results).
There is no system where we have no measurement before and "after"
a measurement appears from nowhere. We have a measured system (of a
given value) or not (no time reference).
>
>
> > At the end, I must apply the born
> > rules to get the statistics (what I see in the experiment).
>
> This is the informal prescription that is used to apply single-particle
> reasoning to a complex multiparticle experiment. It successfully
> avoids looking at the physics happening at the screen, replacing it
> by simply assuming the collapse, i.e., the emergence of an objective
> record according to the probabilities from the Born rule.
> While this is an acceptable attitude it is obviously not the whole
> story.
>
This is what I call the statistical description of the physical
phenomena (we do not explain the outcomes, we just measure their
frequency and their evolution in the space time).
The description of the outcomes production is the deterministic view.
It thus requires a description compatible with the statistical one. I
will say why not to use the bohmian mechanics?
>
> > Are you just searching for a predictive description of a particular
> > outcome in a given QM experiment?
>
> Just an explanation for how particular outcomes arise through
> measurement. Leaving something as complex as 'measurement' as
> an uninterpreted, vague fundamental concept, while practical
> measurement is a whole science in itself seem to me too gross
> a simplification to be tolerable, and one of the reasons why the
> foundations of QM are in the poor present state.
>
Do you reject the deterministic bohmian formulation (at least in the
non relativistic case where it is the best achieved)?
(I mean the mathematical formulation connection predicting the outcomes
and not the interpretations).
Seratend
Seratend
Jun2-05, 12:43 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1117568337.945299.75400@g14g2000cwa.googlegroups. com>,\n> > >\n> > In my opinion, I think you are trying to say more than QM theory says.\n>\n> Funny, I feel the same way.\n>\n: ) . I prefer that.\n\n> > You seem to be a adept of the wave function reality hence you try to\n> > define something out of the scope of the current QM theory formulation\n> > (an explication of the collapse) while I simply take the born rules as\n> > statistics of outcomes and the collapse postulate the property where a\n> > given outcome value of a system is true ("Outcome A=a" true).\n>\n> I don\'t consider the Born rule part of QM. QM is unitary evolution.\n> Everything is else is what we do to make sense of the wavefunction. The\n> Born rules are a pragmatic procedure, but they lack a microscopic\n> mechanism.\n>\nI hope you also consider the statistics of statistical classical\nmechanics as pragmatic procedures. If this is the case, you are simply\nlooking for the deterministic evolution of individual outcomes from a\ngiven initial condition:\nOutcome_i(t)= f(outcome_1(to), outcome_n(to),t).\nIf it is what you are looking for, general unitary evolution tells you\nthat it is most of the time impossible: we have at most a functional\nrelation: Outcome_i= f(outcome_1, outcome_n,t) (the function\nOutcome_i(t) depends on the functions outcome_1...n(t) and not on their\nvalues).\n\n>\n> Are you advocating a sort of consistent histories approach?\n\nWell, I promote the shut up and calculate approach I think: just\nmathematics, where we map formally the values of the mathematical\nobjects/values to the experiments. All of the interpretations of QM are\nvery similar, if you do not try to attach a too strong reality to the\nused words. Consistent, many worlds, many minds, my mind, my leg etc\n... : ) all are flavours of the same mathematical theory, they are ok\nif they do not change the predictive results of the formal theory.\nInterpretation, for me is rather the domain of philosophy. Adding or\nremoving it does not change the results of the mapping.\n\n> That seems to me to be a language in which to describe quantum outcomes, but\n> nothing like an interpretation.\nI think my point of view is closer to the epistemic view. I do not\nrequire any "reality", whatever it is, just that the mapping of the\nmathematical predictions agree with experiment. In this sense, the\ncollapse is a property of the system and not a transformation of the\nsystem ( a given system is "collapsed" or not - the collapse identity -\nbut it cannot become collapsed: no meaning).\n\n> Regardless, when you make a real-world\n> measurement, you better collapse the wavefunction, whether through\n> decoherence or some other manner, or you will get the wrong answer. For\n> future measurements.\n>\nYou really get a classical deterministic point of view. You seem to\nthink that the only possible determinisitc relation is Outcome_i(t)=\nf(outcome_1(to), outcome_n(to),t).\nWhile you may have the deterministic functional relation Outcome_i=\nf(outcome_1, outcome_n,t).\nThe latter tells you that you may not have a relation between future\noutcomes and past outcomes, just between the functions (function of\nsets rather than of points). Therefore, the only way to connect 2\noutcomes in an experiment is the direct "observation" (the formal\nlabelling of the outcomes): the collapse.\n\n>\n> No. You understand your measurement apparatus. It\'s not a mystery. There\n> are macroscopic degrees of freedom -- work backwards from there and you\n> know what your \'preferred basis\' is.\n>\n> [snip to end]\n>\n> I\'m sorry, but I can\'t figure out what you\'re talking about in your\n> experiment.\n>\nWell I simply have constructed a thought experiment (the well known\ndouble slit) where I have a unitary evolution of the photons/electrons\nstate, the slit plate and the screen without *entanglement*.\nI may say that this experiment does not realize any measurement. While\nif I am looking (or a detector) at the light scattered by the screen, I\nmay say the screen has performed a position measurement (the\ninterference pattern) without entanglement with the photons.\n\nHow can you place your decoherence procedure in such a situation to\nfind the preferred basis.\n\nDo you really understand that this simple toy model does not provide\nany entanglement?:\n\nThe interaction between the screen and the electrons/photon is\ndescribed by the Hamiltonian H=|screen><screen|(x)Vdiff(r). It is well\ndefined (formally). You may consider it, if you like, as a "strange\nparticle" with one degree of freedom as a spin 0 particle. The\ninteraction potential does not entangled the screen with the\nelectron/photon.\n\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1117568337.945299.75400@g14g2000cwa.googlegroups.c om>,
> > >
> > In my opinion, I think you are trying to say more than QM theory says.
>
> Funny, I feel the same way.
>
: ) . I prefer that.
> > You seem to be a adept of the wave function reality hence you try to
> > define something out of the scope of the current QM theory formulation
> > (an explication of the collapse) while I simply take the born rules as
> > statistics of outcomes and the collapse postulate the property where a
> > given outcome value of a system is true ("Outcome A=a" true).
>
> I don't consider the Born rule part of QM. QM is unitary evolution.
> Everything is else is what we do to make sense of the wavefunction. The
> Born rules are a pragmatic procedure, but they lack a microscopic
> mechanism.
>
I hope you also consider the statistics of statistical classical
mechanics as pragmatic procedures. If this is the case, you are simply
looking for the deterministic evolution of individual outcomes from a
given initial condition:
Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).
If it is what you are looking for, general unitary evolution tells you
that it is most of the time impossible: we have at most a functional
relation: Outcome_i= f(outcome_1, outcome_n,t) (the function
Outcome_i(t) depends on the functions outcome_1...n(t) and not on their
values).
>
> Are you advocating a sort of consistent histories approach?
Well, I promote the shut up and calculate approach I think: just
mathematics, where we map formally the values of the mathematical
objects/values to the experiments. All of the interpretations of QM are
very similar, if you do not try to attach a too strong reality to the
used words. Consistent, many worlds, many minds, my mind, my leg etc
... : ) all are flavours of the same mathematical theory, they are ok
if they do not change the predictive results of the formal theory.
Interpretation, for me is rather the domain of philosophy. Adding or
removing it does not change the results of the mapping.
> That seems to me to be a language in which to describe quantum outcomes, but
> nothing like an interpretation.
I think my point of view is closer to the epistemic view. I do not
require any "reality", whatever it is, just that the mapping of the
mathematical predictions agree with experiment. In this sense, the
collapse is a property of the system and not a transformation of the
system ( a given system is "collapsed" or not - the collapse identity -
but it cannot become collapsed: no meaning).
> Regardless, when you make a real-world
> measurement, you better collapse the wavefunction, whether through
> decoherence or some other manner, or you will get the wrong answer. For
> future measurements.
>
You really get a classical deterministic point of view. You seem to
think that the only possible determinisitc relation is Outcome_i(t)=f(outcome_1(to), outcome_n(to),t).
While you may have the deterministic functional relation Outcome_i=f(outcome_1, outcome_n,t).
The latter tells you that you may not have a relation between future
outcomes and past outcomes, just between the functions (function of
sets rather than of points). Therefore, the only way to connect 2
outcomes in an experiment is the direct "observation" (the formal
labelling of the outcomes): the collapse.
>
> No. You understand your measurement apparatus. It's not a mystery. There
> are macroscopic degrees of freedom -- work backwards from there and you
> know what your 'preferred basis' is.
>
> [snip to end]
>
> I'm sorry, but I can't figure out what you're talking about in your
> experiment.
>
Well I simply have constructed a thought experiment (the well known
double slit) where I have a unitary evolution of the photons/electrons
state, the slit plate and the screen without *entanglement*.
I may say that this experiment does not realize any measurement. While
if I am looking (or a detector) at the light scattered by the screen, I
may say the screen has performed a position measurement (the
interference pattern) without entanglement with the photons.
How can you place your decoherence procedure in such a situation to
find the preferred basis.
Do you really understand that this simple toy model does not provide
any entanglement?:
The interaction between the screen and the electrons/photon is
described by the Hamiltonian H=|screen><screen|(x)Vdiff(r). It is well
defined (formally). You may consider it, if you like, as a "strange
particle" with one degree of freedom as a spin particle. The
interaction potential does not entangled the screen with the
electron/photon.
Seratend.
Eugene Stefanovich
Jun2-05, 12:44 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n\n> I am looking for an explanation why a particular detector coupled\n> to a particular quantum system produces the observed erratic but\n> objective record of individual results that can be analyzed\n> statistically and quoted in a physics journal.\n\n\nThat\'s a noble goal, but it has nothing to do with quantum mechanics.\nQuantum mechanics does not explain why results of measurements are\nerratic. QM cannot predict the exact sequence of these erratic\nmeasurements. All it can do is to predict with very high accuracy\nthe probabilities of different outcomes.\n\nThe "explanation" of apparently unpredictable behavior of quantum\nsystems has been promised by the "hidden variable" theory, but never\ndelivered. The answers to these questions should be given by a\ntheory more fundamental than quantum mechanics. My personal belief\nis that such a theory does not exist, and the random behavior\nof microsystems will remain unexplained.\n\nEugene Stefanovich.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> I am looking for an explanation why a particular detector coupled
> to a particular quantum system produces the observed erratic but
> objective record of individual results that can be analyzed
> statistically and quoted in a physics journal.
That's a noble goal, but it has nothing to do with quantum mechanics.
Quantum mechanics does not explain why results of measurements are
erratic. QM cannot predict the exact sequence of these erratic
measurements. All it can do is to predict with very high accuracy
the probabilities of different outcomes.
The "explanation" of apparently unpredictable behavior of quantum
systems has been promised by the "hidden variable" theory, but never
delivered. The answers to these questions should be given by a
theory more fundamental than quantum mechanics. My personal belief
is that such a theory does not exist, and the random behavior
of microsystems will remain unexplained.
Eugene Stefanovich.
Joe Rongen
Jun2-05, 02:11 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n> Arnold Neumaier wrote:\n>\n> > I am looking for an explanation why a particular detector coupled\n> > to a particular quantum system produces the observed erratic but\n> > objective record of individual results that can be analyzed\n> > statistically and quoted in a physics journal.\n\n\nSome detector systems employ photomultiplier tube(s).\n\nThe ideal photomultiplier tube is a detector that basically\nabsorbs (photo-electric effect) one photon and internally\nconverts/produces** due to an electron cascade/amplifier\neffect, one measurable event.\n\n** Lawrence and Beams showed in 1928 that photo-electrons are\nsometimes emitted less than 3 *10^(-9) sec after initial illumination.\n\nBest regards Joe\n\n\n--\nNo virus found in this outgoing message.\nChecked by AVG Anti-Virus.\nVersion: 7.0.322 / Virus Database: 267.4.1 - Release Date: 6/2/05\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
>
> > I am looking for an explanation why a particular detector coupled
> > to a particular quantum system produces the observed erratic but
> > objective record of individual results that can be analyzed
> > statistically and quoted in a physics journal.
Some detector systems employ photomultiplier tube(s).
The ideal photomultiplier tube is a detector that basically
absorbs (photo-electric effect) one photon and internally
converts/produces** due to an electron cascade/amplifier
effect, one measurable event.
** Lawrence and Beams showed in 1928 that photo-electrons are
sometimes emitted less than 3 *10^(-9) sec after initial illumination.
Best regards Joe
--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7..322 / Virus Database: 267.4.1 - Release Date: 6/2/05
Aaron Bergman
Jun2-05, 02:11 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117635044.686082.94270@g49g2000cwa.googlegroups. com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n> > In article <1117568337.945299.75400@g14g2000cwa.googlegroups. com>,\n> > > >\n> > > In my opinion, I think you are trying to say more than QM theory says.\n> >\n> > Funny, I feel the same way.\n> >\n> : ) . I prefer that.\n>\n> > > You seem to be a adept of the wave function reality hence you try to\n> > > define something out of the scope of the current QM theory formulation\n> > > (an explication of the collapse) while I simply take the born rules as\n> > > statistics of outcomes and the collapse postulate the property where a\n> > > given outcome value of a system is true ("Outcome A=a" true).\n> >\n> > I don\'t consider the Born rule part of QM. QM is unitary evolution.\n> > Everything is else is what we do to make sense of the wavefunction. The\n> > Born rules are a pragmatic procedure, but they lack a microscopic\n> > mechanism.\n\n> I hope you also consider the statistics of statistical classical\n> mechanics as pragmatic procedures.\n\nNo. You can pretty much derive all of them from fundamental principles.\n\n> If this is the case, you are simply\n> looking for the deterministic evolution of individual outcomes from a\n> given initial condition:\n> Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).\n> If it is what you are looking for, general unitary evolution tells you\n> that it is most of the time impossible: we have at most a functional\n> relation: Outcome_i= f(outcome_1, outcome_n,t) (the function\n> Outcome_i(t) depends on the functions outcome_1...n(t) and not on their\n> values).\n>\n> >\n> > Are you advocating a sort of consistent histories approach?\n>\n> Well, I promote the shut up and calculate approach I think: just\n> mathematics, where we map formally the values of the mathematical\n> objects/values to the experiments. All of the interpretations of QM are\n> very similar, if you do not try to attach a too strong reality to the\n> used words. Consistent, many worlds, many minds, my mind, my leg etc\n> .. : ) all are flavours of the same mathematical theory, they are ok\n> if they do not change the predictive results of the formal theory.\n> Interpretation, for me is rather the domain of philosophy. Adding or\n> removing it does not change the results of the mapping.\n\nThis is where I disagree. There\'s a fundamental _physical_ question:\nwhether or not the wavefunction collapses or not. This is (in principle)\nexperimentally verifiable. It\'s not philosophy; it\'s a question about\nthe real world.\n\nNow, a more philosophical question that is, I think, informed by all of\nthis is why do we not perceive superpositions (which, even in the\npresence of decoherence, still exist)? Or, in other words, why do we\nonly perceive one branch of the wavefunction. I\'d like to think that\nthis has some real, physical answer, but maybe it\'s all just ephemeral.\nBeats me.\n\n> > That seems to me to be a language in which to describe quantum outcomes, but\n> > nothing like an interpretation.\n\n> I think my point of view is closer to the epistemic view. I do not\n> require any "reality", whatever it is, just that the mapping of the\n> mathematical predictions agree with experiment. In this sense, the\n> collapse is a property of the system and not a transformation of the\n> system ( a given system is "collapsed" or not - the collapse identity -\n> but it cannot become collapsed: no meaning).\n\nEither the wavefunction evolves unitarily or it doesn\'t. That\'s a\nquestion amenable to experiment (although the experiments quickly get\nexponentially difficulty.)\n\n> > Regardless, when you make a real-world\n> > measurement, you better collapse the wavefunction, whether through\n> > decoherence or some other manner, or you will get the wrong answer. For\n> > future measurements.\n> >\n> You really get a classical deterministic point of view. You seem to\n> think that the only possible determinisitc relation is Outcome_i(t)=\n> f(outcome_1(to), outcome_n(to),t).\n> While you may have the deterministic functional relation Outcome_i=\n> f(outcome_1, outcome_n,t).\n> The latter tells you that you may not have a relation between future\n> outcomes and past outcomes, just between the functions (function of\n> sets rather than of points). Therefore, the only way to connect 2\n> outcomes in an experiment is the direct "observation" (the formal\n> labelling of the outcomes): the collapse.\n\nI can\'t decipher this.\n\nAnd I still can\'t figure out what you mean by your experiment. If you\nhave a detector and a measured object, it\'s practically a definition\nthat when you do a measurement, you entangle the two, ie, the state ends\nup in (schematically)\n\n|detector measures x>|object has state x>\n\nIn other words, the detector and the object have to be entangled. (In\nreality, the state is much more complicated, of course, but you can\ndefine the reduced density matrix, put it in a macroscopic basis and\nwatch it diagonalize.)\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117635044.686082.94270@g49g2000cwa.googlegroups.c om>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> > In article <1117568337.945299.75400@g14g2000cwa.googlegroups.c om>,
> > > >
> > > In my opinion, I think you are trying to say more than QM theory says.
> >
> > Funny, I feel the same way.
> >
> : ) . I prefer that.
>
> > > You seem to be a adept of the wave function reality hence you try to
> > > define something out of the scope of the current QM theory formulation
> > > (an explication of the collapse) while I simply take the born rules as
> > > statistics of outcomes and the collapse postulate the property where a
> > > given outcome value of a system is true ("Outcome A=a" true).
> >
> > I don't consider the Born rule part of QM. QM is unitary evolution.
> > Everything is else is what we do to make sense of the wavefunction. The
> > Born rules are a pragmatic procedure, but they lack a microscopic
> > mechanism.
> I hope you also consider the statistics of statistical classical
> mechanics as pragmatic procedures.
No. You can pretty much derive all of them from fundamental principles.
> If this is the case, you are simply
> looking for the deterministic evolution of individual outcomes from a
> given initial condition:
> Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).
> If it is what you are looking for, general unitary evolution tells you
> that it is most of the time impossible: we have at most a functional
> relation: Outcome_i= f(outcome_1, outcome_n,t) (the function
> Outcome_i(t) depends on the functions outcome_1...n(t) and not on their
> values).
>
> >
> > Are you advocating a sort of consistent histories approach?
>
> Well, I promote the shut up and calculate approach I think: just
> mathematics, where we map formally the values of the mathematical
> objects/values to the experiments. All of the interpretations of QM are
> very similar, if you do not try to attach a too strong reality to the
> used words. Consistent, many worlds, many minds, my mind, my leg etc
> .. : ) all are flavours of the same mathematical theory, they are ok
> if they do not change the predictive results of the formal theory.
> Interpretation, for me is rather the domain of philosophy. Adding or
> removing it does not change the results of the mapping.
This is where I disagree. There's a fundamental _physical_ question:
whether or not the wavefunction collapses or not. This is (in principle)
experimentally verifiable. It's not philosophy; it's a question about
the real world.
Now, a more philosophical question that is, I think, informed by all of
this is why do we not perceive superpositions (which, even in the
presence of decoherence, still exist)? Or, in other words, why do we
only perceive one branch of the wavefunction. I'd like to think that
this has some real, physical answer, but maybe it's all just ephemeral.
Beats me.
> > That seems to me to be a language in which to describe quantum outcomes, but
> > nothing like an interpretation.
> I think my point of view is closer to the epistemic view. I do not
> require any "reality", whatever it is, just that the mapping of the
> mathematical predictions agree with experiment. In this sense, the
> collapse is a property of the system and not a transformation of the
> system ( a given system is "collapsed" or not - the collapse identity -
> but it cannot become collapsed: no meaning).
Either the wavefunction evolves unitarily or it doesn't. That's a
question amenable to experiment (although the experiments quickly get
exponentially difficulty.)
> > Regardless, when you make a real-world
> > measurement, you better collapse the wavefunction, whether through
> > decoherence or some other manner, or you will get the wrong answer. For
> > future measurements.
> >
> You really get a classical deterministic point of view. You seem to
> think that the only possible determinisitc relation is Outcome_i(t)=
> f(outcome_1(to), outcome_n(to),t).
> While you may have the deterministic functional relation Outcome_i=
> f(outcome_1, outcome_n,t).
> The latter tells you that you may not have a relation between future
> outcomes and past outcomes, just between the functions (function of
> sets rather than of points). Therefore, the only way to connect 2
> outcomes in an experiment is the direct "observation" (the formal
> labelling of the outcomes): the collapse.
I can't decipher this.
And I still can't figure out what you mean by your experiment. If you
have a detector and a measured object, it's practically a definition
that when you do a measurement, you entangle the two, ie, the state ends
up in (schematically)
|detector measures x>|object has state x>
In other words, the detector and the object have to be entangled. (In
reality, the state is much more complicated, of course, but you can
define the reduced density matrix, put it in a macroscopic basis and
watch it diagonalize.)
Aaron
Eugene Stefanovich
Jun2-05, 02:11 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nAaron Bergman wrote:\n> In article <429CC172.3010801@synopsys.com>,\n> Eugene Stefanovich <eugenev@synopsys.com> wrote:\n>\n>\n>>2. Quantum mechanics does not explain the origin of these probabilities.\n>>All QM can do is to calculate these probabilities.\n>>In textbook QM, the formula |<a|psi>|^2 is a postulate, but this\n>>formula can be derived from a more fundamental "quantum logic" approach.\n>>(see chapter 4 in physics/0504062)\n>>If you know the rules of quantum mechanics, you can describe the\n>>state of your system by a vector |psi> in the Hilbert space,\n>>and the measurement by another vector |a>, and calculate/predict\n>>the probability of finding value a in the state |psi> by using above\n>>formula.\n>\n>\n> Outside of this \'envariance\' stuff that I don\'t really understand, I\n> know of no way to derive the probability rules from QM -- in particular,\n> the use of the reduced density matrix really already assumes the Born\n> rule. Even envariance assumes, a priori, that these probabilities exist\n> which seems to be avoiding the central question to me.\n\nLet me see if I understand your question.\nThere are two different sides of probabilities in QM. One side is\n"fundamental", i.e., the question WHY repeated measurements of the\nsame observable in the same condition yield different results.\nIs it possible to predict from theory the exact sequence of measurements\nrather than their probabilities?\nAnother side is "technical": HOW to calculate the probabilities\nof these random outcomes of measurements.\n\nQuantum mechanics has nothing to say about the "fundamental" question.\nThe erratic random character of individual measured data is a postulate\nof QM. However, QM can tell you everything about the "technical" side:\nprobabilities can be calculated with astonishing precision.\nThe formulas for calculating probabilities, e.g., |<a|psi>|^2 are not\npostulated. They can be derived from more general statements in\nthe "quantum logic" approach to QM.\n\nEugene Stefanovich.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <429CC172.3010801@synopsys.com>,
> Eugene Stefanovich <eugenev@synopsys.com> wrote:
>
>
>>2. Quantum mechanics does not explain the origin of these probabilities.
>>All QM can do is to calculate these probabilities.
>>In textbook QM, the formula |<a|\psi>|^2 is a postulate, but this
>>formula can be derived from a more fundamental "quantum logic" approach.
>>(see chapter 4 in http://www.arxiv.org/abs/physics/0504062)
>>If you know the rules of quantum mechanics, you can describe the
>>state of your system by a vector |\psi> in the Hilbert space,
>>and the measurement by another vector |a>, and calculate/predict
>>the probability of finding value a in the state |\psi> by using above
>>formula.
>
>
> Outside of this 'envariance' stuff that I don't really understand, I
> know of no way to derive the probability rules from QM -- in particular,
> the use of the reduced density matrix really already assumes the Born
> rule. Even envariance assumes, a priori, that these probabilities exist
> which seems to be avoiding the central question to me.
Let me see if I understand your question.
There are two different sides of probabilities in QM. One side is
"fundamental", i.e., the question WHY repeated measurements of the
same observable in the same condition yield different results.
Is it possible to predict from theory the exact sequence of measurements
rather than their probabilities?
Another side is "technical": HOW to calculate the probabilities
of these random outcomes of measurements.
Quantum mechanics has nothing to say about the "fundamental" question.
The erratic random character of individual measured data is a postulate
of QM. However, QM can tell you everything about the "technical" side:
probabilities can be calculated with astonishing precision.
The formulas for calculating probabilities, e.g., |<a|\psi>|^2 are not
postulated. They can be derived from more general statements in
the "quantum logic" approach to QM.
Eugene Stefanovich.
Seratend
Jun3-05, 01:02 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n>\n> Outside of this \'envariance\' stuff that I don\'t really understand, I\n> know of no way to derive the probability rules from QM -- in particular,\n> the use of the reduced density matrix really already assumes the Born\n> rule. Even envariance assumes, a priori, that these probabilities exist\n> which seems to be avoiding the central question to me.\n>\n> Aaron\n\nBecause the probabilities are external as in classical mechanics (we\nfilter the initial set of experiment trails to get the initial\nprobability law through the frequency, nothing provides that, it is an\nexternal selection, what we call the preparation).\nThe only "real predictive information" QM theory gives is the unitary\nevolution (functional evolution, what you may call a determinsic\nevolution).\n\nOnce we have a functional evolution, we may formaly deduce the new\nprobability law from the previous one: Pnew(t)(A)=Pold o f-1(A). This\nis the choice of description.\nWhere A is any event (a set of the possible values of the observable),\nand f-1 the inverse function (on the sets, always exist) associated to\nthe "deterministic" unitary evolution (if you prefer the function\nevolution of the operators in the heisenberg view given by e.g.\nihbardP/dt=[P,H] and ihbardQ/dt=[Q,H]).\n\nQM does not explain why we have a probability, but rather, starting\nfrom a selection of systems with a given probability law, we obtain a\nnew probability law through the unitary evolution: it is a choice of\ndescription (statistics). We are free to choose another ones (except\nthat it may not be practical to use other choices).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
>
> Outside of this 'envariance' stuff that I don't really understand, I
> know of no way to derive the probability rules from QM -- in particular,
> the use of the reduced density matrix really already assumes the Born
> rule. Even envariance assumes, a priori, that these probabilities exist
> which seems to be avoiding the central question to me.
>
> Aaron
Because the probabilities are external as in classical mechanics (we
filter the initial set of experiment trails to get the initial
probability law through the frequency, nothing provides that, it is an
external selection, what we call the preparation).
The only "real predictive information" QM theory gives is the unitary
evolution (functional evolution, what you may call a determinsic
evolution).
Once we have a functional evolution, we may formaly deduce the new
probability law from the previous one: Pnew(t)(A)=Pold o f-1(A). This
is the choice of description.
Where A is any event (a set of the possible values of the observable),
and f-1 the inverse function (on the sets, always exist) associated to
the "deterministic" unitary evolution (if you prefer the function
evolution of the operators in the heisenberg view given by e.g.
ihbardP/dt=[P,H] and ihbardQ/dt=[Q,H]).
QM does not explain why we have a probability, but rather, starting
from a selection of systems with a given probability law, we obtain a
new probability law through the unitary evolution: it is a choice of
description (statistics). We are free to choose another ones (except
that it may not be practical to use other choices).
Seratend.
I.Vecchi
Jun3-05, 01:03 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1117557478.880943.122100@g14g2000cwa.googlegroups .com>,\n> "I.Vecchi" <vecchi@weirdtech.com> wrote:\n> > Isn\'t this obviously circular? Aren\'t the "the macrostates by which you\n> > are performing your observation" precisely what decoherence is supposed\n> > to derive from a purely quantum description the process?\n>\n> I don\'t think see how. The macrostates are your pointer states.\n\nWhat determines the pointer states?\n\n> Decoherence is the process wherein the zillions of degrees of freedom in\n> your pointer conspire to diagonalize the reduced density matrix in the\n> pointer basis.\n\nConspire?\nAs a conspiracy, it\'s pretty lame. All DT proofs I have inspected relie\non some unphysical "no-recoil" assumption, either hidden or explicit,\nin order to achieve that diagonalisation.\nIndeed DT arguments follow your outline. First, the "right" pointer\nbasis is selected by the author. Then an "ad hoc", basis-dependent\ndissipative mechanism is introduced to wipe away the off-diagonal\nelements.\n\nRegards,\n\nIV\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1117557478.880943.122100@g14g2000cwa.googlegroups. com>,
> "I.Vecchi" <vecchi@weirdtech.com> wrote:
> > Isn't this obviously circular? Aren't the "the macrostates by which you
> > are performing your observation" precisely what decoherence is supposed
> > to derive from a purely quantum description the process?
>
> I don't think see how. The macrostates are your pointer states.
What determines the pointer states?
> Decoherence is the process wherein the zillions of degrees of freedom in
> your pointer conspire to diagonalize the reduced density matrix in the
> pointer basis.
Conspire?
As a conspiracy, it's pretty lame. All DT proofs I have inspected relie
on some unphysical "no-recoil" assumption, either hidden or explicit,
in order to achieve that diagonalisation.
Indeed DT arguments follow your outline. First, the "right" pointer
basis is selected by the author. Then an "ad hoc", basis-dependent
dissipative mechanism is introduced to wipe away the off-diagonal
elements.
Regards,
IV
I.Vecchi
Jun3-05, 01:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n...\n> Orthodox QM itself, or the Copenhagen interpretation, features\n> collapse but doesn\'t consider it physical. From the Copenhagen point\n> of view, the wavefunction encodes knowledge about the system, and\n> it collapses when a measurement is performed; that is, when we\n> acquire new knowledge, we have to update the mathematical object\n> which we use to represent knowledge. Hence different observers will\n> use different wavefunctions to describe the same system. The\n> Copenhagen view is still the officially recognised majority view,\n> but I doubt there are many physicists today who would agree that,\n> for example, the ground state orbital of an electron in a hydrogen\n> atom represents knowledge.\n\nSome (pretty good ones imo) apparently do. Take this example : "It is\nhelpful to remember that the quantum state is just an expectation\ncatalog.\nIts purpose is to make predictions about possible measurement results a\nspecific observer does not know yet" ([1]).\n\n> Physicists dislike knowledge because\n> knowledge is subjective, and subjective things are bad.\n\nThe point is that the belief in an objective, inherently existing\nuniverse is unfounded. Such superstition is unnecessary and actually\nharmful for scientific discourse, which requires only intersubjective\nagreement on measurement outcomes (aka reproducibility).\nWhether they proclaim themselves raelians or "physicists",\nsuperstitious people are loath to see their beliefs undermined.\nThat may be the root of the "dislike" you mention.\n\nIV\n\n[1] Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, Anton Zeilinger\n"Reply to Ryff\'s comment ..." http://arxiv.org/abs/quant-ph/0303104\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
...
> Orthodox QM itself, or the Copenhagen interpretation, features
> collapse but doesn't consider it physical. From the Copenhagen point
> of view, the wavefunction encodes knowledge about the system, and
> it collapses when a measurement is performed; that is, when we
> acquire new knowledge, we have to update the mathematical object
> which we use to represent knowledge. Hence different observers will
> use different wavefunctions to describe the same system. The
> Copenhagen view is still the officially recognised majority view,
> but I doubt there are many physicists today who would agree that,
> for example, the ground state orbital of an electron in a hydrogen
> atom represents knowledge.
Some (pretty good ones imo) apparently do. Take this example : "It is
helpful to remember that the quantum state is just an expectation
catalog.
Its purpose is to make predictions about possible measurement results a
specific observer does not know yet" ([1]).
> Physicists dislike knowledge because
> knowledge is subjective, and subjective things are bad.
The point is that the belief in an objective, inherently existing
universe is unfounded. Such superstition is unnecessary and actually
harmful for scientific discourse, which requires only intersubjective
agreement on measurement outcomes (aka reproducibility).
Whether they proclaim themselves raelians or "physicists",
superstitious people are loath to see their beliefs undermined.
That may be the root of the "dislike" you mention.
IV
[1] Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, Anton Zeilinger
"Reply to Ryff's comment ..." http://arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0303104
Hendrik van Hees
Jun3-05, 01:55 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n\n> This is where I disagree. There\'s a fundamental _physical_ question:\n> whether or not the wavefunction collapses or not. This is (in\n> principle) experimentally verifiable. It\'s not philosophy; it\'s a\n> question about the real world.\n\nIt is interesting how quickly proponents for more "philosophy" in\nphysics rash over tough physics questions ;-)!\n\nI do not understand, how you can distinguish experimentally between a\ncollaps a la Kopenhagen (i.e., state interpreted as a physical entity\nof a single quantum system) and the minimal statistical interpretation\n(i.e., state describes only our (objective) statistical knowledge about\nensembles of similarly prepared quantum systems). I am not aware of any\nreal experiment so far, which can verify or disprove something like the\nstate collaps for a single quantum system.\n>\n> Now, a more philosophical question that is, I think, informed by all\n> of this is why do we not perceive superpositions (which, even in the\n> presence of decoherence, still exist)? Or, in other words, why do we\n> only perceive one branch of the wavefunction. I\'d like to think that\n> this has some real, physical answer, but maybe it\'s all just\n> ephemeral. Beats me.\n\nThe point is that you call only such devices measurement devices which\nreally measure something (like the position of an electron). This means\nyou have some macroscopic object like a particle detector at a certain\nplace, which makes "click" if it is "hit by an electron". Then the\nobservable "position of the electron" becomes an objective reality\n(within a certain finite detector resolution of course!).\n\n--\nHendrik van Hees Texas A&M University\nPhone: +1 979/845-1411 Cyclotron Institute, MS-3366\nFax: +1 979/845-1899 College Station, TX 77843-3366\nhttp://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> This is where I disagree. There's a fundamental _physical_ question:
> whether or not the wavefunction collapses or not. This is (in
> principle) experimentally verifiable. It's not philosophy; it's a
> question about the real world.
It is interesting how quickly proponents for more "philosophy" in
physics rash over tough physics questions ;-)!
I do not understand, how you can distinguish experimentally between a
collaps a la Kopenhagen (i.e., state interpreted as a physical entity
of a single quantum system) and the minimal statistical interpretation
(i.e., state describes only our (objective) statistical knowledge about
ensembles of similarly prepared quantum systems). I am not aware of any
real experiment so far, which can verify or disprove something like the
state collaps for a single quantum system.
>
> Now, a more philosophical question that is, I think, informed by all
> of this is why do we not perceive superpositions (which, even in the
> presence of decoherence, still exist)? Or, in other words, why do we
> only perceive one branch of the wavefunction. I'd like to think that
> this has some real, physical answer, but maybe it's all just
> ephemeral. Beats me.
The point is that you call only such devices measurement devices which
really measure something (like the position of an electron). This means
you have some macroscopic object like a particle detector at a certain
place, which makes "click" if it is "hit by an electron". Then the
observable "position of the electron" becomes an objective reality
(within a certain finite detector resolution of course!).
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu
Aaron Bergman
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117700311.197096.236850@g47g2000cwa.googlegroups .com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n> >\n> > Outside of this \'envariance\' stuff that I don\'t really understand, I\n> > know of no way to derive the probability rules from QM -- in particular,\n> > the use of the reduced density matrix really already assumes the Born\n> > rule. Even envariance assumes, a priori, that these probabilities exist\n> > which seems to be avoiding the central question to me.\n> >\n> > Aaron\n>\n> Because the probabilities are external as in classical mechanics (we\n> filter the initial set of experiment trails to get the initial\n> probability law through the frequency, nothing provides that, it is an\n> external selection, what we call the preparation).\n\nI have no idea what this means.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117700311.197096.236850@g47g2000cwa.googlegroups. com>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> >
> > Outside of this 'envariance' stuff that I don't really understand, I
> > know of no way to derive the probability rules from QM -- in particular,
> > the use of the reduced density matrix really already assumes the Born
> > rule. Even envariance assumes, a priori, that these probabilities exist
> > which seems to be avoiding the central question to me.
> >
> > Aaron
>
> Because the probabilities are external as in classical mechanics (we
> filter the initial set of experiment trails to get the initial
> probability law through the frequency, nothing provides that, it is an
> external selection, what we call the preparation).
I have no idea what this means.
Aaron
Aaron Bergman
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <7e6dna0joO6X7gLfRVn-sw@pghconnect.com>,\nHendrik van Hees <hees@comp.tamu.edu> wrote:\n\n> Aaron Bergman wrote:\n>\n> > This is where I disagree. There\'s a fundamental _physical_ question:\n> > whether or not the wavefunction collapses or not. This is (in\n> > principle) experimentally verifiable. It\'s not philosophy; it\'s a\n> > question about the real world.\n>\n> It is interesting how quickly proponents for more "philosophy" in\n> physics rash over tough physics questions ;-)!\n>\n> I do not understand, how you can distinguish experimentally between a\n> collaps a la Kopenhagen (i.e., state interpreted as a physical entity\n> of a single quantum system) and the minimal statistical interpretation\n> (i.e., state describes only our (objective) statistical knowledge about\n> ensembles of similarly prepared quantum systems).\n\nI\'m not sure what you\'re referring to by a \'minimal statistical\ninterpretation\'. It seems to me that what you\'re indicating is a hidden\nvariables theory and that is experimentally ruled out (assuming\nlocality).\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <7e6dna0joO6X7gLfRVn-sw@pghconnect.com>,
Hendrik van Hees <hees@comp.tamu.edu> wrote:
> Aaron Bergman wrote:
>
> > This is where I disagree. There's a fundamental _physical_ question:
> > whether or not the wavefunction collapses or not. This is (in
> > principle) experimentally verifiable. It's not philosophy; it's a
> > question about the real world.
>
> It is interesting how quickly proponents for more "philosophy" in
> physics rash over tough physics questions ;-)!
>
> I do not understand, how you can distinguish experimentally between a
> collaps a la Kopenhagen (i.e., state interpreted as a physical entity
> of a single quantum system) and the minimal statistical interpretation
> (i.e., state describes only our (objective) statistical knowledge about
> ensembles of similarly prepared quantum systems).
I'm not sure what you're referring to by a 'minimal statistical
interpretation'. It seems to me that what you're indicating is a hidden
variables theory and that is experimentally ruled out (assuming
locality).
Aaron
Seratend
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n>\n> > I hope you also consider the statistics of statistical classical\n> > mechanics as pragmatic procedures.\n>\n> No. You can pretty much derive all of them from fundamental principles.\n>\nI do not follow you. Do you think you are able to explain the\nprobabilities of statistical classical mechanics?\nOr do you think fundamental each time you have a functional relation of\nthe type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?\n> > >\n> > > Are you advocating a sort of consistent histories approach?\n> >\n> > Well, I promote the shut up and calculate approach I think: just\n> > mathematics, where we map formally the values of the mathematical\n> > objects/values to the experiments. All of the interpretations of QM are\n> > very similar, if you do not try to attach a too strong reality to the\n> > used words. Consistent, many worlds, many minds, my mind, my leg etc\n> > .. : ) all are flavours of the same mathematical theory, they are ok\n> > if they do not change the predictive results of the formal theory.\n> > Interpretation, for me is rather the domain of philosophy. Adding or\n> > removing it does not change the results of the mapping.\n>\n> This is where I disagree. There\'s a fundamental _physical_ question:\n> whether or not the wavefunction collapses or not. This is (in principle)\n> experimentally verifiable. It\'s not philosophy; it\'s a question about\n> the real world.\n>\nHow can it be experimentally verifiable? You seem to work with a kind\nof absolute states/probability laws. Let me try to explain you:\nIn classical mechanics, when you write the position of a particle, q,\nyou agree you are implicitly referring to a reference point. You have\nno way to escape this fundamental way of description (because we just\ndescribe modifications - choice).\n\nThis is the same thing for probabilities. We have no absolute\nprobabilities. We always assume a probability law reference (in QM\ncase, the preparation of the system) and then we may deduce the\nprobability of a given measurement event with respect to the system\npreparation.\n\nOnce you accept the preparation of a system is also an outcome, and\nhence a collapse, how can you break this logical chain of assertions\n(the collapses) in order to verify experimentally an absolute collapse\nof an absolute wave function?\n\n> Now, a more philosophical question that is, I think, informed by all of\n> this is why do we not perceive superpositions (which, even in the\n> presence of decoherence, still exist)? Or, in other words, why do we\n> only perceive one branch of the wavefunction. I\'d like to think that\n> this has some real, physical answer, but maybe it\'s all just ephemeral.\n> Beats me.\n>\n: )\nNow, you are trying to move towards the perception of superpositions:\nthis is the same initial question: does QM allow to predict the\npreferred basis of a measurement?\n\nA superposition of vectors is only defined relatively to a given basis.\nWe define outcomes on a given basis, by defining the measurement. Any\nvector has a unique decomposition on a given basis: the possible\nsingles outcomes of the measurement associated to this basis. Hence, we\ncan see the superposition of states (i.e. |psi>= sum_i ai |i>), only by\nstudying the statistics of outcomes (of multiple identically prepared\nsystem) and not by direct observation of a single outcome. There is no\nproblem with superposition, even with classical probability, each time\na random variable produces different outcomes, we may see it, formally,\nin a superposition of states. The only problem remains the prediction\nof the experiment basis.\n\n> > > Regardless, when you make a real-world\n> > > measurement, you better collapse the wavefunction, whether through\n> > > decoherence or some other manner, or you will get the wrong answer. For\n> > > future measurements.\n> > >\n> > You really get a classical deterministic point of view. You seem to\n> > think that the only possible determinisitc relation is Outcome_i(t)=\n> > f(outcome_1(to), outcome_n(to),t).\n> > While you may have the deterministic functional relation Outcome_i=\n> > f(outcome_1, outcome_n,t).\n> > The latter tells you that you may not have a relation between future\n> > outcomes and past outcomes, just between the functions (function of\n> > sets rather than of points). Therefore, the only way to connect 2\n> > outcomes in an experiment is the direct "observation" (the formal\n> > labelling of the outcomes): the collapse.\n>\n> I can\'t decipher this.\n>\nReplace outcome_i(t) by q(t).\nf in this case is the path of the particle solving the Newton equation\n(the deterministic evolution).\n\nI think you have a classical point of view on how to describe a system.\nI understand you think that given an initial condition (the preparation\nof the system), these initial conditions infer the future measurements\noutcomes i.e. q(t)= f(qo, d/dtqo, t).\n\nYou have to enlarge your possibilities: you also have the possibility\nwhere, the function q(t) (i.e. the position of the particle) does not\ndepend on the initial conditions, but rather on other functions (i.e.\nposition of other particles) and not their values (the initial\nconditions): q(t)= f(q1, ... qn, t)=/= f(q1(t), ... qn(t), t)\n\nThis is just an example, on how we can describe the physical world.\nThis last description includes the classical deterministic evolution,\nbut it allows plenty of other possibilities. One important result of\nthis description is that you have no more q(t)= f(qo, d/dtqo, t): the\nposition of a particle at time t in not a function of initials\nconditions (e.g. qo, d/dtqo).\n\nIf you are able to understand this simple example, I think you can\nbetter understand the mathematical meaning of collapse when applied to\nthis description (identical to the quantum case).\n\n> And I still can\'t figure out what you mean by your experiment. If you\n> have a detector and a measured object, it\'s practically a definition\n> that when you do a measurement, you entangle the two, ie, the state ends\n> up in (schematically)\n>\n> |detector measures x>|object has state x>\n>\n> In other words, the detector and the object have to be entangled. (In\n> reality, the state is much more complicated, of course, but you can\n> define the reduced density matrix, put it in a macroscopic basis and\n> watch it diagonalize.)\n>\nNo, you do not see what I want to show you. All the states remain\nsimple, except for the detector I have not described. But the detector\nis just the "though" in this experiment. We can add or remove it,\njust to verify that the screen is a measurement of the interference\npattern (we cannot make the distinction):\n\na) I may say that the screen is a measurement apparatus or not (it\ncollapses the wavefunction): this does not change the result of the\ndetector in this toy model (because the projector associated to the\ncollapse of the screen commutes with the projector of the detector).\n\nb) Therefore in this toy model, I may have 2 measurements apparatus:\nthe screen and the detector. I can remove or add the measurement\ndetector: it does not change the behaviour of screen (no interaction).\nThe detector is just a virtual detector (we add or remove it by\nthought).\nHence, I may say that the screen is a measurement apparatus that does\nnot entangled the photons with itself (I have chosen the interaction\nsuch that no entanglement occurs).\n\nIn this case, I ask you how decoherence solves the problem as we have\nno decoherence at all. This example is really close to the collapse\nmeaning. Assuming the presence of the detector outcome or assuming that\none instance of this experiment without the detector gives the result\ndoes not change the system behaviour.\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
>
> > I hope you also consider the statistics of statistical classical
> > mechanics as pragmatic procedures.
>
> No. You can pretty much derive all of them from fundamental principles.
>
I do not follow you. Do you think you are able to explain the
probabilities of statistical classical mechanics?
Or do you think fundamental each time you have a functional relation of
the type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?
> > >
> > > Are you advocating a sort of consistent histories approach?
> >
> > Well, I promote the shut up and calculate approach I think: just
> > mathematics, where we map formally the values of the mathematical
> > objects/values to the experiments. All of the interpretations of QM are
> > very similar, if you do not try to attach a too strong reality to the
> > used words. Consistent, many worlds, many minds, my mind, my leg etc
> > .. : ) all are flavours of the same mathematical theory, they are ok
> > if they do not change the predictive results of the formal theory.
> > Interpretation, for me is rather the domain of philosophy. Adding or
> > removing it does not change the results of the mapping.
>
> This is where I disagree. There's a fundamental _physical_ question:
> whether or not the wavefunction collapses or not. This is (in principle)
> experimentally verifiable. It's not philosophy; it's a question about
> the real world.
>
How can it be experimentally verifiable? You seem to work with a kind
of absolute states/probability laws. Let me try to explain you:
In classical mechanics, when you write the position of a particle, q,
you agree you are implicitly referring to a reference point. You have
no way to escape this fundamental way of description (because we just
describe modifications - choice).
This is the same thing for probabilities. We have no absolute
probabilities. We always assume a probability law reference (in QM
case, the preparation of the system) and then we may deduce the
probability of a given measurement event with respect to the system
preparation.
Once you accept the preparation of a system is also an outcome, and
hence a collapse, how can you break this logical chain of assertions
(the collapses) in order to verify experimentally an absolute collapse
of an absolute wave function?
> Now, a more philosophical question that is, I think, informed by all of
> this is why do we not perceive superpositions (which, even in the
> presence of decoherence, still exist)? Or, in other words, why do we
> only perceive one branch of the wavefunction. I'd like to think that
> this has some real, physical answer, but maybe it's all just ephemeral.
> Beats me.
>
: )
Now, you are trying to move towards the perception of superpositions:
this is the same initial question: does QM allow to predict the
preferred basis of a measurement?
A superposition of vectors is only defined relatively to a given basis.
We define outcomes on a given basis, by defining the measurement. Any
vector has a unique decomposition on a given basis: the possible
singles outcomes of the measurement associated to this basis. Hence, we
can see the superposition of states (i.e. |\psi>= sum_i ai |i>), only by
studying the statistics of outcomes (of multiple identically prepared
system) and not by direct observation of a single outcome. There is no
problem with superposition, even with classical probability, each time
a random variable produces different outcomes, we may see it, formally,
in a superposition of states. The only problem remains the prediction
of the experiment basis.
> > > Regardless, when you make a real-world
> > > measurement, you better collapse the wavefunction, whether through
> > > decoherence or some other manner, or you will get the wrong answer. For
> > > future measurements.
> > >
> > You really get a classical deterministic point of view. You seem to
> > think that the only possible determinisitc relation is Outcome_i(t)=
> > f(outcome_1(to), outcome_n(to),t).
> > While you may have the deterministic functional relation Outcome_i=
> > f(outcome_1, outcome_n,t).
> > The latter tells you that you may not have a relation between future
> > outcomes and past outcomes, just between the functions (function of
> > sets rather than of points). Therefore, the only way to connect 2
> > outcomes in an experiment is the direct "observation" (the formal
> > labelling of the outcomes): the collapse.
>
> I can't decipher this.
>
Replace outcome_i(t) by q(t).
f in this case is the path of the particle solving the Newton equation
(the deterministic evolution).
I think you have a classical point of view on how to describe a system.
I understand you think that given an initial condition (the preparation
of the system), these initial conditions infer the future measurements
outcomes i.e. q(t)= f(qo, d/dtqo, t).
You have to enlarge your possibilities: you also have the possibility
where, the function q(t) (i.e. the position of the particle) does not
depend on the initial conditions, but rather on other functions (i.e.
position of other particles) and not their values (the initial
conditions): q(t)= f(q1, ... qn, t)=/= f(q1(t), ... qn(t), t)
This is just an example, on how we can describe the physical world.
This last description includes the classical deterministic evolution,
but it allows plenty of other possibilities. One important result of
this description is that you have no more q(t)= f(qo, d/dtqo, t): the
position of a particle at time t in not a function of initials
conditions (e.g. qo, d/dtqo).
If you are able to understand this simple example, I think you can
better understand the mathematical meaning of collapse when applied to
this description (identical to the quantum case).
> And I still can't figure out what you mean by your experiment. If you
> have a detector and a measured object, it's practically a definition
> that when you do a measurement, you entangle the two, ie, the state ends
> up in (schematically)
>
> |detector measures x>|object has state x>
>
> In other words, the detector and the object have to be entangled. (In
> reality, the state is much more complicated, of course, but you can
> define the reduced density matrix, put it in a macroscopic basis and
> watch it diagonalize.)
>
No, you do not see what I want to show you. All the states remain
simple, except for the detector I have not described. But the detector
is just the "though" in this experiment. We can add or remove it,
just to verify that the screen is a measurement of the interference
pattern (we cannot make the distinction):
a) I may say that the screen is a measurement apparatus or not (it
collapses the wavefunction): this does not change the result of the
detector in this toy model (because the projector associated to the
collapse of the screen commutes with the projector of the detector).
b) Therefore in this toy model, I may have 2 measurements apparatus:
the screen and the detector. I can remove or add the measurement
detector: it does not change the behaviour of screen (no interaction).
The detector is just a virtual detector (we add or remove it by
thought).
Hence, I may say that the screen is a measurement apparatus that does
not entangled the photons with itself (I have chosen the interaction
such that no entanglement occurs).
In this case, I ask you how decoherence solves the problem as we have
no decoherence at all. This example is really close to the collapse
meaning. Assuming the presence of the detector outcome or assuming that
one instance of this experiment without the detector gives the result
does not change the system behaviour.
Seratend.
Seratend
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I.Vecchi wrote:\n> All DT proofs I have inspected relie\n> on some unphysical "no-recoil" assumption, either hidden or explicit,\n> in order to achieve that diagonalisation.\n> Indeed DT arguments follow your outline. First, the "right" pointer\n> basis is selected by the author. Then an "ad hoc", basis-dependent\n> dissipative mechanism is introduced to wipe away the off-diagonal\n> elements.\n\nThat\'s also my understanding, but I need to understand the people who\nthink decoherence solves the problem as I am not sure I have understood\nthe whole problem.\nHave you got some data concerning the "no-recoil" assumption?\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I.Vecchi wrote:
> All DT proofs I have inspected relie
> on some unphysical "no-recoil" assumption, either hidden or explicit,
> in order to achieve that diagonalisation.
> Indeed DT arguments follow your outline. First, the "right" pointer
> basis is selected by the author. Then an "ad hoc", basis-dependent
> dissipative mechanism is introduced to wipe away the off-diagonal
> elements.
That's also my understanding, but I need to understand the people who
think decoherence solves the problem as I am not sure I have understood
the whole problem.
Have you got some data concerning the "no-recoil" assumption?
Seratend.
Arnold Neumaier
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>I am looking for an explanation why a particular detector coupled\n>>to a particular quantum system produces the observed erratic but\n>>objective record of individual results that can be analyzed\n>>statistically and quoted in a physics journal.\n>>\n> Me too. I just consider mathematics and experiment results to build\n> logical deductions.\n>\n>>If you want to claim more than that these outcomes are just the\n>>results of changes of belief (aka \'knowledge\') in an observer\'s mind\n>>- and I think physics does and should claim more than that -\n>\n> I agree. I prefer to have a logical view (mathematics) of what we\n> describe: the only thing I know. In my sentences, the "we see" may\n> be anybody: a machine, a particle etc ... (very weak signification)\n> and should not considered as a mind or everything else out of the\n> subject.\n> There are no minds just logical propositions or properties if you\n> prefer that are true in each considered case (logical view). Everything\n> else is interpretation. We have to map these properties to the\n> "reality" to verify the results, that\'s all (what you may call\n> the objective record in some cases). (like the mathematical circle\n> object and the drawing of a circle). The mapping may be falsified by\n> the experiments not the mathematical theory (supposed to be\n> consistent).\n> Hence, I may choose to describe a system by statistical or\n> deterministic tools.\n\nOK; then we agree in the basic assumptions of what the model building\nis about. This makes mutual understanding possible without having all\nthe time to talk about the reality issue.\n\n\n>>>a) what is the initial state of the photon (assuming a wave packet) :\n>>>|psi>= |path1>+|path2> with <path1|path2>=0?\n>>\n>>Not quite. Roughly,\n>> |psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>\n>>with spatial coherent states |pathi(t)> (i=1,2) moving at the\n>>velocity of light and monochromatic 1-Photon Fock states |1>, say.\n>\n> Ok, usually when I write a state |path1>, this state may be the tensor\n> product of whatever we want (we may expand it when it is required).\n> Therefore, you seem to require the detail of this state:\n>\n> |psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?\n\nNo; there is no need for orthogonality. Indeed, coherent states are\nnot quite orthogonal, although their overlap is small if the paths are\nfar away.\n\n\n>\n> Where <x|path1(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given\n> transversal area we may call it A\n> And <x|path2(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given\n> transversal area we may call it B\n>\n> Such that {A} intersection {B} is empty.\n\nAgain, this is only an approximation, since as mathematical entities,\ncoherent states extend everywhere. Working with coherent states is\nmuch easier than with truly local wave functions. Moreover, truly\nlocal solutions of the free Maxwell equations do not exist.\n\n\n>>The challenge allows, however, any specific setting (even\n>>idealized, or with massive particles, etc.) that matches the\n>>informal description in a reasonable way.\n>>\n> In other words we are free to choose the interactions and the\n> Hamiltonians\n\nYes; as long as it resembles the informal description.\n\n\n> as I have done it in another post in this thread for the\n> interference toy model.\n\nI haven\'t seen that (lack of time to read all postings...)\n\n\n>>>I mean, I have a system that is well described through unitary\n>>>evolution (superposition of states).\n>>\n>>Absorption by a screen is an irreversible macroscopic process\n>>accompanied by a minute increase of temperature. The claim that\n>>it is described by unitary evolution requires proof, which,\n>>if successful, would be part of an answer of the challenge.\n>>\n> See my description of the interference pattern toy model. I have\n\nPlease copy the relevant part for easy reference.\n\n\n> choosen Hamiltonians and interactions such that we have no entanglement\n> between the photons and the screens (formal choice): H_screen=\n> |screen><screen|(x)V(r)\n> I usually prefer to replace photons by electrons, whenever it does not\n> change the global result as the free propagator of photons and\n> electrons are the same.\n\nSo you ignore spin and assume a mass. But then it is simpler to\ntake spin 0 (rather than electrons), and simply talk about a \'particle\'.\n\n\n> In the case of photons, V(r) is the effective\n> potential giving the source of the reflection or the transmission.\n> This model supposes the energy conservation between photons and the\n> screens (choice) and it is easy to see that everything evolves unitary,\n> just by taking the wave packet.\n>\n> I may expand my explanation if required.\n\nYes please. I haven\'t read the initial description of your setting\n(and my remarks below might reflect musunderstanding because of that).\n\nIf the dynamics is unitary, how do you get the permanent record (the\ndefinite click or macroscopic spot) that constitutes a measurement?\n\n\n>>If there is unitary dynamics only then the final result is not\n>>the state |0,1,1> or |0,0,1> as observed, but a superposition\n>>of the two. Invoking Born\'s rule is _assuming_ the collapse\n>>rather than explaining it.\n>>\n> I like this toy model where we force no entanglement between the\n> photons states and the screens and where we have the simple unitary\n> evolution of the initial state. It reflects perfectly what we do on an\n> experiment that reflects this unitary evolution:\n> a) we have to choose between all the photons, the one with the initial\n> state (hence an initial measurement result)\n\nHow do we choose that?\n\nIn my terminology, this would be a preparation, not a measurement,\nsince measurement is _acquiring_ new information or _confirming/testing_\nold information, while preparation is _assuming_ information based on\npast experience with one\'s equipment.\n\n\n> b) we simultaneously measure the reflected photons by either the first\n> screen or the second one outside the area of the local interaction of\n> the screens (here I suppose the plane of the reflecting screens are not\n> orthogonal to the beam direction in order to put the "real"\n> detector outside the incoming beam. We have only a single detector that\n> clicks at a time assuming the good energy trigger level on a restricted\n> area.\n>\n> We can put the detectors or not,\n\nBut they change the system under consideration and hence the analysis\nneeded to get correct predictions.\n\n\n> they do not change the result of the\n> transformation of the wave function by the two screens before it is\n> detected by the detectors (we assume a local interaction of the\n> detectors: a choice). If we develop more, we see that the projector of\n> the detectors (the spatial location) commutes with the interaction of\n> the screens.\n\n\n>\n> Assuming this, we can say (interpretation) that the screens do not\n> collapse the wave function if we have no detectors, while if we put the\n> detectors we can say that the screen collapses the wave function.\n\nAnything which is part of the system modelled unitarily does not\nproduce collapse, while anything does that isn\'t modelled in full\ndetail but whose interaction with the unmodelled dof\'s is nontrival.\n\n\n>>That something remains to be explained even from the Copenhagen\n>>point of view (some version of which you seem to adhere to)\n>>is discussed in Section 3.\n>>\n>\n> Copenhagen interpretation does not assume the "reality" of the\n> wavefunction.\n\nBut it assumes the reality of the classical equipment, which\ntherefore gives an N-particle system with large N an ontological\nstatus different from one with small N. It forgets to say at which\nvalue of N one is entitled to swich from one status to the other.\n\n\n> What it says is very analogue to what I say. There is\n> most of the time, with CI, in my opinion, a misunderstanding on the\n> meaning of "before" or "after" the measurement. Just replace\n> the word "before" by "there is no measurement" and "after"\n> by "there is a measurement". Therefore, each instance of a system\n> has a single property: either there is a measurement or not (with its\n> associated definite single results).\n> There is no system where we have no measurement before and "after"\n> a measurement appears from nowhere. We have a measured system (of a\n> given value) or not (no time reference).\n\nThis is neither Kopenhagen nor true. The descriptions in\nthe authoritative treatises by von neumann, Londson and Bauer,\nor Wigner tell me quite a different story.\n\n\n>>>At the end, I must apply the born\n>>>rules to get the statistics (what I see in the experiment).\n>>\n>>This is the informal prescription that is used to apply single-particle\n>>reasoning to a complex multiparticle experiment. It successfully\n>>avoids looking at the physics happening at the screen, replacing it\n>>by simply assuming the collapse, i.e., the emergence of an objective\n>>record according to the probabilities from the Born rule.\n>>While this is an acceptable attitude it is obviously not the whole\n>>story.\n>>\n> This is what I call the statistical description of the physical\n> phenomena (we do not explain the outcomes, we just measure their\n> frequency and their evolution in the space time).\n\nYes.\n\n\n>>>Are you just searching for a predictive description of a particular\n>>>outcome in a given QM experiment?\n>>\n>>Just an explanation for how particular outcomes arise through\n>>measurement. Leaving something as complex as \'measurement\' as\n>>an uninterpreted, vague fundamental concept, while practical\n>>measurement is a whole science in itself seem to me too gross\n>>a simplification to be tolerable, and one of the reasons why the\n>>foundations of QM are in the poor present state.\n>>\n> Do you reject the deterministic bohmian formulation (at least in the\n> non relativistic case where it is the best achieved)?\n> (I mean the mathematical formulation connection predicting the outcomes\n> and not the interpretations).\n\nYes. They have to postulate the probabilities in an unconvincing\nprestabilized way to get the equivalence to the standard formalism.\nThey _don\'t_ follow from the equations of motion. An isolated\nhydrogen atom in the ground state consists of an electron at rest\nat some distance from the proton, and to explain the observations\nthey need to _assume_ that there is an averaging according to a\nparticular concocted distribution...\n\nAnd their trajectories are too bizarre to appeal to me.\n\nBut I don\'t want to discuss Bohmian mechanics. I want to discuss the\nbest interpretation of the traditional quantum formalism without any\nenhancement.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>I am looking for an explanation why a particular detector coupled
>>to a particular quantum system produces the observed erratic but
>>objective record of individual results that can be analyzed
>>statistically and quoted in a physics journal.
>>
> Me too. I just consider mathematics and experiment results to build
> logical deductions.
>
>>If you want to claim more than that these outcomes are just the
>>results of changes of belief (aka 'knowledge') in an observer's mind
>>- and I think physics does and should claim more than that -
>
> I agree. I prefer to have a logical view (mathematics) of what we
> describe: the only thing I know. In my sentences, the "we see" may
> be anybody: a machine, a particle etc ... (very weak signification)
> and should not considered as a mind or everything else out of the
> subject.
> There are no minds just logical propositions or properties if you
> prefer that are true in each considered case (logical view). Everything
> else is interpretation. We have to map these properties to the
> "reality" to verify the results, that's all (what you may call
> the objective record in some cases). (like the mathematical circle
> object and the drawing of a circle). The mapping may be falsified by
> the experiments not the mathematical theory (supposed to be
> consistent).
> Hence, I may choose to describe a system by statistical or
> deterministic tools.
OK; then we agree in the basic assumptions of what the model building
is about. This makes mutual understanding possible without having all
the time to talk about the reality issue.
>>>a) what is the initial state of the photon (assuming a wave packet) :
>>>|\psi>= |path1>+|path2> with <path1|path2>=0?
>>
>>Not quite. Roughly,
>> |\psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>
>>with spatial coherent states |pathi(t)> (i=1,2) moving at the
>>velocity of light and monochromatic 1-Photon Fock states |1>, say.
>
> Ok, usually when I write a state |path1>, this state may be the tensor
> product of whatever we want (we may expand it when it is required).
> Therefore, you seem to require the detail of this state:
>
> |\psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?
No; there is no need for orthogonality. Indeed, coherent states are
not quite orthogonal, although their overlap is small if the paths are
far away.
>
> Where <x|path1(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given
> transversal area we may call it A
> And <x|path2(t)>= <x|(|path1(t)>+|path2(t)>) for x in a given
> transversal area we may call it B
>
> Such that {A} intersection {B} is empty.
Again, this is only an approximation, since as mathematical entities,
coherent states extend everywhere. Working with coherent states is
much easier than with truly local wave functions. Moreover, truly
local solutions of the free Maxwell equations do not exist.
>>The challenge allows, however, any specific setting (even
>>idealized, or with massive particles, etc.) that matches the
>>informal description in a reasonable way.
>>
> In other words we are free to choose the interactions and the
> Hamiltonians
Yes; as long as it resembles the informal description.
> as I have done it in another post in this thread for the
> interference toy model.
I haven't seen that (lack of time to read all postings...)
>>>I mean, I have a system that is well described through unitary
>>>evolution (superposition of states).
>>
>>Absorption by a screen is an irreversible macroscopic process
>>accompanied by a minute increase of temperature. The claim that
>>it is described by unitary evolution requires proof, which,
>>if successful, would be part of an answer of the challenge.
>>
> See my description of the interference pattern toy model. I have
Please copy the relevant part for easy reference.
> choosen Hamiltonians and interactions such that we have no entanglement
> between the photons and the screens (formal choice): H_{screen}=
> |screen><screen|(x)V(r)
> I usually prefer to replace photons by electrons, whenever it does not
> change the global result as the free propagator of photons and
> electrons are the same.
So you ignore spin and assume a mass. But then it is simpler to
take spin (rather than electrons), and simply talk about a 'particle'.
> In the case of photons, V(r) is the effective
> potential giving the source of the reflection or the transmission.
> This model supposes the energy conservation between photons and the
> screens (choice) and it is easy to see that everything evolves unitary,
> just by taking the wave packet.
>
> I may expand my explanation if required.
Yes please. I haven't read the initial description of your setting
(and my remarks below might reflect musunderstanding because of that).
If the dynamics is unitary, how do you get the permanent record (the
definite click or macroscopic spot) that constitutes a measurement?
>>If there is unitary dynamics only then the final result is not
>>the state |0,1,1> or |0,0,1> as observed, but a superposition
>>of the two. Invoking Born's rule is _assuming_ the collapse
>>rather than explaining it.
>>
> I like this toy model where we force no entanglement between the
> photons states and the screens and where we have the simple unitary
> evolution of the initial state. It reflects perfectly what we do on an
> experiment that reflects this unitary evolution:
> a) we have to choose between all the photons, the one with the initial
> state (hence an initial measurement result)
How do we choose that?
In my terminology, this would be a preparation, not a measurement,
since measurement is _acquiring_ new information or _confirming/testing_
old information, while preparation is _assuming_ information based on
past experience with one's equipment.
> b) we simultaneously measure the reflected photons by either the first
> screen or the second one outside the area of the local interaction of
> the screens (here I suppose the plane of the reflecting screens are not
> orthogonal to the beam direction in order to put the "real"
> detector outside the incoming beam. We have only a single detector that
> clicks at a time assuming the good energy trigger level on a restricted
> area.
>
> We can put the detectors or not,
But they change the system under consideration and hence the analysis
needed to get correct predictions.
> they do not change the result of the
> transformation of the wave function by the two screens before it is
> detected by the detectors (we assume a local interaction of the
> detectors: a choice). If we develop more, we see that the projector of
> the detectors (the spatial location) commutes with the interaction of
> the screens.
>
> Assuming this, we can say (interpretation) that the screens do not
> collapse the wave function if we have no detectors, while if we put the
> detectors we can say that the screen collapses the wave function.
Anything which is part of the system modelled unitarily does not
produce collapse, while anything does that isn't modelled in full
detail but whose interaction with the unmodelled dof's is nontrival.
>>That something remains to be explained even from the Copenhagen
>>point of view (some version of which you seem to adhere to)
>>is discussed in Section 3.
>>
>
> Copenhagen interpretation does not assume the "reality" of the
> wavefunction.
But it assumes the reality of the classical equipment, which
therefore gives an N-particle system with large N an ontological
status different from one with small N. It forgets to say at which
value of N one is entitled to swich from one status to the other.
> What it says is very analogue to what I say. There is
> most of the time, with CI, in my opinion, a misunderstanding on the
> meaning of "before" or "after" the measurement. Just replace
> the word "before" by "there is no measurement" and "after"
> by "there is a measurement". Therefore, each instance of a system
> has a single property: either there is a measurement or not (with its
> associated definite single results).
> There is no system where we have no measurement before and "after"
> a measurement appears from nowhere. We have a measured system (of a
> given value) or not (no time reference).
This is neither Kopenhagen nor true. The descriptions in
the authoritative treatises by von neumann, Londson and Bauer,
or Wigner tell me quite a different story.
>>>At the end, I must apply the born
>>>rules to get the statistics (what I see in the experiment).
>>
>>This is the informal prescription that is used to apply single-particle
>>reasoning to a complex multiparticle experiment. It successfully
>>avoids looking at the physics happening at the screen, replacing it
>>by simply assuming the collapse, i.e., the emergence of an objective
>>record according to the probabilities from the Born rule.
>>While this is an acceptable attitude it is obviously not the whole
>>story.
>>
> This is what I call the statistical description of the physical
> phenomena (we do not explain the outcomes, we just measure their
> frequency and their evolution in the space time).
Yes.
>>>Are you just searching for a predictive description of a particular
>>>outcome in a given QM experiment?
>>
>>Just an explanation for how particular outcomes arise through
>>measurement. Leaving something as complex as 'measurement' as
>>an uninterpreted, vague fundamental concept, while practical
>>measurement is a whole science in itself seem to me too gross
>>a simplification to be tolerable, and one of the reasons why the
>>foundations of QM are in the poor present state.
>>
> Do you reject the deterministic bohmian formulation (at least in the
> non relativistic case where it is the best achieved)?
> (I mean the mathematical formulation connection predicting the outcomes
> and not the interpretations).
Yes. They have to postulate the probabilities in an unconvincing
prestabilized way to get the equivalence to the standard formalism.
They _don't_ follow from the equations of motion. An isolated
hydrogen atom in the ground state consists of an electron at rest
at some distance from the proton, and to explain the observations
they need to _assume_ that there is an averaging according to a
particular concocted distribution...
And their trajectories are too bizarre to appeal to me.
But I don't want to discuss Bohmian mechanics. I want to discuss the
best interpretation of the traditional quantum formalism without any
enhancement.
Arnold Neumaier
Arnold Neumaier
Jun3-05, 10:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Joe Rongen wrote:\n\n>>Arnold Neumaier wrote:\n>>\n>>>I am looking for an explanation why a particular detector coupled\n>>>to a particular quantum system produces the observed erratic but\n>>>objective record of individual results that can be analyzed\n>>>statistically and quoted in a physics journal.\n>\n> Some detector systems employ photomultiplier tube(s).\n>\n> The ideal photomultiplier tube is a detector that basically\n> absorbs (photo-electric effect) one photon and internally\n> converts/produces** due to an electron cascade/amplifier\n> effect, one measurable event.\n>\n> ** Lawrence and Beams showed in 1928 that photo-electrons are\n> sometimes emitted less than 3 *10^(-9) sec after initial illumination.\n\nCould you please explain how this relates to my statement?\nEven a photomultiplier tube will trigger an erratic response\nfollowing a Poisson process when fed with a low intensity coherent\nlaser beam.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Joe Rongen wrote:
>>Arnold Neumaier wrote:
>>
>>>I am looking for an explanation why a particular detector coupled
>>>to a particular quantum system produces the observed erratic but
>>>objective record of individual results that can be analyzed
>>>statistically and quoted in a physics journal.
>
> Some detector systems employ photomultiplier tube(s).
>
> The ideal photomultiplier tube is a detector that basically
> absorbs (photo-electric effect) one photon and internally
> converts/produces** due to an electron cascade/amplifier
> effect, one measurable event.
>
> ** Lawrence and Beams showed in 1928 that photo-electrons are
> sometimes emitted less than 3 *10^(-9) sec after initial illumination.
Could you please explain how this relates to my statement?
Even a photomultiplier tube will trigger an erratic response
following a Poisson process when fed with a low intensity coherent
laser beam.
Arnold Neumaier
Aaron Bergman
Jun3-05, 02:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117794648.382861.95220@g43g2000cwa.googlegroups. com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n> >\n> > > I hope you also consider the statistics of statistical classical\n> > > mechanics as pragmatic procedures.\n> >\n> > No. You can pretty much derive all of them from fundamental principles.\n> >\n> I do not follow you. Do you think you are able to explain the\n> probabilities of statistical classical mechanics?\n\nIt\'s not completely rigorous, but generally, yeah. That\'s what\nstatistical mechanics is.\n\n> Or do you think fundamental each time you have a functional relation of\n> the type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?\n\nSorry. I don\'t know what you mean.\n>\n> > > > Are you advocating a sort of consistent histories approach?\n> > >\n> > > Well, I promote the shut up and calculate approach I think: just\n> > > mathematics, where we map formally the values of the mathematical\n> > > objects/values to the experiments. All of the interpretations of QM are\n> > > very similar, if you do not try to attach a too strong reality to the\n> > > used words. Consistent, many worlds, many minds, my mind, my leg etc\n> > > .. : ) all are flavours of the same mathematical theory, they are ok\n> > > if they do not change the predictive results of the formal theory.\n> > > Interpretation, for me is rather the domain of philosophy. Adding or\n> > > removing it does not change the results of the mapping.\n> >\n> > This is where I disagree. There\'s a fundamental _physical_ question:\n> > whether or not the wavefunction collapses or not. This is (in principle)\n> > experimentally verifiable. It\'s not philosophy; it\'s a question about\n> > the real world.\n> >\n> How can it be experimentally verifiable?\n\nYou entangle your system with a large measuring device. Then you try to\ndisentangle it and see if the superposition remains. Such experiments\nhave been done for small systems.\n\n[...]\n\n> Now, you are trying to move towards the perception of superpositions:\n> this is the same initial question: does QM allow to predict the\n> preferred basis of a measurement?\n>\n> A superposition of vectors is only defined relatively to a given basis.\n> We define outcomes on a given basis, by defining the measurement. Any\n> vector has a unique decomposition on a given basis: the possible\n> singles outcomes of the measurement associated to this basis. Hence, we\n> can see the superposition of states (i.e. |psi>= sum_i ai |i>), only by\n> studying the statistics of outcomes (of multiple identically prepared\n> system) and not by direct observation of a single outcome. There is no\n> problem with superposition, even with classical probability, each time\n> a random variable produces different outcomes, we may see it, formally,\n> in a superposition of states. The only problem remains the prediction\n> of the experiment basis.\n\nI don\'t go for this instrumentalist viewpoint (if I understand you). It\nseems to be essentially the old Copenhagen interpretation where there\nare simply questions we are not allowed to ask. I\'m not sure it\'s\ncompletely consistent, for one.\n\n[...]\n\n> > And I still can\'t figure out what you mean by your experiment. If you\n> > have a detector and a measured object, it\'s practically a definition\n> > that when you do a measurement, you entangle the two, ie, the state ends\n> > up in (schematically)\n> >\n> > |detector measures x>|object has state x>\n> >\n> > In other words, the detector and the object have to be entangled. (In\n> > reality, the state is much more complicated, of course, but you can\n> > define the reduced density matrix, put it in a macroscopic basis and\n> > watch it diagonalize.)\n> >\n> No, you do not see what I want to show you. All the states remain\n> simple, except for the detector I have not described. But the detector\n> is just the "though" in this experiment.\n\nI don\'t know what this means.\n\n> We can add or remove it,\n> just to verify that the screen is a measurement of the interference\n> pattern (we cannot make the distinction):\n>\n> a) I may say that the screen is a measurement apparatus or not (it\n> collapses the wavefunction): this does not change the result of the\n> detector in this toy model (because the projector associated to the\n> collapse of the screen commutes with the projector of the detector).\n\nAre you discussing an example with commuting observables, then?\n\n> b) Therefore in this toy model, I may have 2 measurements apparatus:\n> the screen and the detector. I can remove or add the measurement\n> detector: it does not change the behaviour of screen (no interaction).\n> The detector is just a virtual detector (we add or remove it by\n> thought).\n> Hence, I may say that the screen is a measurement apparatus that does\n> not entangled the photons with itself (I have chosen the interaction\n> such that no entanglement occurs).\n\nIf the screen does anything that allows us to make an observation, it is\nentangled with the photons. I don\'t see how you can simply render this\nfalse by fiat.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117794648.382861.95220@g43g2000cwa.googlegroups.c om>,
Seratend <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> >
> > > I hope you also consider the statistics of statistical classical
> > > mechanics as pragmatic procedures.
> >
> > No. You can pretty much derive all of them from fundamental principles.
> >
> I do not follow you. Do you think you are able to explain the
> probabilities of statistical classical mechanics?
It's not completely rigorous, but generally, yeah. That's what
statistical mechanics is.
> Or do you think fundamental each time you have a functional relation of
> the type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?
Sorry. I don't know what you mean.
>
> > > > Are you advocating a sort of consistent histories approach?
> > >
> > > Well, I promote the shut up and calculate approach I think: just
> > > mathematics, where we map formally the values of the mathematical
> > > objects/values to the experiments. All of the interpretations of QM are
> > > very similar, if you do not try to attach a too strong reality to the
> > > used words. Consistent, many worlds, many minds, my mind, my leg etc
> > > .. : ) all are flavours of the same mathematical theory, they are ok
> > > if they do not change the predictive results of the formal theory.
> > > Interpretation, for me is rather the domain of philosophy. Adding or
> > > removing it does not change the results of the mapping.
> >
> > This is where I disagree. There's a fundamental _physical_ question:
> > whether or not the wavefunction collapses or not. This is (in principle)
> > experimentally verifiable. It's not philosophy; it's a question about
> > the real world.
> >
> How can it be experimentally verifiable?
You entangle your system with a large measuring device. Then you try to
disentangle it and see if the superposition remains. Such experiments
have been done for small systems.
[...]
> Now, you are trying to move towards the perception of superpositions:
> this is the same initial question: does QM allow to predict the
> preferred basis of a measurement?
>
> A superposition of vectors is only defined relatively to a given basis.
> We define outcomes on a given basis, by defining the measurement. Any
> vector has a unique decomposition on a given basis: the possible
> singles outcomes of the measurement associated to this basis. Hence, we
> can see the superposition of states (i.e. |\psi>= sum_i ai |i>), only by
> studying the statistics of outcomes (of multiple identically prepared
> system) and not by direct observation of a single outcome. There is no
> problem with superposition, even with classical probability, each time
> a random variable produces different outcomes, we may see it, formally,
> in a superposition of states. The only problem remains the prediction
> of the experiment basis.
I don't go for this instrumentalist viewpoint (if I understand you). It
seems to be essentially the old Copenhagen interpretation where there
are simply questions we are not allowed to ask. I'm not sure it's
completely consistent, for one.
[...]
> > And I still can't figure out what you mean by your experiment. If you
> > have a detector and a measured object, it's practically a definition
> > that when you do a measurement, you entangle the two, ie, the state ends
> > up in (schematically)
> >
> > |detector measures x>|object has state x>
> >
> > In other words, the detector and the object have to be entangled. (In
> > reality, the state is much more complicated, of course, but you can
> > define the reduced density matrix, put it in a macroscopic basis and
> > watch it diagonalize.)
> >
> No, you do not see what I want to show you. All the states remain
> simple, except for the detector I have not described. But the detector
> is just the "though" in this experiment.
I don't know what this means.
> We can add or remove it,
> just to verify that the screen is a measurement of the interference
> pattern (we cannot make the distinction):
>
> a) I may say that the screen is a measurement apparatus or not (it
> collapses the wavefunction): this does not change the result of the
> detector in this toy model (because the projector associated to the
> collapse of the screen commutes with the projector of the detector).
Are you discussing an example with commuting observables, then?
> b) Therefore in this toy model, I may have 2 measurements apparatus:
> the screen and the detector. I can remove or add the measurement
> detector: it does not change the behaviour of screen (no interaction).
> The detector is just a virtual detector (we add or remove it by
> thought).
> Hence, I may say that the screen is a measurement apparatus that does
> not entangled the photons with itself (I have chosen the interaction
> such that no entanglement occurs).
If the screen does anything that allows us to make an observation, it is
entangled with the photons. I don't see how you can simply render this
false by fiat.
Aaron
Aaron Bergman
Jun5-05, 01:24 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117721240.680017.134550@g43g2000cwa.googlegroups .com>,\n"I.Vecchi" <vecchi@weirdtech.com> wrote:\n\n> Aaron Bergman wrote:\n> > In article <1117557478.880943.122100@g14g2000cwa.googlegroups .com>,\n> > "I.Vecchi" <vecchi@weirdtech.com> wrote:\n> > > Isn\'t this obviously circular? Aren\'t the "the macrostates by which you\n> > > are performing your observation" precisely what decoherence is supposed\n> > > to derive from a purely quantum description the process?\n> >\n> > I don\'t think see how. The macrostates are your pointer states.\n>\n> What determines the pointer states?\n>\n> > Decoherence is the process wherein the zillions of degrees of freedom in\n> > your pointer conspire to diagonalize the reduced density matrix in the\n> > pointer basis.\n>\n> Conspire?\n> As a conspiracy, it\'s pretty lame. All DT proofs I have inspected relie\n> on some unphysical "no-recoil" assumption, either hidden or explicit,\n> in order to achieve that diagonalisation.\n\nProving decoherence in general is, as I understand it, hard (but this\nisn\'t really my field.) The thing is, we can experimentally observe it\nhappening.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117721240.680017.134550@g43g2000cwa.googlegroups. com>,
"I.Vecchi" <vecchi@weirdtech.com> wrote:
> Aaron Bergman wrote:
> > In article <1117557478.880943.122100@g14g2000cwa.googlegroups. com>,
> > "I.Vecchi" <vecchi@weirdtech.com> wrote:
> > > Isn't this obviously circular? Aren't the "the macrostates by which you
> > > are performing your observation" precisely what decoherence is supposed
> > > to derive from a purely quantum description the process?
> >
> > I don't think see how. The macrostates are your pointer states.
>
> What determines the pointer states?
>
> > Decoherence is the process wherein the zillions of degrees of freedom in
> > your pointer conspire to diagonalize the reduced density matrix in the
> > pointer basis.
>
> Conspire?
> As a conspiracy, it's pretty lame. All DT proofs I have inspected relie
> on some unphysical "no-recoil" assumption, either hidden or explicit,
> in order to achieve that diagonalisation.
Proving decoherence in general is, as I understand it, hard (but this
isn't really my field.) The thing is, we can experimentally observe it
happening.
Aaron
Arnold Neumaier
Jun5-05, 01:24 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> I hope you also consider the statistics of statistical classical\n> mechanics as pragmatic procedures. If this is the case, you are simply\n> looking for the deterministic evolution of individual outcomes from a\n> given initial condition:\n> Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).\n> If it is what you are looking for, general unitary evolution tells you\n> that it is most of the time impossible:\n\nNo. Only a closed system evolves unitarily, and of course it cannot\nbe observed and hence does not produce outcomes.\n\nAny system that can be observed from the outside is open, however,\nand for an open system, modern quantum physics prescribes _nonunitary_\nevolution.\n\nThis even holds in the traditional Copenhagen interpretation.\nThe view is that the system is closed most of the time and then\nevolves unitarity. At certain very short moments, it is assumed\nto be in contact with a detector for measurement - then the\nsystem is open and evolves nonunitarily, by collapse.\n\nAlthough not very clearly separated in many discussions,\nthese two processes happen never simultaneously but context\ndependent, and are of course only approximations to more\nrealistic measurement situations.\n\nFor example, in a Stern-Gerlach experiment, the system (silver atom)\nmoves from the source along the magnet towards the screen with very\ngood accuracy in a unitary (and indeed reversible) way. But a few\nsplit moments before it hits the screen it feels its interactions,\nand describing it as a closed system becomes hopelessly inaccurate.\nInstead, since the interaction time is very short, it can be\ndescribed very accurately by an instantaneous collapse.\n\nThe probabilistic nature comes about since of course modeling\nthe system without its interacting partner leaves one in lack of\ndeterministic information about the environment that would be\nneeded for an accurate prediction.\n\nQualitatively, the situation would be the same even in classical\nmechanics; one couldn\'t predict the outcome of a classical particle\ninteracting with a classical screen without knowing the details\nof the screen.\n\nI\'d find it strange if one would expect more from quantum mechanics.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> I hope you also consider the statistics of statistical classical
> mechanics as pragmatic procedures. If this is the case, you are simply
> looking for the deterministic evolution of individual outcomes from a
> given initial condition:
> Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).
> If it is what you are looking for, general unitary evolution tells you
> that it is most of the time impossible:
No. Only a closed system evolves unitarily, and of course it cannot
be observed and hence does not produce outcomes.
Any system that can be observed from the outside is open, however,
and for an open system, modern quantum physics prescribes _nonunitary_
evolution.
This even holds in the traditional Copenhagen interpretation.
The view is that the system is closed most of the time and then
evolves unitarity. At certain very short moments, it is assumed
to be in contact with a detector for measurement - then the
system is open and evolves nonunitarily, by collapse.
Although not very clearly separated in many discussions,
these two processes happen never simultaneously but context
dependent, and are of course only approximations to more
realistic measurement situations.
For example, in a Stern-Gerlach experiment, the system (silver atom)
moves from the source along the magnet towards the screen with very
good accuracy in a unitary (and indeed reversible) way. But a few
split moments before it hits the screen it feels its interactions,
and describing it as a closed system becomes hopelessly inaccurate.
Instead, since the interaction time is very short, it can be
described very accurately by an instantaneous collapse.
The probabilistic nature comes about since of course modeling
the system without its interacting partner leaves one in lack of
deterministic information about the environment that would be
needed for an accurate prediction.
Qualitatively, the situation would be the same even in classical
mechanics; one couldn't predict the outcome of a classical particle
interacting with a classical screen without knowing the details
of the screen.
I'd find it strange if one would expect more from quantum mechanics.
Arnold Neumaier
Arnold Neumaier
Jun5-05, 01:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n>>>Interesting.\n>>>You seem to view the measurement results exclusively through the mean\n>>>value filter\n>>\n>>Yes. Mean values of thermodynamic origin are the raw observables\n>>in all experiments; everything else is derived from these by theory\n>>or speculation.\n>>I call this the \'consistent experiment interpretation\', following\n>>first steps in this direction taken in Section 10 of\n>> quant-ph/0303047 =3D Int. J. Mod. Phys. B 17 (2003), 2937-2980.\n>>Since I wrote this, my view has considerably gained in strength.\n>>If you read German, you can find much more about it at\n>> http://www.mat.univie.ac.at/~neum/physik-faq.tex\n>\n> Unfortunately, I do not read German (and I regret it today : ).\n> However, I am greatly interested by the mean value filter and hope that\n> you will be able to post soon the English version.\n> I have also looked at your paper, section 10, but it not easy to\n> understand the section alone (as the document is consistent : ) and\n> more precisely what do you intend by consistent experiment. Currently,\n> I would like to understand what part of thermodynamics you want to use\n> to derive some results.\n\nNonequilibrium statistical mechanics shows the meaning of _single_\nmacroscopic observations of thermodynamic observables as\napproximations to the expectations of corresponding microscopic\noperators, and their attainable accuracy as the corresponding\nstandard deviation. In this sense, macroscopic expectations are\napproximately measurable, independent of whether the underlying\nmicroscopic theory is classical or quantum.\n\nThis defines realism for me, in accordance with the engineering point\nof view. My interpretation extends this realist view of expectations\n(rather than eigenvalues - which never figure in thermodynamics)\ndown to the microworld. Measurements of expectations simply become\nmore inaccurate, up to the point where they must be inferred by\naveraging from very inaccurate raw measurements.\n\nTo analyze the measurement process and to recover Born\'s rule,\none needs the projection operator formalism. The most useful\nexposition I found in the literature is in:\nH Grabert,\nProjection Operator Techniques in Nonequilibrium\nStatistical Mechanics,\nSpringer Tracts in Modern Physics, 1982.\n\n\n>>>in my point of view (like the interference pattern: single\n>>>photon screen impact event versus multiple independent photons\n>>>interference pattern event).\n>>>How do you explain the observed state of a single photon event?\n>>\n>>It is only a sloppy way of speaking, not a real physical event.\n>>What actually happens is the following:\n>>\n>>The light ray of a laser is an electromagnetic field localized in a\n>>small region along the ray that begins in the laser and ends at the\n>>photodetector. A ray of intensity I is described by a coherent state\n>> |I>> = |0> + I|1> + I^2/2|2> + I^3/6|3> + ...\n>>If I is tiny then, from time to time, an electron responds (in some\n>>loose way of speaking that itself would need correction) to the\n>>energy continuously transmitted by the ray by going into an excited\n>>state, an event which is magnified in the detector and recorded.\n>>These occasional events form a Poisson process, with a rate proportional\n>>to the intensity I. This, no more and no less, is the experimental\n>>observation. It is precisely what is predicted by quantum mechanics.\n>>\n> Yes, but we have 2 possible observations for this experiment assuming\n> the independence of the triggering events of the detectors (e.g. CCD to\n> cover the space of the interference pattern): Single events or the\n> complete set of events (the complete interference pattern).\n> By single events, I mean an experiment where the intensity is so weak\n> as we just have one click for one experiment trial (the electron case).\n\nIn this case, the click just reveals the presence of the beam (which\nI think of being present all the time, though not always transmitting\nenough energy to cause a click), but not the presence of a photon.\n\nThe single event is, however, simply not enough to estimate the\nintensity of the beam. The intensity is the objective contents in the\nsense of my interpretation, while the clicks are the rough\napproximations to it that can be read off the detecting equipment.\nSince the response is so irregular, one needs a long observation time\nto get a reliable estimate of the real thing, the intensity.\n\nIn a similar way, much of the observable information about distant\nstars is collected by astronomers. Reliable measurements simply take\nsometimes a lot of time, independent of whether the system observed is\nclassical or qwuantum. What decides about the number of repetitions\nneeded is the predicted accuracy, given by the standard deviation.\n\n\n\n> For the second experiment trial, there is sufficient intensity to\n> trigger the whole pattern (multiple independent electron case in time).\n\nThis has no interpretation problem.\n\n\n>>The traditional sloppy way of picturing this in an intuitive way is to\n>>say that, from time to time, a photon arrives at the screen and kicks\n>>an electron out of its orbit. This is a nice picture, especially for\n>>the newcomer or the lay man, but it cannot be taken any more seriously\n>>than Bohr\'s picture of an atom, in which electrons orbit a nucleus in\n>>certain quantum orbits. For nothing of this can be checked by experiment\n>>- it is empty talk intended to serve intuition, but in fact causing more\n>>damange than understanding.\n>>\n> I agree, I do not care about the reality of the photon. I just want\n> that the generic mathematical model may be applied to every experiment\n> and in some experiments, this model may be compatible with the particle\n> view.\n\nIt can, in the consistent experiment interpretation.\n\n\n>>Another way to see that is that the photo effect also happens for\n>>fermionic matter in a classical external field. (See, e.g., the\n>>quantum optics book by mandel and Wolf.) Thus the observed\n>>Poisson process cannot be a consequence of quantized light, but\n>>rather is an indication of quantized detectors.\n>>\n> Yes. However, in the case of single events (of the detector), we are\n> just able to apply the mean value statistics to the detector (huge set\n> of random variables/observables).\n\nYes. And this gives the click - an observable, macroscopic state of\nthe air hitting our ear (which hears the click). We then can\nspeculate about its origin. It proves the presence of the weak beam\nonly if repeatable; otherwise it might as well be discounted as an artifact.\n\n\n> In this case, I think the mean value\n> filter does not apply to the "particle" but only to the single\n> triggered detector: we may explain its "deterministic" triggering\n> value but not the cause of its triggering (except for the peculiar case\n> where the triggering value is equal to the photon state).\n\nYes. A single click tells very little about the state of the beam.\nQuantum optics experts use sophisticated and long series of raw\nmeasuremnts to measure the state of a beam. See, e.g., the nice\nbooklet\nU. Leonhardt,\nMeasuring the Quantum State of Light,\nCambridge, 1997.\n\n>>>What do you intend by irreversible effects?\n>>\n>>Dissipation, introduced by the Markov approximation necessary to get\n>>a sensible dynamics of a system smaller than the whole universe.\n>>\n> Dissipation means energy exchange or does it also includes other types\n> of exchange (such as momentum, assuming energy conservation)?\n\nDissipation means lack of unitarity and the presence of a Lyapunov\nfunction to reveal that. This implies a second law. Depending on the\ncontext, it may mean energy loss, momentum loss, entropy increase, etc..\n\n\n>>>>Everything in thermodynamics and kinetic theory\n>>>>is real, objective, without any of the dubiosities that characterize\n>>>>the traditional interpretations of the quantum world.\n>>>>\n>>>Frankly, I have a real problem to see reality behind pressure, volume\n>>>and energy/temperature.\n>>\n>>Ask any engineer. They know what is real. I understand reality in the\n>>engineering sense. They can determine the pressure, to within the\n>>accuracy allowed by statistical mechanics. A single measurement on a\n>>single large quantum system (such as a cup of tee) is usually sufficient\n>>to get a reasonable objective value.\n>>If this is not real, there is no reality at all, and we are all dreaming.\n>>\n>\n> Ok, I begin to understand better what you may mean when you use the\n> world reality. You are close to the epistemic view of physics, aren\'t\n> you? (the engineering sense).\n> If this is the case, it ok for me: you are not trying to say more that\n> it is: what "we" can "see".\n\nNo. What any inanimate but reliable recording device can permanently\nrecord (with respect to the time scale of interest), and what we could\ncheck if we\'d bother to do. Generally we only check a small summary of\nit in which we happen to be interested.\n\n\n>>How can you measure a microscopic object without measuring something\n>>macroscopic. You need the macroscopic, thermodynamic state of something\n>>to assert that indeed some definite, objective event happened.\n>>Take away objectivity and you lose all of physics.\n>>\n> Ok, for the macroscopic interface. See my previous answer with the\n> photons as I think there is a misunderstanding. I just question how you\n> can describe the trigger of such a macroscopic device by a single\n> particle event (e.g. an electron in a given quantum state).\n\nI don\'t understand what precisely you want.\nIt is described by an increase in the electron density at the place\nwhere the current is measured and turned into a record.\n\n\n> If you only describe it through statistics (hence requires multiple\n> outcomes), Is your description able to predict a preferred basis of the\n> quantum state of the particle?\n\nEvery single click is a macroscopic event. A single click lets us infer\nonly an ypper bound on the intensity of the quantum system (the beam).\nA multitude of clicks gives more and more information about it.\n\n\n>>>>The quest is to show that the interaction of a quantum system with\n>>>>a macroscopic detector describable by thermodynamics (and hence,\n>>>>through statistical mechanics, by quantum theory)\n>>>\n>>>Statistical classical mechanics?\n>>\n>>No. Statistical mechanics as taught in textbooks. Which includes\n>>(and on the deepest level is only) quantum mechanics.\n>>\n> (you mean modern statistical mechanics, thus bases on QM and not the\n> old gibbs statistical mechanics based on classical mechanics. I always\n> try to separate them as I seem to be an old-fashioned man : ).\n\nThey are essentially he same thing. Formally very close, only the\ndetails of the dynamics differs.\n\nBut quantum statistical mechanics is OK for our discussion.\n\n\n> Ok, I think I begin to understand what you are trying to say (tell me\n> If I am wrong).\n> You are using the mean value filter to try to get deterministic results\n> of macroscopic systems (on a given basis of this system: e.g. pressure,\n> energy, position, volume, etc ...).\n\nYes. Since this is universal agreement of physicists and engineers.\nIt is the best approximation to a concept of reality that physcis ever\ndeveloped.\n\n> If this is correct, all these\n> macroscopic observables will commute between themselves (simultaneous\n> measurement possible).\n\nNo. There are no eigenvalues involved. Expectations are the real things,\nnot eigenvalues. This is a complete renouncement of the Copenhagen\ninterpretation! For example, spin is a continuous variable,\nnot a discrete one, though it is measured by collecting and\naveraging discrete events.\n\nSome macroscopic observables, however, commute, when taken at a fixed\ntime. Others nearly commute.\n\n\n> If you have a theorem stating that all the\n> observables of a macroscopic system (at the infinite number limit)\n> commute, you solve the preferred basis problem of the measurement.\n\nThe preferred basis problem is solved in a different way, using the\nprojection operator formalism. (This is still unpublished work, that\nI hoe to write up during the summer.)\n\n\n> Therefore, once we define the quantum interaction between the quantum\n> particle and the macroscopic system, we are able to know the states of\n> the quantum particle through the values of the commuting observables of\n> the macroscopic system (e.g. pressure, energy, position, volume, etc\n> ..) if the decoherence results apply.\n\nNo. Please try again, given the new information expounded above.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
>>>Interesting.
>>>You seem to view the measurement results exclusively through the mean
>>>value filter
>>
>>Yes. Mean values of thermodynamic origin are the raw observables
>>in all experiments; everything else is derived from these by theory
>>or speculation.
>>I call this the 'consistent experiment interpretation', following
>>first steps in this direction taken in Section 10 of
>> http://www.arxiv.org/abs/quant-ph/0303047 =3D \Int. J. Mod. Phys. B 17 (2003), 2937-2980.
>>Since I wrote this, my view has considerably gained in strength.
>>If you read German, you can find much more about it at
>> http://www.mat.univie.ac.at/~neum/physik-faq.tex
>
> Unfortunately, I do not read German (and I regret it today : ).
> However, I am greatly interested by the mean value filter and hope that
> you will be able to post soon the English version.
> I have also looked at your paper, section 10, but it not easy to
> understand the section alone (as the document is consistent : ) and
> more precisely what do you intend by consistent experiment. Currently,
> I would like to understand what part of thermodynamics you want to use
> to derive some results.
Nonequilibrium statistical mechanics shows the meaning of _single_
macroscopic observations of thermodynamic observables as
approximations to the expectations of corresponding microscopic
operators, and their attainable accuracy as the corresponding
standard deviation. In this sense, macroscopic expectations are
approximately measurable, independent of whether the underlying
microscopic theory is classical or quantum.
This defines realism for me, in accordance with the engineering point
of view. My interpretation extends this realist view of expectations
(rather than eigenvalues - which never figure in thermodynamics)
down to the microworld. Measurements of expectations simply become
more inaccurate, up to the point where they must be inferred by
averaging from very inaccurate raw measurements.
To analyze the measurement process and to recover Born's rule,
one needs the projection operator formalism. The most useful
exposition I found in the literature is in:
H Grabert,
Projection Operator Techniques in Nonequilibrium
Statistical Mechanics,
Springer Tracts in Modern Physics, 1982.
>>>in my point of view (like the interference pattern: single
>>>photon screen impact event versus multiple independent photons
>>>interference pattern event).
>>>How do you explain the observed state of a single photon event?
>>
>>It is only a sloppy way of speaking, not a real physical event.
>>What actually happens is the following:
>>
>>The light ray of a laser is an electromagnetic field localized in a
>>small region along the ray that begins in the laser and ends at the
>>photodetector. A ray of intensity I is described by a coherent state
>> |I>> = |0> + I|1> + I^2/2|2> + I^3/6|3> + ...
>>If I is tiny then, from time to time, an electron responds (in some
>>loose way of speaking that itself would need correction) to the
>>energy continuously transmitted by the ray by going into an excited
>>state, an event which is magnified in the detector and recorded.
>>These occasional events form a Poisson process, with a rate proportional
>>to the intensity I. This, no more and no less, is the experimental
>>observation. It is precisely what is predicted by quantum mechanics.
>>
> Yes, but we have 2 possible observations for this experiment assuming
> the independence of the triggering events of the detectors (e.g. CCD to
> cover the space of the interference pattern): Single events or the
> complete set of events (the complete interference pattern).
> By single events, I mean an experiment where the intensity is so weak
> as we just have one click for one experiment trial (the electron case).
In this case, the click just reveals the presence of the beam (which
I think of being present all the time, though not always transmitting
enough energy to cause a click), but not the presence of a photon.
The single event is, however, simply not enough to estimate the
intensity of the beam. The intensity is the objective contents in the
sense of my interpretation, while the clicks are the rough
approximations to it that can be read off the detecting equipment.
Since the response is so irregular, one needs a long observation time
to get a reliable estimate of the real thing, the intensity.
In a similar way, much of the observable information about distant
stars is collected by astronomers. Reliable measurements simply take
sometimes a lot of time, independent of whether the system observed is
classical or qwuantum. What decides about the number of repetitions
needed is the predicted accuracy, given by the standard deviation.
> For the second experiment trial, there is sufficient intensity to
> trigger the whole pattern (multiple independent electron case in time).
This has no interpretation problem.
>>The traditional sloppy way of picturing this in an intuitive way is to
>>say that, from time to time, a photon arrives at the screen and kicks
>>an electron out of its orbit. This is a nice picture, especially for
>>the newcomer or the lay man, but it cannot be taken any more seriously
>>than Bohr's picture of an atom, in which electrons orbit a nucleus in
>>certain quantum orbits. For nothing of this can be checked by experiment
>>- it is empty talk intended to serve intuition, but in fact causing more
>>damange than understanding.
>>
> I agree, I do not care about the reality of the photon. I just want
> that the generic mathematical model may be applied to every experiment
> and in some experiments, this model may be compatible with the particle
> view.
It can, in the consistent experiment interpretation.
>>Another way to see that is that the photo effect also happens for
>>fermionic matter in a classical external field. (See, e.g., the
>>quantum optics book by mandel and Wolf.) Thus the observed
>>Poisson process cannot be a consequence of quantized light, but
>>rather is an indication of quantized detectors.
>>
> Yes. However, in the case of single events (of the detector), we are
> just able to apply the mean value statistics to the detector (huge set
> of random variables/observables).
Yes. And this gives the click - an observable, macroscopic state of
the air hitting our ear (which hears the click). We then can
speculate about its origin. It proves the presence of the weak beam
only if repeatable; otherwise it might as well be discounted as an artifact.
> In this case, I think the mean value
> filter does not apply to the "particle" but only to the single
> triggered detector: we may explain its "deterministic" triggering
> value but not the cause of its triggering (except for the peculiar case
> where the triggering value is equal to the photon state).
Yes. A single click tells very little about the state of the beam.
Quantum optics experts use sophisticated and long series of raw
measuremnts to measure the state of a beam. See, e.g., the nice
booklet
U. Leonhardt,
Measuring the Quantum State of Light,
Cambridge, 1997.
>>>What do you intend by irreversible effects?
>>
>>Dissipation, introduced by the Markov approximation necessary to get
>>a sensible dynamics of a system smaller than the whole universe.
>>
> Dissipation means energy exchange or does it also includes other types
> of exchange (such as momentum, assuming energy conservation)?
Dissipation means lack of unitarity and the presence of a Lyapunov
function to reveal that. This implies a second law. Depending on the
context, it may mean energy loss, momentum loss, entropy increase, etc..
>>>>Everything in thermodynamics and kinetic theory
>>>>is real, objective, without any of the dubiosities that characterize
>>>>the traditional interpretations of the quantum world.
>>>>
>>>Frankly, I have a real problem to see reality behind pressure, volume
>>>and energy/temperature.
>>
>>Ask any engineer. They know what is real. I understand reality in the
>>engineering sense. They can determine the pressure, to within the
>>accuracy allowed by statistical mechanics. A single measurement on a
>>single large quantum system (such as a cup of tee) is usually sufficient
>>to get a reasonable objective value.
>>If this is not real, there is no reality at all, and we are all dreaming.
>>
>
> Ok, I begin to understand better what you may mean when you use the
> world reality. You are close to the epistemic view of physics, aren't
> you? (the engineering sense).
> If this is the case, it ok for me: you are not trying to say more that
> it is: what "we" can "see".
No. What any inanimate but reliable recording device can permanently
record (with respect to the time scale of interest), and what we could
check if we'd bother to do. Generally we only check a small summary of
it in which we happen to be interested.
>>How can you measure a microscopic object without measuring something
>>macroscopic. You need the macroscopic, thermodynamic state of something
>>to assert that indeed some definite, objective event happened.
>>Take away objectivity and you lose all of physics.
>>
> Ok, for the macroscopic interface. See my previous answer with the
> photons as I think there is a misunderstanding. I just question how you
> can describe the trigger of such a macroscopic device by a single
> particle event (e.g. an electron in a given quantum state).
I don't understand what precisely you want.
It is described by an increase in the electron density at the place
where the current is measured and turned into a record.
> If you only describe it through statistics (hence requires multiple
> outcomes), Is your description able to predict a preferred basis of the
> quantum state of the particle?
Every single click is a macroscopic event. A single click lets us infer
only an ypper bound on the intensity of the quantum system (the beam).
A multitude of clicks gives more and more information about it.
>>>>The quest is to show that the interaction of a quantum system with
>>>>a macroscopic detector describable by thermodynamics (and hence,
>>>>through statistical mechanics, by quantum theory)
>>>
>>>Statistical classical mechanics?
>>
>>No. Statistical mechanics as taught in textbooks. Which includes
>>(and on the deepest level is only) quantum mechanics.
>>
> (you mean modern statistical mechanics, thus bases on QM and not the
> old gibbs statistical mechanics based on classical mechanics. I always
> try to separate them as I seem to be an old-fashioned man : ).
They are essentially he same thing. Formally very close, only the
details of the dynamics differs.
But quantum statistical mechanics is OK for our discussion.
> Ok, I think I begin to understand what you are trying to say (tell me
> If I am wrong).
> You are using the mean value filter to try to get deterministic results
> of macroscopic systems (on a given basis of this system: e.g. pressure,
> energy, position, volume, etc ...).
Yes. Since this is universal agreement of physicists and engineers.
It is the best approximation to a concept of reality that physcis ever
developed.
> If this is correct, all these
> macroscopic observables will commute between themselves (simultaneous
> measurement possible).
No. There are no eigenvalues involved. Expectations are the real things,
not eigenvalues. This is a complete renouncement of the Copenhagen
interpretation! For example, spin is a continuous variable,
not a discrete one, though it is measured by collecting and
averaging discrete events.
Some macroscopic observables, however, commute, when taken at a fixed
time. Others nearly commute.
> If you have a theorem stating that all the
> observables of a macroscopic system (at the infinite number limit)
> commute, you solve the preferred basis problem of the measurement.
The preferred basis problem is solved in a different way, using the
projection operator formalism. (This is still unpublished work, that
I hoe to write up during the summer.)
> Therefore, once we define the quantum interaction between the quantum
> particle and the macroscopic system, we are able to know the states of
> the quantum particle through the values of the commuting observables of
> the macroscopic system (e.g. pressure, energy, position, volume, etc
> ..) if the decoherence results apply.
No. Please try again, given the new information expounded above.
Arnold Neumaier
Hendrik van Hees
Jun5-05, 01:26 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n\n> I\'m not sure what you\'re referring to by a \'minimal statistical\n> interpretation\'. It seems to me that what you\'re indicating is a\n> hidden variables theory and that is experimentally ruled out (assuming\n> locality).\n\nThe minimal statistical interpretation is not a hidden-variable theory,\nwhich indeed is ruled out experimentally assuming locality.\n\nIt is simply quantum mechanics, taking the probabilistic physical\ncontent of the states seriously and does not associate the state with\nsingle systems but only as a description of ensembles. With this\ninterpretation all the conceptional troubles of quantum theory vanish\nat the price that one admits that quantum theory cannot describe single\nsystems.\n\nNevertheless it is sufficient to use quantum theory to all experimental\nfacts, known so far. A very nice introduction to this point of view can\nbe found in\n\nL. E. Ballentine, The Statistical Interpretation of Quantum Mechanics,\nRev. Mod. Phys. *42* (1970) 358\nhttp://link.aps.org/abstract/RMP/v42/p358\n\nor in the marvelous textbook by the same author\n\nL.E. Ballentine, Quantum Mechanics, a Modern Develeopment, World\nScientific\n\n--\nHendrik van Hees Texas A&M University\nPhone: +1 979/845-1411 Cyclotron Institute, MS-3366\nFax: +1 979/845-1899 College Station, TX 77843-3366\nhttp://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> I'm not sure what you're referring to by a 'minimal statistical
> interpretation'. It seems to me that what you're indicating is a
> hidden variables theory and that is experimentally ruled out (assuming
> locality).
The minimal statistical interpretation is not a hidden-variable theory,
which indeed is ruled out experimentally assuming locality.
It is simply quantum mechanics, taking the probabilistic physical
content of the states seriously and does not associate the state with
single systems but only as a description of ensembles. With this
interpretation all the conceptional troubles of quantum theory vanish
at the price that one admits that quantum theory cannot describe single
systems.
Nevertheless it is sufficient to use quantum theory to all experimental
facts, known so far. A very nice introduction to this point of view can
be found in
L. E. Ballentine, The Statistical Interpretation of Quantum Mechanics,
Rev. Mod. Phys. *42* (1970) 358
http://link.aps.org/abstract/RMP/v42/p358
or in the marvelous textbook by the same author
L.E. Ballentine, Quantum Mechanics, a Modern Develeopment, World
Scientific
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu
I.Vecchi
Jun5-05, 01:28 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n...\n> That\'s also my understanding, but I need to understand the people who\n> think decoherence solves the problem as I am not sure I have understood\n> the whole problem.\n\nNow that\'s a labyrinthine psychological problem. I guess some people\nhate the idea that their reference frames (pointer states or whatever}\nare just that and not the universe\'s fundamental structure.\n\n> Have you got some data concerning the "no-recoil" assumption?\n\nI am not sure I understand the question. Do you expect me to provide\ndata falsifying Newton\'s third law?\nIf you need a reference where the "no-recoil" assumption is introduced\nexplicitly I suggest Joos\' article in the classic "Decoherence and the\nAppearance of a Classical World in Quantum Theory". Joos is a believer\nin decoherence, but he writes and argues with remarkable clarity,\nmaking it easy to spot DT\'s hidden assumptions.\n\nCheers, or even better, je vous prie d\'accepter, Monsieur Seratend,\nl\'expression sinc=E8re de mes sentiments les plus distingu=E9s.=20\n\nIV\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
...
> That's also my understanding, but I need to understand the people who
> think decoherence solves the problem as I am not sure I have understood
> the whole problem.
Now that's a labyrinthine psychological problem. I guess some people
hate the idea that their reference frames (pointer states or whatever}
are just that and not the universe's fundamental structure.
> Have you got some data concerning the "no-recoil" assumption?
I am not sure I understand the question. Do you expect me to provide
data falsifying Newton's third law?
If you need a reference where the "no-recoil" assumption is introduced
explicitly I suggest Joos' article in the classic "Decoherence and the
Appearance of a Classical World in Quantum Theory". Joos is a believer
in decoherence, but he writes and argues with remarkable clarity,
making it easy to spot DT's hidden assumptions.
Cheers, or even better, je vous prie d'accepter, Monsieur Seratend,
l'expression sinc=E8re de mes sentiments les plus distingu=E9s.=20
IV
Seratend
Jun5-05, 01:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> > I do not follow you. Do you think you are able to explain the\n> > probabilities of statistical classical mechanics?\n>\n> It\'s not completely rigorous, but generally, yeah. That\'s what\n> statistical mechanics is.\n>\nIf you say that, I really think you have not really understood the\nprobabilities of classical statistical mechanics and I understand now\nwhy you do not understand my explanations in the previous posts (e.g.\nfunction q(t)=f(qo,d/dtqo, t) and the probability law and determinism,\n...).\nDo you really understand (formally) probabilities and how we use them\nin the prediction of statistics of a system?\nDo you understand that in order to predict a statistics, we need before\nan externally given probability law? (e.g. the coin flipping\nexperiment: to say the frequency of the head/tails is the probability\nlaw, we must assume the independence of the trials => a given\nprobability law on the space of all trials).\nDo you understand that nothing (logic) predicts this probability,\nexcept if it is the result of another experiment? (and hence, we have\nanother probability that is not predicted).\nWe need it in order to make a logical prediction of the statistics as\nwe need a reference point to give the logical position of a particle.\n\nI have just written these questions in order to show you that if you\nare not able to see how we construct (the logic) the statistical\ndescription of experiments (quantum or classical: does not matter), it\nwill be difficult for you to understand what the measurement and the\ncollapse are: the logic (and not its multiple interpretations) of the\nexperiments. Therefore, it will be difficult to remove all the\nnon-mathematical results from the mathematical ones (the logic\nexplaination).\nIt will also be difficult for me to explain you and to understand what\nyou are trying to mean, if you have not a clear view of statistics (the\nlogic and not the belief). I only have the logic to build a common\nground of understanding.\n\nUsual statistics are a very pragmatic description choice (nothing\nmagic). With QM or with a basic coin flipping experiment we always do\nthe same thing: we label the experimental trials and compute the\nfrequencies of the outcomes. This is a choice of description and not a\nmysterious physical process:\na) you have a random variable, a function, that express your experiment\nlogic: for the trial labelled e, you have the result a (logic true).\nThe experiment trials implicitly define the function: the set {e, a} is\nequivalent to a function a=f(e) (i.e. the proposition "the result of\nthe experiment label e is a" is true).\nThis is the formal meaning of the random variable in the experiment.\nThe function f defines the true propositions of the experimental\ntrials.\nDo you understand that the function does not have to exist if the\nexperiment trials do not exist? (logical meaning).\nDo you understand that without this function we are not able to\nassociate the frequencies to the outcomes of the experiment?\nDo you understand that there is no time reference, just propositions\nthat we define by the realization of the experimental trials? (such a\na=f(e))\n\nb) Each time you want (logic) to say you observe a given statistics [of\na random variable] in a given experiment, you need to get a probability\nlaw on the abstract set of the considered experiment trials. This is\nwhat we call the preparation of the system (or of the coin). This is\nthe basic expression of the induced probability law by the function f\ndefined by the experimental trials associated to the law of large\nnumbers theorem (the logic behind the sentence/proposition, "I\nobserve a given statistics"):\nProbability law of the statistics P_f= P o f-1.\nWhere P is the probability law on the set of all experiment trials\n(E={e}) and P_f the induced probability law on the set A={a}. Without\nthat, you cannot define a logical meaning to the frequency of the\noutcomes.\nDo you understand that nothing explains why we have the probability P\nin this description choice? (Externally given). And this is not\nmysterious, just a logical choice.\n\nDo you understand that this description is independent of the theory\n(QM or Classical mechanics)?\n\nAre you able to see the connection between the function f and the\nobservables of QM and the collapse postulate?\n\nNow given this description choice explanation, are you able to\nunderstand we are not able to explain the probabilities of a given\nexperiment, just the probabilities induced by an external probability\nlaw? Do you understand that QM and classical statistical mechanics just\ndescribe the induced probability law (hence the "preparation" of a set\nof systems is required to compute the induced probability)?\n\nI really think that if you are not able to understand this simple basic\nlogical choice of description (the statistics), it will be very\ndifficult to for me to see the logical ground of your affirmations.\n\n\n> > Or do you think fundamental each time you have a functional relation of\n> > the type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?\n>\n> Sorry. I don\'t know what you mean.\n>\ncf above. P_t= P_{t=o} o f-1\n\n> [...]\n\n> > We can add or remove it,\n> > just to verify that the screen is a measurement of the interference\n> > pattern (we cannot make the distinction):\n> >\n> > a) I may say that the screen is a measurement apparatus or not (it\n> > collapses the wavefunction): this does not change the result of the\n> > detector in this toy model (because the projector associated to the\n> > collapse of the screen commutes with the projector of the detector).\n>\n> Are you discussing an example with commuting observables, then?\n\nYes (the observable of the screen and the observable of the detector).\n\n>\n> > b) Therefore in this toy model, I may have 2 measurements apparatus:\n> > the screen and the detector. I can remove or add the measurement\n> > detector: it does not change the behaviour of screen (no interaction).\n> > The detector is just a virtual detector (we add or remove it by\n> > thought).\n> > Hence, I may say that the screen is a measurement apparatus that does\n> > not entangled the photons with itself (I have chosen the interaction\n> > such that no entanglement occurs).\n>\n> If the screen does anything that allows us to make an observation, it is\n> entangled with the photons. I don\'t see how you can simply render this\n> false by fiat.\n>\nPlease once again, I gave you a very simple interaction hamiltonian to\ndescribe the interaction of screen with the photons. I assume you are\nable to understand that such a basic Hamiltonian does not entangle the\nstate of the photons/electrons with the state of the screen. (H=\n|screen><screen|(x)V(r))\n\nI use the detector to prove that nothing (logic) prevents you, in QM\ntheory, to say the screen is a measurement apparatus (producing the\ninterference pattern.\n\nNow, you are free to give your own definition of a measurement\napparatus requiring an entanglement interaction and choose an ad hoc\ninteraction such that the Schmitt basis is the one where we get the\nobservations. However, in this case this is completely out of the scope\nof QM theory and it is much more simpler to say that we simply know the\npreferred basis by doing experiments (we use our knowledge of known\nexperiment results to deduce other experiment results and basis): no\nprediction by QM theory.\n\nSeratend\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> > I do not follow you. Do you think you are able to explain the
> > probabilities of statistical classical mechanics?
>
> It's not completely rigorous, but generally, yeah. That's what
> statistical mechanics is.
>
If you say that, I really think you have not really understood the
probabilities of classical statistical mechanics and I understand now
why you do not understand my explanations in the previous posts (e.g.
function q(t)=f(qo,d/dtqo, t) and the probability law and determinism,
...).
Do you really understand (formally) probabilities and how we use them
in the prediction of statistics of a system?
Do you understand that in order to predict a statistics, we need before
an externally given probability law? (e.g. the coin flipping
experiment: to say the frequency of the head/tails is the probability
law, we must assume the independence of the trials => a given
probability law on the space of all trials).
Do you understand that nothing (logic) predicts this probability,
except if it is the result of another experiment? (and hence, we have
another probability that is not predicted).
We need it in order to make a logical prediction of the statistics as
we need a reference point to give the logical position of a particle.
I have just written these questions in order to show you that if you
are not able to see how we construct (the logic) the statistical
description of experiments (quantum or classical: does not matter), it
will be difficult for you to understand what the measurement and the
collapse are: the logic (and not its multiple interpretations) of the
experiments. Therefore, it will be difficult to remove all the
non-mathematical results from the mathematical ones (the logic
explaination).
It will also be difficult for me to explain you and to understand what
you are trying to mean, if you have not a clear view of statistics (the
logic and not the belief). I only have the logic to build a common
ground of understanding.
Usual statistics are a very pragmatic description choice (nothing
magic). With QM or with a basic coin flipping experiment we always do
the same thing: we label the experimental trials and compute the
frequencies of the outcomes. This is a choice of description and not a
mysterious physical process:
a) you have a random variable, a function, that express your experiment
logic: for the trial labelled e, you have the result a (logic true).
The experiment trials implicitly define the function: the set {e, a} is
equivalent to a function a=f(e) (i.e. the proposition "the result of
the experiment label e is a" is true).
This is the formal meaning of the random variable in the experiment.
The function f defines the true propositions of the experimental
trials.
Do you understand that the function does not have to exist if the
experiment trials do not exist? (logical meaning).
Do you understand that without this function we are not able to
associate the frequencies to the outcomes of the experiment?
Do you understand that there is no time reference, just propositions
that we define by the realization of the experimental trials? (such a
a=f(e))
b) Each time you want (logic) to say you observe a given statistics [of
a random variable] in a given experiment, you need to get a probability
law on the abstract set of the considered experiment trials. This is
what we call the preparation of the system (or of the coin). This is
the basic expression of the induced probability law by the function f
defined by the experimental trials associated to the law of large
numbers theorem (the logic behind the sentence/proposition, "I
observe a given statistics"):
Probability law of the statistics P_f= P o f-1.
Where P is the probability law on the set of all experiment trials
(E={e}) and P_f the induced probability law on the set A={a}. Without
that, you cannot define a logical meaning to the frequency of the
outcomes.
Do you understand that nothing explains why we have the probability P
in this description choice? (Externally given). And this is not
mysterious, just a logical choice.
Do you understand that this description is independent of the theory
(QM or Classical mechanics)?
Are you able to see the connection between the function f and the
observables of QM and the collapse postulate?
Now given this description choice explanation, are you able to
understand we are not able to explain the probabilities of a given
experiment, just the probabilities induced by an external probability
law? Do you understand that QM and classical statistical mechanics just
describe the induced probability law (hence the "preparation" of a set
of systems is required to compute the induced probability)?
I really think that if you are not able to understand this simple basic
logical choice of description (the statistics), it will be very
difficult to for me to see the logical ground of your affirmations.
> > Or do you think fundamental each time you have a functional relation of
> > the type q(t)=f(qo,d/dtqo, t) where you apply porbabilities?
>
> Sorry. I don't know what you mean.
>
cf above. P_t= P_{t=o} o f-1
> [...]
> > We can add or remove it,
> > just to verify that the screen is a measurement of the interference
> > pattern (we cannot make the distinction):
> >
> > a) I may say that the screen is a measurement apparatus or not (it
> > collapses the wavefunction): this does not change the result of the
> > detector in this toy model (because the projector associated to the
> > collapse of the screen commutes with the projector of the detector).
>
> Are you discussing an example with commuting observables, then?
Yes (the observable of the screen and the observable of the detector).
>
> > b) Therefore in this toy model, I may have 2 measurements apparatus:
> > the screen and the detector. I can remove or add the measurement
> > detector: it does not change the behaviour of screen (no interaction).
> > The detector is just a virtual detector (we add or remove it by
> > thought).
> > Hence, I may say that the screen is a measurement apparatus that does
> > not entangled the photons with itself (I have chosen the interaction
> > such that no entanglement occurs).
>
> If the screen does anything that allows us to make an observation, it is
> entangled with the photons. I don't see how you can simply render this
> false by fiat.
>
Please once again, I gave you a very simple interaction hamiltonian to
describe the interaction of screen with the photons. I assume you are
able to understand that such a basic Hamiltonian does not entangle the
state of the photons/electrons with the state of the screen. (H=
|screen><screen|(x)V(r))
I use the detector to prove that nothing (logic) prevents you, in QM
theory, to say the screen is a measurement apparatus (producing the
interference pattern.
Now, you are free to give your own definition of a measurement
apparatus requiring an entanglement interaction and choose an ad hoc
interaction such that the Schmitt basis is the one where we get the
observations. However, in this case this is completely out of the scope
of QM theory and it is much more simpler to say that we simply know the
preferred basis by doing experiments (we use our knowledge of known
experiment results to deduce other experiment results and basis): no
prediction by QM theory.
Seratend
I.Vecchi
Jun5-05, 10:55 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nAaron Bergman wrote:\n...\n> Proving decoherence in general is, as I understand it, hard (but this\n> isn\'t really my field.)\n> The thing is, we can experimentally observe it\n> happening.\n\nWhat we can experimentally observe is that interference patterns that\nmay reveal macroscopic superpositions are in general hard to track.\nThat\'s hardly surprising and does not require grotesque unphysical\nassumptions to be explained.\n\nAnyways, in current QM there are far more interesting perspectives than\nDT\'s conceptual ratholes. Macroscopic superpositions are already being\ndetected ([1],[2]) and I am looking forward to experiments detecting\nsuperposed observers.\n\nIV\n\n[1] http://physicsweb.org/article/*world/13/8/3\n[2] www.nobel.se/physics/symposia/*ncs-2001-1/leggett.pdf\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
...
> Proving decoherence in general is, as I understand it, hard (but this
> isn't really my field.)
> The thing is, we can experimentally observe it
> happening.
What we can experimentally observe is that interference patterns that
may reveal macroscopic superpositions are in general hard to track.
That's hardly surprising and does not require grotesque unphysical
assumptions to be explained.
Anyways, in current QM there are far more interesting perspectives than
DT's conceptual ratholes. Macroscopic superpositions are already being
detected ([1],[2]) and I am looking forward to experiments detecting
superposed observers.
IV
[1] http://physicsweb.org/article/*world/13/8/3
[2] www.nobel.se/physics/symposia/*ncs-2001-1/leggett.pdf
Aaron Bergman
Jun5-05, 07:19 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117984312.453258.10390@o13g2000cwo.googlegroups. com>,\n"I.Vecchi" <vecchi@weirdtech.com> wrote:\n\n> Aaron Bergman wrote:\n> ..\n> > Proving decoherence in general is, as I understand it, hard (but this\n> > isn\'t really my field.)\n> > The thing is, we can experimentally observe it\n> > happening.\n>\n> What we can experimentally observe is that interference patterns that\n> may reveal macroscopic superpositions are in general hard to track.\n> That\'s hardly surprising and does not require grotesque unphysical\n> assumptions to be explained.\n\nAs I understand it, it\'s more than just not seeing macroscopic\nsuperpositions; the actual process of decoherence has been observed.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117984312.453258.10390@o13g2000cwo.googlegroups.c om>,
"I.Vecchi" <vecchi@weirdtech.com> wrote:
> Aaron Bergman wrote:
> ..
> > Proving decoherence in general is, as I understand it, hard (but this
> > isn't really my field.)
> > The thing is, we can experimentally observe it
> > happening.
>
> What we can experimentally observe is that interference patterns that
> may reveal macroscopic superpositions are in general hard to track.
> That's hardly surprising and does not require grotesque unphysical
> assumptions to be explained.
As I understand it, it's more than just not seeing macroscopic
superpositions; the actual process of decoherence has been observed.
Aaron
Aaron Bergman
Jun5-05, 07:19 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1117885132.982867.64950@g43g2000cwa.googlegroups. com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Do you understand that nothing (logic) predicts this probability,\n> except if it is the result of another experiment? (and hence, we have\n> another probability that is not predicted).\n\nI\'m a frequentist. In statistical mechanics, you assume that you fully\nsample the phase space and the probabilities fall out. I\'m well aware of\nthe philosophical difficulties in defining probabilities and the like,\nbut generally I don\'t particularly care.\n\n[...]\n\n> I use the detector to prove that nothing (logic) prevents you, in QM\n> theory, to say the screen is a measurement apparatus (producing the\n> interference pattern.\n\nYou use the word \'logic\' as if there were some fundamental set of axioms\nthat we know have to be correct. It\'s just not true.\n\n> Now, you are free to give your own definition of a measurement\n> apparatus requiring an entanglement interaction and choose an ad hoc\n> interaction such that the Schmitt basis is the one where we get the\n> observations.\n\nThe Schmitt basis is only the correct basis after we wait the\ndecoherence time.\n\n> However, in this case this is completely out of the scope\n> of QM theory and it is much more simpler to say that we simply know the\n> preferred basis by doing experiments (we use our knowledge of known\n> experiment results to deduce other experiment results and basis): no\n> prediction by QM theory.\n\nAgain, if you describe a real experiment, ie, one where and actual\nperson makes and actual measurement, you can determine the basis\nselected by decoherence. The only inputs are the macrostates, but that\'s\njust mechanics. If your claim is that we can\'t determine macrostates ab\ninitio, then I just disagree.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1117885132.982867.64950@g43g2000cwa.googlegroups.c om>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Do you understand that nothing (logic) predicts this probability,
> except if it is the result of another experiment? (and hence, we have
> another probability that is not predicted).
I'm a frequentist. In statistical mechanics, you assume that you fully
sample the phase space and the probabilities fall out. I'm well aware of
the philosophical difficulties in defining probabilities and the like,
but generally I don't particularly care.
[...]
> I use the detector to prove that nothing (logic) prevents you, in QM
> theory, to say the screen is a measurement apparatus (producing the
> interference pattern.
You use the word 'logic' as if there were some fundamental set of axioms
that we know have to be correct. It's just not true.
> Now, you are free to give your own definition of a measurement
> apparatus requiring an entanglement interaction and choose an ad hoc
> interaction such that the Schmitt basis is the one where we get the
> observations.
The Schmitt basis is only the correct basis after we wait the
decoherence time.
> However, in this case this is completely out of the scope
> of QM theory and it is much more simpler to say that we simply know the
> preferred basis by doing experiments (we use our knowledge of known
> experiment results to deduce other experiment results and basis): no
> prediction by QM theory.
Again, if you describe a real experiment, ie, one where and actual
person makes and actual measurement, you can determine the basis
selected by decoherence. The only inputs are the macrostates, but that's
just mechanics. If your claim is that we can't determine macrostates ab
initio, then I just disagree.
Aaron
Seratend
Jun6-05, 09:32 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Seratend wrote:\n>\n> > I hope you also consider the statistics of statistical classical\n> > mechanics as pragmatic procedures. If this is the case, you are simply\n> > looking for the deterministic evolution of individual outcomes from a\n> > given initial condition:\n> > Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).\n> > If it is what you are looking for, general unitary evolution tells you\n> > that it is most of the time impossible:\n>\n> No. Only a closed system evolves unitarily, and of course it cannot\n> be observed and hence does not produce outcomes.\n>\n\nThe state of a closed system evolves unitary and the above text does\nnot say the contrary. However, the sentence "the closed system cannot\nbe observed and hence cannot produce outcomes" is already an\ninterpretation of the measurement formalism [of QM axiomatic theory].\nThe formal measurement (the "preparation" and the "result"\noutcome) and the collapse postulate logic do not assume such a\nrequirement and closed systems may be logically built where we have\nformal measurements and outcome results.\n\n> This even holds in the traditional Copenhagen interpretation.\n> The view is that the system is closed most of the time and then\n> evolves unitarity. At certain very short moments, it is assumed\n> to be in contact with a detector for measurement - then the\n> system is open and evolves nonunitarily, by collapse.\n>\nThis is interpretation, and as already said, if it does not change the\naxiomatic base (the logic) of QM, it is ok for me (no impact on the\nlogic content of the theory: it is just a re labelling of the words).\nNote, in the QM formalism, there is no classical/quantum boundary (only\nin the interpretations of QM). Just postulates that may be applied,\nhopefully (for the consistence of the theory) on closed systems as well\nas opened ones.\n\nThe formal measurement (collapse and born rules) are just the\nstatistical description of experiments:\n\na) The collapse postulate describes 2 topics, a property of the system\n(Outcome a of a given observable A is true) and the state of the system\nif this property is true (stability of the property: the "true\nremains true").\nb) the born rules: a state and an observable define the probability law\nof the outcomes of the observable.\n\nTherefore, the probability law of the outcomes (the statistics) of an\nexperiment is completely defined by the couple (|psi>, A). However to\ncalculate the statistics on experiments (the mapping), we need the\ncollapse: the formal mapping between the experiment outcomes and the\nstatistics simply expressed by the collapse property: the outcome\n"a" for this experiment trial is true.\nNote that in order to recover the probability law in the frequency of\noutcomes we must have the independence of identical systems (hence, we\nneed a "preparation" to select the systems).\nUnderstanding that the formal collapse only exists (logically) in the\ncontext of experimental trials allows one to separate the choice of\ndescription (the statistics) from the predictive role of the theory\n(i.e. the unitary evolution of the probability law).\n\nA physical theory is mainly a choice of description (formally, we are\nfree to choose what we want) and the prediction (the useful content\nimposed by the "reality") in the context of this choice of\ndescription.\n\nUsually (my knowledge : ), we use 2 logical type of descriptions in\nphysical theories: the "determinist" (i.e. the description of a\nfunction) and the statistical description of a system (i.e. the\nstatistics induced by the function). QM and Statistical classical\nmechanics are both based on the use of the formal statistical\ndescription of a system; therefore, I will describe what I mean (the\nlogic) by the logical content of a statistical description (the\nmathematics).\n\na) Math: A function is a collection of true propositions, by the\nlogical mapping a=f(e) <=> if e then a.\nb) Math: giving a function f or a set F= {(a,e), for all e in the\ndomain of the function} is equivalent.\nc) statistical description:\n\nStatistical description is a very pragmatic description choice (and not\na mysterious physical process). With QM or with a basic coin flipping\nexperiment we always do the same thing: we label the experimental\ntrials and compute the frequencies of the outcomes:\n1) We have an implicitly defined random variable, an abstract function\nf, which expresses the experiment logic results: for the trial labelled\ne, we associate the result a (logic true): "if e then result a".\nThe function/random variable is defined by the set {(e, a), for all e}\nis equivalent to a=f(e) (i.e. the proposition "the result of the\nexperiment trial label e is a" is true).\n\nThis is the logical content of the description of the experiments. It\nis a logical choice, no physical meaning is involved at this step.\n\nThe function f defines the true propositions of the experimental\ntrials. Without additional hypothesis, the function only exists in the\ncontext of the experiment trials. It is important to understand that\nthe function f is only defined in the context of the experiment\n(without extra properties, it is a contextual random variable) and does\nnot have a "reality" outside this experiment.\n\n2) In order to say (logic) we observe a given statistics [of outcomes]\nin a given set of experimental trials, we need to define logically this\nset of systems where we observe a given statistics (the set E), where\nthe function f is defined. This is the generally the set of labels of\nindependent identical systems (or the preparation word in the QM\nformalism).\nThis set of trials is either given or either defined by another\nproperty.\n\nOn this set E, we define the formal probability law P by induction:\nP_f= P o f-1\n\n-- P is the formal probability law on the set of all the concerned\nexperiment trials (E={e, for all e})\n--- P_f the induced probability law on the set A={a, for all outcomes\na}.\n-- f-1 is the inverse function defined on the sets of events: f-1:\nParts(A) --> Parts(E)\n(Parts(A) is the collection of all the subsets of A, idem for\nParts(E)).\n\nWithout this logical specification (the set of trials and the set of\noutcomes, the function f), we cannot define a logical meaning (a\nprobability law p_f) to the frequency of the outcomes (using the\nresults of the mathematical probability theory).\n\nThis is the basic expression of the induced probability law by the\nfunction f defined by the experimental trials associated to the law of\nlarge numbers theorem (the logic behind the sentence/proposition, "I\nobserve a given statistics").\n\nFormally, the QM measurement reflects this description choice with the\nobjects of QM.\n\n> Although not very clearly separated in many discussions,\n> these two processes happen never simultaneously but context\n> dependent, and are of course only approximations to more\n> realistic measurement situations.\n>\n> For example, in a Stern-Gerlach experiment, the system (silver atom)\n> moves from the source along the magnet towards the screen with very\n> good accuracy in a unitary (and indeed reversible) way. But a few\n> split moments before it hits the screen it feels its interactions,\n> and describing it as a closed system becomes hopelessly inaccurate.\n> Instead, since the interaction time is very short, it can be\n> described very accurately by an instantaneous collapse.\n>\nWhy do you say it becomes hopelessly inaccurate? And How can you really\napply a collapse to a non closed system? In this case, don\'t you\nthink the collapse result (the outcome) should be independent of the\npartial system description versus the whole system (including the\nuniverse if necessary)?\n\nThis is the problem of interpretation. Once you define a system that is\nno more described by the QM theory formalism, you are free to say. I\njust say, that QM collapse is compatible with unitary evolution (as\nwell as non unitary descirptions) in the sense it is a property that\nformally defines the "branch" of the unitary evolution (defined by\nthe outcome "a" of A is true) of the whole system (closed). This\ndefinition of the "branch" is not predictive; it is the formal\nmapping between the theory and the observation (the logic behind the\noutcome "a" is true).\n\nIn addition, we can easily model a macroscopic system (the screen) such\nthat it evolves unitary (hence closed) and blocks a particle within an\narea, just by using, for example, the quantum well models with a\npotential triggered by time. .\n\nI think it is important to accept the collapse formalism meaning on\nclosed systems (it is logically coherent). If we reject the collapse on\nclosed systems, we are already modifying the QM theory (either its\ndescriptions or its predictions). And currently, the experiments tend\nto show the validity of QM theory results in systems with a non\nnegligible number of particles.\n\nIn addition, the collapse does not prevent some determinist results on\nthe limit of the large numbers (reversible and irreversible results),\nit should be independant (e.g. the macroscopic outcome value is the\nmean value)\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Seratend wrote:
>
> > I hope you also consider the statistics of statistical classical
> > mechanics as pragmatic procedures. If this is the case, you are simply
> > looking for the deterministic evolution of individual outcomes from a
> > given initial condition:
> > Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).
> > If it is what you are looking for, general unitary evolution tells you
> > that it is most of the time impossible:
>
> No. Only a closed system evolves unitarily, and of course it cannot
> be observed and hence does not produce outcomes.
>
The state of a closed system evolves unitary and the above text does
not say the contrary. However, the sentence "the closed system cannot
be observed and hence cannot produce outcomes" is already an
interpretation of the measurement formalism [of QM axiomatic theory].
The formal measurement (the "preparation" and the "result"
outcome) and the collapse postulate logic do not assume such a
requirement and closed systems may be logically built where we have
formal measurements and outcome results.
> This even holds in the traditional Copenhagen interpretation.
> The view is that the system is closed most of the time and then
> evolves unitarity. At certain very short moments, it is assumed
> to be in contact with a detector for measurement - then the
> system is open and evolves nonunitarily, by collapse.
>
This is interpretation, and as already said, if it does not change the
axiomatic base (the logic) of QM, it is ok for me (no impact on the
logic content of the theory: it is just a re labelling of the words).
Note, in the QM formalism, there is no classical/quantum boundary (only
in the interpretations of QM). Just postulates that may be applied,
hopefully (for the consistence of the theory) on closed systems as well
as opened ones.
The formal measurement (collapse and born rules) are just the
statistical description of experiments:
a) The collapse postulate describes 2 topics, a property of the system
(Outcome a of a given observable A is true) and the state of the system
if this property is true (stability of the property: the "true
remains true").
b) the born rules: a state and an observable define the probability law
of the outcomes of the observable.
Therefore, the probability law of the outcomes (the statistics) of an
experiment is completely defined by the couple (|\psi>, A). However to
calculate the statistics on experiments (the mapping), we need the
collapse: the formal mapping between the experiment outcomes and the
statistics simply expressed by the collapse property: the outcome
"a" for this experiment trial is true.
Note that in order to recover the probability law in the frequency of
outcomes we must have the independence of identical systems (hence, we
need a "preparation" to select the systems).
Understanding that the formal collapse only exists (logically) in the
context of experimental trials allows one to separate the choice of
description (the statistics) from the predictive role of the theory
(i.e. the unitary evolution of the probability law).
A physical theory is mainly a choice of description (formally, we are
free to choose what we want) and the prediction (the useful content
imposed by the "reality") in the context of this choice of
description.
Usually (my knowledge : ), we use 2 logical type of descriptions in
physical theories: the "determinist" (i.e. the description of a
function) and the statistical description of a system (i.e. the
statistics induced by the function). QM and Statistical classical
mechanics are both based on the use of the formal statistical
description of a system; therefore, I will describe what I mean (the
logic) by the logical content of a statistical description (the
mathematics).
a) Math: A function is a collection of true propositions, by the
logical mapping a=f(e) <=> if e then a.
b) Math: giving a function f or a set F= {(a,e), for all e in the
domain of the function} is equivalent.
c) statistical description:
Statistical description is a very pragmatic description choice (and not
a mysterious physical process). With QM or with a basic coin flipping
experiment we always do the same thing: we label the experimental
trials and compute the frequencies of the outcomes:
1) We have an implicitly defined random variable, an abstract function
f, which expresses the experiment logic results: for the trial labelled
e, we associate the result a (logic true): "if e then result a".
The function/random variable is defined by the set {(e, a), for all e}
is equivalent to a=f(e) (i.e. the proposition "the result of the
experiment trial label e is a" is true).
This is the logical content of the description of the experiments. It
is a logical choice, no physical meaning is involved at this step.
The function f defines the true propositions of the experimental
trials. Without additional hypothesis, the function only exists in the
context of the experiment trials. It is important to understand that
the function f is only defined in the context of the experiment
(without extra properties, it is a contextual random variable) and does
not have a "reality" outside this experiment.
2) In order to say (logic) we observe a given statistics [of outcomes]
in a given set of experimental trials, we need to define logically this
set of systems where we observe a given statistics (the set E), where
the function f is defined. This is the generally the set of labels of
independent identical systems (or the preparation word in the QM
formalism).
This set of trials is either given or either defined by another
property.
On this set E, we define the formal probability law P by induction:
P_f= P o f-1
-- P is the formal probability law on the set of all the concerned
experiment trials (E={e, for all e})
--- P_f the induced probability law on the set A={a, for all outcomes
a}.
-- f-1 is the inverse function defined on the sets of events: f-1:
Parts(A) --> Parts(E)
(Parts(A) is the collection of all the subsets of A, idem for
Parts(E)).
Without this logical specification (the set of trials and the set of
outcomes, the function f), we cannot define a logical meaning (a
probability law p_f) to the frequency of the outcomes (using the
results of the mathematical probability theory).
This is the basic expression of the induced probability law by the
function f defined by the experimental trials associated to the law of
large numbers theorem (the logic behind the sentence/proposition, "I
observe a given statistics").
Formally, the QM measurement reflects this description choice with the
objects of QM.
> Although not very clearly separated in many discussions,
> these two processes happen never simultaneously but context
> dependent, and are of course only approximations to more
> realistic measurement situations.
>
> For example, in a Stern-Gerlach experiment, the system (silver atom)
> moves from the source along the magnet towards the screen with very
> good accuracy in a unitary (and indeed reversible) way. But a few
> split moments before it hits the screen it feels its interactions,
> and describing it as a closed system becomes hopelessly inaccurate.
> Instead, since the interaction time is very short, it can be
> described very accurately by an instantaneous collapse.
>
Why do you say it becomes hopelessly inaccurate? And How can you really
apply a collapse to a non closed system? In this case, don't you
think the collapse result (the outcome) should be independent of the
partial system description versus the whole system (including the
universe if necessary)?
This is the problem of interpretation. Once you define a system that is
no more described by the QM theory formalism, you are free to say. I
just say, that QM collapse is compatible with unitary evolution (as
well as non unitary descirptions) in the sense it is a property that
formally defines the "branch" of the unitary evolution (defined by
the outcome "a" of A is true) of the whole system (closed). This
definition of the "branch" is not predictive; it is the formal
mapping between the theory and the observation (the logic behind the
outcome "a" is true).
In addition, we can easily model a macroscopic system (the screen) such
that it evolves unitary (hence closed) and blocks a particle within an
area, just by using, for example, the quantum well models with a
potential triggered by time. .
I think it is important to accept the collapse formalism meaning on
closed systems (it is logically coherent). If we reject the collapse on
closed systems, we are already modifying the QM theory (either its
descriptions or its predictions). And currently, the experiments tend
to show the validity of QM theory results in systems with a non
negligible number of particles.
In addition, the collapse does not prevent some determinist results on
the limit of the large numbers (reversible and irreversible results),
it should be independant (e.g. the macroscopic outcome value is the
mean value)
Seratend.
Daryl McCullough
Jun6-05, 04:41 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman says...\n\n>I\'m a frequentist. In statistical mechanics, you assume that you fully\n>sample the phase space and the probabilities fall out.\n\nDo they? It seems to me that the usual development of classical\nstatistical mechanics depends crucially on the assumption that\nall microstates that are consistent with a given macrostate are\nequally likely. That allows us to use density of states as a\nstand-in for probability density. But why should all microstates\nbe equally likely?\n\nIn certain special cases, it is possible to prove (terminology: is\nthis ergodicity?) that the trajectory through phase space comes\narbitrarily close to every point consistent with the macroscopic\nvariables (energy, volume, number of particles, etc.) In this case,\nthe statistical assumption of equal likelihood will be true, *provided*\nthat the system has been in equilibrium long enough to "sample" all\nof the allowed phase space, which in practice is never true, since\nphase space is so huge.\n\n--\nDaryl McCullough\nIthaca, NY\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman says...
>I'm a frequentist. In statistical mechanics, you assume that you fully
>sample the phase space and the probabilities fall out.
Do they? It seems to me that the usual development of classical
statistical mechanics depends crucially on the assumption that
all microstates that are consistent with a given macrostate are
equally likely. That allows us to use density of states as a
stand-in for probability density. But why should all microstates
be equally likely?
In certain special cases, it is possible to prove (terminology: is
this ergodicity?) that the trajectory through phase space comes
arbitrarily close to every point consistent with the macroscopic
variables (energy, volume, number of particles, etc.) In this case,
the statistical assumption of equal likelihood will be true, *provided*
that the system has been in equilibrium long enough to "sample" all
of the allowed phase space, which in practice is never true, since
phase space is so huge.
--
Daryl McCullough
Ithaca, NY
Arnold Neumaier
Jun7-05, 02:26 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hendrik van Hees wrote:\n> Aaron Bergman wrote:\n>\n>\n>>I\'m not sure what you\'re referring to by a \'minimal statistical\n>>interpretation\'. It seems to me that what you\'re indicating is a\n>>hidden variables theory and that is experimentally ruled out (assuming\n>>locality).\n>\n>\n> The minimal statistical interpretation is not a hidden-variable theory,\n> which indeed is ruled out experimentally assuming locality.\n>\n> It is simply quantum mechanics, taking the probabilistic physical\n> content of the states seriously and does not associate the state with\n> single systems but only as a description of ensembles. With this\n> interpretation all the conceptional troubles of quantum theory vanish\n> at the price that one admits that quantum theory cannot describe single\n> systems.\n>\n> Nevertheless it is sufficient to use quantum theory to all experimental\n> facts, known so far.\n\nNo. There are many experimental facts associated with single systems.\n\nFor example, an ion trap models a single, well-defined quantum\nsystem over time. Experiments routinely get measurable time series\nthat define the detector\'s response to this single quantum system.\nEach time series is a realization of a stochastic process.\nBut its time correlation functions computed from a _single_\nrealization are in accordance with quantum mechanics.\nThus these are quantum predictions about single quantum systems\nobserved over time.\n\nIntroducing ensembles in this case is simply closing the eyes\nto the facts. These ensembles are as ficticious as those\nintroduced by Gibbs to explain macroscopic thermodynamics\nmicroscopically.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hendrik van Hees wrote:
> Aaron Bergman wrote:
>
>
>>I'm not sure what you're referring to by a 'minimal statistical
>>interpretation'. It seems to me that what you're indicating is a
>>hidden variables theory and that is experimentally ruled out (assuming
>>locality).
>
>
> The minimal statistical interpretation is not a hidden-variable theory,
> which indeed is ruled out experimentally assuming locality.
>
> It is simply quantum mechanics, taking the probabilistic physical
> content of the states seriously and does not associate the state with
> single systems but only as a description of ensembles. With this
> interpretation all the conceptional troubles of quantum theory vanish
> at the price that one admits that quantum theory cannot describe single
> systems.
>
> Nevertheless it is sufficient to use quantum theory to all experimental
> facts, known so far.
No. There are many experimental facts associated with single systems.
For example, an ion trap models a single, well-defined quantum
system over time. Experiments routinely get measurable time series
that define the detector's response to this single quantum system.
Each time series is a realization of a stochastic process.
But its time correlation functions computed from a _single_
realization are in accordance with quantum mechanics.
Thus these are quantum predictions about single quantum systems
observed over time.
Introducing ensembles in this case is simply closing the eyes
to the facts. These ensembles are as ficticious as those
introduced by Gibbs to explain macroscopic thermodynamics
microscopically.
Arnold Neumaier
Seratend
Jun7-05, 02:27 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n\n> >>>a) what is the initial state of the photon (assuming a wave packet) :\n> >>>|psi>= |path1>+|path2> with <path1|path2>=0?\n> >>\n> >>Not quite. Roughly,\n> >> |psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>\n> >>with spatial coherent states |pathi(t)> (i=1,2) moving at the\n> >>velocity of light and monochromatic 1-Photon Fock states |1>, say.\n> >\n> > Ok, usually when I write a state |path1>, this state may be the tensor\n> > product of whatever we want (we may expand it when it is required).\n> > Therefore, you seem to require the detail of this state:\n> >\n> > |psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?\n>\n> No; there is no need for orthogonality. Indeed, coherent states are\n> not quite orthogonal, although their overlap is small if the paths are\n> far away.\n>\nOk. However, this is not important as long as we can introduce later\nthe specificities we want. We use the linearity of the states to add,\nlater, additional features when we think they are really required for\nthe current study.\nGeneral wave packets and free propagation between local interactions\nare almost always sufficient to describe the behaviour of the\nexperiments, once we know the behaviour of the interactions on the\nstates (screen with slits etc ...).\nThere is no need to detail precisely the wave packet as long as we\nconsider only coarse localizations, etc ...\nLet\'s assume we have the orthogonality, or if you prefer the\napproximated orthogonality (strong separation in space of the 2\nstates).\n(we can modify later this requirement if really required)\n>\n> > choosen Hamiltonians and interactions such that we have no entanglement\n> > between the photons and the screens (formal choice): H_screen=\n> > |screen><screen|(x)V(r)\n> > I usually prefer to replace photons by electrons, whenever it does not\n> > change the global result as the free propagator of photons and\n> > electrons are the same.\n>\n> So you ignore spin and assume a mass. But then it is simpler to\n> take spin 0 (rather than electrons), and simply talk about a \'particle\'.\n>\n: )\nSometimes, I prefer to take well known particles with simple\ninteractions (independent of spin) in order to verify some descriptions\nbehaviour with well known experiments.\nOk for spin 0 or with spin but without spin interaction (no polarizer\nfor photons, etc ...).\n>\n> > In the case of photons, V(r) is the effective\n> > potential giving the source of the reflection or the transmission.\n> > This model supposes the energy conservation between photons and the\n> > screens (choice) and it is easy to see that everything evolves unitary,\n> > just by taking the wave packet.\n> >\n> > I may expand my explanation if required.\n\n> Yes please. I haven\'t read the initial description of your setting\n> (and my remarks below might reflect musunderstanding because of that).\n>\n\nOk, we have an initial state |psi(0)>|screen1>|screen2>.\n\nWith |psi(0)>= [|path1(0)>+|path2(0)>](x)|1>.\n\nWhere |path1(t)> and |path2(t)> are partially localised wave packets\n((x,y) plane), propagating along the z direction at the same speed.\n\nWe assume (we choose), the interactions of the screen 1 and screen 2 to\nbe:\nH_int1= |screen1><screen1|(x)V1(r)\nH_int2= |screen2><screen2|(x)V2(r)\n\nV1(r) is a reflective potential (a quantum wall potential) localized\nwith the screen1 area. This potential vanishes within the hole of\nscreen 1. let\'s call A this hole area.\n\nV2(r) is a reflective potential (a quantum wall potential) localized\nwith the screen2 area.\n\nWe assume <r|path1(t)>=0 for r in the area A, for any t. (the path 1\nfully interacts with screen 1)\n\nWe assume <r|path2(t)>= 0 for r *not* in the area A, for any t. (the\npath 2 is located in the hole of the potential of screen 1).\n\nWe have the global Hamiltonian (photons or electrons, screen 1 and\nscreen 2):\n\nH_tot=Ho + H_oscreen1+ H_oscreen2 + H_int1+ H_int2\n\nWhere:\n\na) Ho, H_oscreen1, H_oscreen2 are the free Hamiltonians of the\nparticle, screen1 and screen2.\nb) |screen1> and |screen2> are eigenstates of the free scren\nHamiltonians.\n\n-------------------------------------------------------> z\n\\ screen1 \\screen2\n\n\\ \\\n[source]+----1-----\\ \\\n| / \\ \\\n+----2---/------------------\\\n/ \\ / \\\n/ \\ / \\\n/ \\ / \\\nV V\n(reflected wavepackets when the screen\nplanes are not orthogonal to the z propagation direction)\n\n\n> If the dynamics is unitary, how do you get the permanent record (the\n> definite click or macroscopic spot) that constitutes a measurement?\n>\nThis is what I want to show. The figure above shows that the screens\nmodify the wave packets and that this modification is described by a\nunitary evolution.\n\nQM formalism does not describe the occurrence of clicks. The clicks are\nthe observed properties on the experimental trials (in this case\n"reflection by a screen" or "click by a distant detector").\nIf a property is true (e.g. the reflection by screen2), the associated\nformal collapse is also true. If the property is false the collapse is\nalso false.\nIn any case, we have for a given instance of this system a property\nfalse that becomes true. This has no meaning in this formalism.\nNote that the property: "reflection by screen2" implicitly means\nthe particle is reflected by screen 2 at time tref (the observed time\nin the considered experimental trial). Without the complete\nspecification of the property, we cannot map the observed experiment\nresults to the collapse.\n\nI hope you better understand, my meaning of the formal collapse: I do\nnot say more than the formalism of the theory does.\n\n(note: if you add the detectors, we can choose, formally, a model of\ndetectors with potentials that block the wavepackets in the area of the\ndetectors: we have a new unitary evolution => the clicks in this case\nare again a property of a given experiment trial: "the detector 1\nclicks").\n\n\n\n>\n> >>If there is unitary dynamics only then the final result is not\n> >>the state |0,1,1> or |0,0,1> as observed, but a superposition\n> >>of the two. Invoking Born\'s rule is _assuming_ the collapse\n> >>rather than explaining it.\n> >>\n> > I like this toy model where we force no entanglement between the\n> > photons states and the screens and where we have the simple unitary\n> > evolution of the initial state. It reflects perfectly what we do on an\n> > experiment that reflects this unitary evolution:\n> > a) we have to choose between all the photons, the one with the initial\n> > state (hence an initial measurement result)\n>\n> How do we choose that?\n>\nThis is the recursivity of statistical description model. By another\nmeasurement (the preparation) that defines the properties we observe,\nwe use to say a given experiment trial is the good one (it is in the\ngood state).\nThis preparation can be as simple as a lamp with a slit plate. We know\nthat at a long distances of the slit plate, if we do a measurement\n(the thought measurement), we recover wavepackets (approximation).\nTherefore, we can say, from the formalism point of view, that the lamp+\nslit plate is a measurement that gives as an output state wave packets.\nNow, to understand better the recursivity, you can ask, how we know it\nis a lamp with a screen? Etc ...\n\n> In my terminology, this would be a preparation, not a measurement,\n> since measurement is _acquiring_ new information or _confirming/testing_\n> old information, while preparation is _assuming_ information based on\n> past experience with one\'s equipment.\n>\nYes, this is the usual preparation of the Copenhagen interpretation if\nI am correct. However, the preparation interpretation means you known\nthe state with 100% confidence. It is therefore undistinguishable from\na collapse with the same state (note on how the correct description of\nthis property may require, the time, the space, etc ...).\nFor me it is logic to say: I have an instance of a system with a given\nproperty. The preparation word is in this sense redundant with the\ncollapse word of the QM formalism. We brake the recursivity of the\ncollapse by artificially defining another word: the preparation.\n\nIn this section of your post, it is interesting to see the mixture of\ninterpretation with the QM formal results.\nI say, formally, in a given experiment, we have properties (the results\nof experiments, expressed by the collapse postulate). I do not specify,\nif we learn or not this information as it is completely out of scope of\nthe formalism (the description choice).\nIn other words, assuming or not the acquisition of new information does\nnot change the properties of the system in this formalism.\n\n>\n> > b) we simultaneously measure the reflected photons by either the first\n> > screen or the second one outside the area of the local interaction of\n> > the screens (here I suppose the plane of the reflecting screens are not\n> > orthogonal to the beam direction in order to put the "real"\n> > detector outside the incoming beam. We have only a single detector that\n> > clicks at a time assuming the good energy trigger level on a restricted\n> > area.\n> >\n> > We can put the detectors or not,\n>\n> But they change the system under consideration and hence the analysis\n> needed to get correct predictions.\n>\nYes. The interactions are changed. The properties may be changed or not\ndepending on the type of interactions. The local detectors interaction\nare compatible with the properties, the particle is reflected by the\nscreen (the projectors commute)\n\n>\n> >\n> > Assuming this, we can say (interpretation) that the screens do not\n> > collapse the wave function if we have no detectors, while if we put the\n> > detectors we can say that the screen collapses the wave function.\n>\n> Anything which is part of the system modelled unitarily does not\n> produce collapse, while anything does that isn\'t modelled in full\n> detail but whose interaction with the unmodelled dof\'s is nontrival.\n>\nI am not saying that a mysterious physical process defines the\ncollapse. I just say, that in the statistical description choice of the\nQM theory formalism, the collapse is just the notification of the\nresults of experimental trials (a property is true). Saying more than\nthat is interpreting the theory with the risk of modifying the theory.\n\nNote: This does not change the observed results in the limit of the\nlarge numbers. We always have outcomes but with more cases where we\nhave a 100% probability distribution.\n\n>\n> >>That something remains to be explained even from the Copenhagen\n> >>point of view (some version of which you seem to adhere to)\n> >>is discussed in Section 3.\n> >>\n> >\n> > Copenhagen interpretation does not assume the "reality" of the\n> > wavefunction.\n>\n> But it assumes the reality of the classical equipment, which\n> therefore gives an N-particle system with large N an ontological\n> status different from one with small N. It forgets to say at which\n> value of N one is entitled to swich from one status to the other.\n>\nThis is where Copenhagen interpretation may limit the validity of QM\ntheory, depending on how we interpret the words of the Copenhagen\ninterpretation. This is questionable.\n\nWe may also view this undefined limit as the boundary where large\nnumber statistical results apply (the probability to get an outcome is\n100%, the "mean value"). In this case, QM continues to apply.\n\nIt is why I prefer to apply the "shut up and calculate" point of\nview, with the formal mapping of collapse with the experiments results\n(the statistical description). It avoids to say more than the formalism\nof the theory says.\n>\n> > What it says is very analogue to what I say. There is\n> > most of the time, with CI, in my opinion, a misunderstanding on the\n> > meaning of "before" or "after" the measurement. Just replace\n> > the word "before" by "there is no measurement" and "after"\n> > by "there is a measurement". Therefore, each instance of a system\n> > has a single property: either there is a measurement or not (with its\n> > associated definite single results).\n> > There is no system where we have no measurement before and "after"\n> > a measurement appears from nowhere. We have a measured system (of a\n> > given value) or not (no time reference).\n>\n> This is neither Kopenhagen nor true. The descriptions in\n> the authoritative treatises by von neumann, Londson and Bauer,\n> or Wigner tell me quite a different story.\n>\nOk : ) I am not I expert of the Copenhagen interpretation. I just use\nthe formal results: the logical content of the words are defined by the\nQM theory and not by their interpretations nor by their definitions in\nthe dictionary. Therefore, this is where the formal consideration of\nthe theory (what my logic understands) may differ from the Copenhagen\ninterpretation.\n\n>\n> >>>At the end, I must apply the born\n> >>>rules to get the statistics (what I see in the experiment).\n> >>\n> >>This is the informal prescription that is used to apply single-particle\n> >>reasoning to a complex multiparticle experiment. It successfully\n> >>avoids looking at the physics happening at the screen, replacing it\n> >>by simply assuming the collapse, i.e., the emergence of an objective\n> >>record according to the probabilities from the Born rule.\n> >>While this is an acceptable attitude it is obviously not the whole\n> >>story.\n> >>\n> > This is what I call the statistical description of the physical\n> > phenomena (we do not explain the outcomes, we just measure their\n> > frequency and their evolution in the space time).\n>\n> Yes.\n>\nSo, why are you searching a physical meaning of to the collapse?\nHere, I want to understand what you really mean by physical collapse.\nI mean, I accept your search in other posts of limits in large number\ndomain. However, what we obtain is a 100% probability distribution: we\nstill need the collapse postulate to map logically the observed result\nto the predictions (i.e. we will observe, formally, that we only have\nsystems with the same single outcome, the one with the 100%\nprobability).\n\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> >>>a) what is the initial state of the photon (assuming a wave packet) :
> >>>|\psi>= |path1>+|path2> with <path1|path2>=0?
> >>
> >>Not quite. Roughly,
> >> |\psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>
> >>with spatial coherent states |pathi(t)> (i=1,2) moving at the
> >>velocity of light and monochromatic 1-Photon Fock states |1>, say.
> >
> > Ok, usually when I write a state |path1>, this state may be the tensor
> > product of whatever we want (we may expand it when it is required).
> > Therefore, you seem to require the detail of this state:
> >
> > |\psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?
>
> No; there is no need for orthogonality. Indeed, coherent states are
> not quite orthogonal, although their overlap is small if the paths are
> far away.
>
Ok. However, this is not important as long as we can introduce later
the specificities we want. We use the linearity of the states to add,
later, additional features when we think they are really required for
the current study.
General wave packets and free propagation between local interactions
are almost always sufficient to describe the behaviour of the
experiments, once we know the behaviour of the interactions on the
states (screen with slits etc ...).
There is no need to detail precisely the wave packet as long as we
consider only coarse localizations, etc ...
Let's assume we have the orthogonality, or if you prefer the
approximated orthogonality (strong separation in space of the 2
states).
(we can modify later this requirement if really required)
>
> > choosen Hamiltonians and interactions such that we have no entanglement
> > between the photons and the screens (formal choice): H_{screen}=
> > |screen><screen|(x)V(r)
> > I usually prefer to replace photons by electrons, whenever it does not
> > change the global result as the free propagator of photons and
> > electrons are the same.
>
> So you ignore spin and assume a mass. But then it is simpler to
> take spin (rather than electrons), and simply talk about a 'particle'.
>
: )
Sometimes, I prefer to take well known particles with simple
interactions (independent of spin) in order to verify some descriptions
behaviour with well known experiments.
Ok for spin or with spin but without spin interaction (no polarizer
for photons, etc ...).
>
> > In the case of photons, V(r) is the effective
> > potential giving the source of the reflection or the transmission.
> > This model supposes the energy conservation between photons and the
> > screens (choice) and it is easy to see that everything evolves unitary,
> > just by taking the wave packet.
> >
> > I may expand my explanation if required.
> Yes please. I haven't read the initial description of your setting
> (and my remarks below might reflect musunderstanding because of that).
>
Ok, we have an initial state |\psi(0)>|screen1>|screen2>.
With |\psi(0)>= [|path1(0)>+|path2(0)>](x)|1>.
Where |path1(t)> and |path2(t)> are partially localised wave packets
((x,y) plane), propagating along the z direction at the same speed.
We assume (we choose), the interactions of the screen 1 and screen 2 to
be:
H_{int1}= |screen1><screen1|(x)V1(r)
H_{int2}= |screen2><screen2|(x)V2(r)
V1(r) is a reflective potential (a quantum wall potential) localized
with the screen1 area. This potential vanishes within the hole of
screen 1. let's call A this hole area.
V2(r) is a reflective potential (a quantum wall potential) localized
with the screen2 area.
We assume <r|path1(t)>=0 for r in the area A, for any t. (the path 1
fully interacts with screen 1)
We assume <r|path2(t)>= for r *not* in the area A, for any t. (the
path 2 is located in the hole of the potential of screen 1).
We have the global Hamiltonian (photons or electrons, screen 1 and
screen 2):
H_{tot}=Ho + H_{oscreen1}+ H_{oscreen2} + H_{int1}+ H_{int2}
Where:
a) Ho, H_{oscreen1}, H_{oscreen2} are the free Hamiltonians of the
particle, screen1 and screen2.
b) |screen1> and |screen2> are eigenstates of the free scren
Hamiltonians.
-------------------------------------------------------> z
\ screen1 \screen2\ \[source]+----1-----\ \| / \ \+----2---/------------------\/ \ / \/ \ / \/ \ / \
V V
(reflected wavepackets when the screen
planes are not orthogonal to the z propagation direction)
> If the dynamics is unitary, how do you get the permanent record (the
> definite click or macroscopic spot) that constitutes a measurement?
>
This is what I want to show. The figure above shows that the screens
modify the wave packets and that this modification is described by a
unitary evolution.
QM formalism does not describe the occurrence of clicks. The clicks are
the observed properties on the experimental trials (in this case
"reflection by a screen" or "click by a distant detector").
If a property is true (e.g. the reflection by screen2), the associated
formal collapse is also true. If the property is false the collapse is
also false.
In any case, we have for a given instance of this system a property
false that becomes true. This has no meaning in this formalism.
Note that the property: "reflection by screen2" implicitly means
the particle is reflected by screen 2 at time tref (the observed time
in the considered experimental trial). Without the complete
specification of the property, we cannot map the observed experiment
results to the collapse.
I hope you better understand, my meaning of the formal collapse: I do
not say more than the formalism of the theory does.
(note: if you add the detectors, we can choose, formally, a model of
detectors with potentials that block the wavepackets in the area of the
detectors: we have a new unitary evolution => the clicks in this case
are again a property of a given experiment trial: "the detector 1
clicks").
>
> >>If there is unitary dynamics only then the final result is not
> >>the state |0,1,1> or |0,0,1> as observed, but a superposition
> >>of the two. Invoking Born's rule is _assuming_ the collapse
> >>rather than explaining it.
> >>
> > I like this toy model where we force no entanglement between the
> > photons states and the screens and where we have the simple unitary
> > evolution of the initial state. It reflects perfectly what we do on an
> > experiment that reflects this unitary evolution:
> > a) we have to choose between all the photons, the one with the initial
> > state (hence an initial measurement result)
>
> How do we choose that?
>
This is the recursivity of statistical description model. By another
measurement (the preparation) that defines the properties we observe,
we use to say a given experiment trial is the good one (it is in the
good state).
This preparation can be as simple as a lamp with a slit plate. We know
that at a long distances of the slit plate, if we do a measurement
(the thought measurement), we recover wavepackets (approximation).
Therefore, we can say, from the formalism point of view, that the lamp+
slit plate is a measurement that gives as an output state wave packets.
Now, to understand better the recursivity, you can ask, how we know it
is a lamp with a screen? Etc ...
> In my terminology, this would be a preparation, not a measurement,
> since measurement is _acquiring_ new information or _confirming/testing_
> old information, while preparation is _assuming_ information based on
> past experience with one's equipment.
>
Yes, this is the usual preparation of the Copenhagen interpretation if
I am correct. However, the preparation interpretation means you known
the state with 100% confidence. It is therefore undistinguishable from
a collapse with the same state (note on how the correct description of
this property may require, the time, the space, etc ...).
For me it is logic to say: I have an instance of a system with a given
property. The preparation word is in this sense redundant with the
collapse word of the QM formalism. We brake the recursivity of the
collapse by artificially defining another word: the preparation.
In this section of your post, it is interesting to see the mixture of
interpretation with the QM formal results.
I say, formally, in a given experiment, we have properties (the results
of experiments, expressed by the collapse postulate). I do not specify,
if we learn or not this information as it is completely out of scope of
the formalism (the description choice).
In other words, assuming or not the acquisition of new information does
not change the properties of the system in this formalism.
>
> > b) we simultaneously measure the reflected photons by either the first
> > screen or the second one outside the area of the local interaction of
> > the screens (here I suppose the plane of the reflecting screens are not
> > orthogonal to the beam direction in order to put the "real"
> > detector outside the incoming beam. We have only a single detector that
> > clicks at a time assuming the good energy trigger level on a restricted
> > area.
> >
> > We can put the detectors or not,
>
> But they change the system under consideration and hence the analysis
> needed to get correct predictions.
>
Yes. The interactions are changed. The properties may be changed or not
depending on the type of interactions. The local detectors interaction
are compatible with the properties, the particle is reflected by the
screen (the projectors commute)
>
> >
> > Assuming this, we can say (interpretation) that the screens do not
> > collapse the wave function if we have no detectors, while if we put the
> > detectors we can say that the screen collapses the wave function.
>
> Anything which is part of the system modelled unitarily does not
> produce collapse, while anything does that isn't modelled in full
> detail but whose interaction with the unmodelled dof's is nontrival.
>
I am not saying that a mysterious physical process defines the
collapse. I just say, that in the statistical description choice of the
QM theory formalism, the collapse is just the notification of the
results of experimental trials (a property is true). Saying more than
that is interpreting the theory with the risk of modifying the theory.
Note: This does not change the observed results in the limit of the
large numbers. We always have outcomes but with more cases where we
have a 100% probability distribution.
>
> >>That something remains to be explained even from the Copenhagen
> >>point of view (some version of which you seem to adhere to)
> >>is discussed in Section 3.
> >>
> >
> > Copenhagen interpretation does not assume the "reality" of the
> > wavefunction.
>
> But it assumes the reality of the classical equipment, which
> therefore gives an N-particle system with large N an ontological
> status different from one with small N. It forgets to say at which
> value of N one is entitled to swich from one status to the other.
>
This is where Copenhagen interpretation may limit the validity of QM
theory, depending on how we interpret the words of the Copenhagen
interpretation. This is questionable.
We may also view this undefined limit as the boundary where large
number statistical results apply (the probability to get an outcome is
100%, the "mean value"). In this case, QM continues to apply.
It is why I prefer to apply the "shut up and calculate" point of
view, with the formal mapping of collapse with the experiments results
(the statistical description). It avoids to say more than the formalism
of the theory says.
>
> > What it says is very analogue to what I say. There is
> > most of the time, with CI, in my opinion, a misunderstanding on the
> > meaning of "before" or "after" the measurement. Just replace
> > the word "before" by "there is no measurement" and "after"
> > by "there is a measurement". Therefore, each instance of a system
> > has a single property: either there is a measurement or not (with its
> > associated definite single results).
> > There is no system where we have no measurement before and "after"
> > a measurement appears from nowhere. We have a measured system (of a
> > given value) or not (no time reference).
>
> This is neither Kopenhagen nor true. The descriptions in
> the authoritative treatises by von neumann, Londson and Bauer,
> or Wigner tell me quite a different story.
>
Ok : ) I am not I expert of the Copenhagen interpretation. I just use
the formal results: the logical content of the words are defined by the
QM theory and not by their interpretations nor by their definitions in
the dictionary. Therefore, this is where the formal consideration of
the theory (what my logic understands) may differ from the Copenhagen
interpretation.
>
> >>>At the end, I must apply the born
> >>>rules to get the statistics (what I see in the experiment).
> >>
> >>This is the informal prescription that is used to apply single-particle
> >>reasoning to a complex multiparticle experiment. It successfully
> >>avoids looking at the physics happening at the screen, replacing it
> >>by simply assuming the collapse, i.e., the emergence of an objective
> >>record according to the probabilities from the Born rule.
> >>While this is an acceptable attitude it is obviously not the whole
> >>story.
> >>
> > This is what I call the statistical description of the physical
> > phenomena (we do not explain the outcomes, we just measure their
> > frequency and their evolution in the space time).
>
> Yes.
>
So, why are you searching a physical meaning of to the collapse?
Here, I want to understand what you really mean by physical collapse.
I mean, I accept your search in other posts of limits in large number
domain. However, what we obtain is a 100% probability distribution: we
still need the collapse postulate to map logically the observed result
to the predictions (i.e. we will observe, formally, that we only have
systems with the same single outcome, the one with the 100%
probability).
Seratend.
Seratend
Jun7-05, 02:28 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1117885132.982867.64950@g43g2000cwa.googlegroups. com>,\n> "Seratend" <ser_monmail@yahoo.fr> wrote:\n>\n> > Do you understand that nothing (logic) predicts this probability,\n> > except if it is the result of another experiment? (and hence, we have\n> > another probability that is not predicted).\n>\n> I\'m a frequentist. In statistical mechanics, you assume that you fully\n> sample the phase space and the probabilities fall out.\n\nYou should look carefully at this assumption in order to understand why\nwe correctly measure the frequency. The calculated frequency induces,\nthe probability law on the trial space (hence a correct probability).\nThis why we can say formally we have a probability law and why we can\nuse it as a description tool.\n\n>I\'m well aware of\n> the philosophical difficulties in defining probabilities and the like,\n> but generally I don\'t particularly care.\n>\nI wasn\'t speaking about philosophy, just the formal use of\nprobabilities.\n\n> [...]\n>\n> > I use the detector to prove that nothing (logic) prevents you, in QM\n> > theory, to say the screen is a measurement apparatus (producing the\n> > interference pattern.\n>\n> You use the word \'logic\' as if there were some fundamental set of axioms\n> that we know have to be correct. It\'s just not true.\n>\nI use the word logic (say bi valued), to define what I think our basic\ncommon ground of understanding: the logic. Hence, I assume you take the\nlogic and its set of axioms for granted. If it is not the case, I am\nafraid it will be difficult to make constructive deductions and to\nspeak about the deduction of a preferred basis by decoherence.\n\nAll the physical theories, I know, use the logic results (and I assume,\ndecoherence theory use the logic to make its deductions; may be, I am\nwrong, am I? ; ).\n\nTherefore, to describe an experiment, I use the logic (I hope you too :\n). I use this logic to say that in the QM formalism context, which\nuses logic too, nothing prevents one to say the screen is a measurement\napparatus (the proposition is not falsified by the QM formalism\ncontent). Therefore saying the screen is a measurement apparatus is\ncompatible with QM theory. QED.\n\n> > Now, you are free to give your own definition of a measurement\n> > apparatus requiring an entanglement interaction and choose an ad hoc\n> > interaction such that the Schmitt basis is the one where we get the\n> > observations.\n>\n> The Schmitt basis is only the correct basis after we wait the\n> decoherence time.\n>\nAnother affirmation. I have tried to give constructive remarks on why I\ndo not understand your affirmation. These previous remarks do not\ninclude time (at least formally). I have given one basic example, where\nI think we have no entanglement and thus where we are not able apply\nthe schmidt decomposition, even after the time of universe.\nI may be wrong and I accept this possibility (I want to understand).\nHowever, If I am wrong, I want to have a better answer than this short\none.\n\n> > However, in this case this is completely out of the scope\n> > of QM theory and it is much more simpler to say that we simply know the\n> > preferred basis by doing experiments (we use our knowledge of known\n> > experiment results to deduce other experiment results and basis): no\n> > prediction by QM theory.\n>\n> Again, if you describe a real experiment, ie, one where and actual\n> person makes and actual measurement, you can determine the basis\n> selected by decoherence. The only inputs are the macrostates, but that\'s\n> just mechanics. If your claim is that we can\'t determine macrostates ab\n> initio, then I just disagree.\n>\nI just claim I do not know/understand, where from QM formalism, you can\ndeduce the preferred basis of experiments. If you claim that\ndecoherence is able to determine ab initio the macrostates of the\n*preferred basis* (and not macrostates of a basis), I just say, prove\nme and explain me why it does not work in my toy model.\n\nIf you claim that the "actual person" has a preferred basis and\nhence it solves the preferred basis of the experiment through the\ninteractions. I will yes, ok, prove that the actual person has a\npreferred basis. If you answer, you can\'t (too complicate) but he\ndoes have a preferred basis, I will conclude, you have not a\ndemonstration (the logic).\n\nI accept the results of decoherence, how the entanglement transforms\nthe evolution of macroscopic states. I just do not understand (the\nlogic behind such an affirmation) on how it can solve the preferred\nbasis prediction (ab initio).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1117885132.982867.64950@g43g2000cwa.googlegroups.c om>,
> "Seratend" <ser_monmail@yahoo.fr> wrote:
>
> > Do you understand that nothing (logic) predicts this probability,
> > except if it is the result of another experiment? (and hence, we have
> > another probability that is not predicted).
>
> I'm a frequentist. In statistical mechanics, you assume that you fully
> sample the phase space and the probabilities fall out.
You should look carefully at this assumption in order to understand why
we correctly measure the frequency. The calculated frequency induces,
the probability law on the trial space (hence a correct probability).
This why we can say formally we have a probability law and why we can
use it as a description tool.
>I'm well aware of
> the philosophical difficulties in defining probabilities and the like,
> but generally I don't particularly care.
>
I wasn't speaking about philosophy, just the formal use of
probabilities.
> [...]
>
> > I use the detector to prove that nothing (logic) prevents you, in QM
> > theory, to say the screen is a measurement apparatus (producing the
> > interference pattern.
>
> You use the word 'logic' as if there were some fundamental set of axioms
> that we know have to be correct. It's just not true.
>
I use the word logic (say bi valued), to define what I think our basic
common ground of understanding: the logic. Hence, I assume you take the
logic and its set of axioms for granted. If it is not the case, I am
afraid it will be difficult to make constructive deductions and to
speak about the deduction of a preferred basis by decoherence.
All the physical theories, I know, use the logic results (and I assume,
decoherence theory use the logic to make its deductions; may be, I am
wrong, am I? ; ).
Therefore, to describe an experiment, I use the logic (I hope you too :
). I use this logic to say that in the QM formalism context, which
uses logic too, nothing prevents one to say the screen is a measurement
apparatus (the proposition is not falsified by the QM formalism
content). Therefore saying the screen is a measurement apparatus is
compatible with QM theory. QED.
> > Now, you are free to give your own definition of a measurement
> > apparatus requiring an entanglement interaction and choose an ad hoc
> > interaction such that the Schmitt basis is the one where we get the
> > observations.
>
> The Schmitt basis is only the correct basis after we wait the
> decoherence time.
>
Another affirmation. I have tried to give constructive remarks on why I
do not understand your affirmation. These previous remarks do not
include time (at least formally). I have given one basic example, where
I think we have no entanglement and thus where we are not able apply
the schmidt decomposition, even after the time of universe.
I may be wrong and I accept this possibility (I want to understand).
However, If I am wrong, I want to have a better answer than this short
one.
> > However, in this case this is completely out of the scope
> > of QM theory and it is much more simpler to say that we simply know the
> > preferred basis by doing experiments (we use our knowledge of known
> > experiment results to deduce other experiment results and basis): no
> > prediction by QM theory.
>
> Again, if you describe a real experiment, ie, one where and actual
> person makes and actual measurement, you can determine the basis
> selected by decoherence. The only inputs are the macrostates, but that's
> just mechanics. If your claim is that we can't determine macrostates ab
> initio, then I just disagree.
>
I just claim I do not know/understand, where from QM formalism, you can
deduce the preferred basis of experiments. If you claim that
decoherence is able to determine ab initio the macrostates of the
*preferred basis* (and not macrostates of a basis), I just say, prove
me and explain me why it does not work in my toy model.
If you claim that the "actual person" has a preferred basis and
hence it solves the preferred basis of the experiment through the
interactions. I will yes, ok, prove that the actual person has a
preferred basis. If you answer, you can't (too complicate) but he
does have a preferred basis, I will conclude, you have not a
demonstration (the logic).
I accept the results of decoherence, how the entanglement transforms
the evolution of macroscopic states. I just do not understand (the
logic behind such an affirmation) on how it can solve the preferred
basis prediction (ab initio).
Seratend.
Seratend
Jun7-05, 02:28 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I.Vecchi wrote:\n> > Have you got some data concerning the "no-recoil" assumption?\n>\n> I am not sure I understand the question. Do you expect me to provide\n> data falsifying Newton\'s third law?\n\n: ))) no.\n\n> If you need a reference where the "no-recoil" assumption is introduced\n> explicitly I suggest Joos\' article in the classic "Decoherence and the\n> Appearance of a Classical World in Quantum Theory". Joos is a believer\n> in decoherence, but he writes and argues with remarkable clarity,\n> making it easy to spot DT\'s hidden assumptions.\n>\nThanks a lot. I will recheck Joos paper again (I have missed this part\nwhen I have read it : ).\n> Cheers, or even better, je vous prie d\'accepter, Monsieur Seratend,\n> l\'expression sinc=E8re de mes sentiments les plus distingu=E9s.=20\n>\n> IV\n\nWaow. I am impressed. : )))). However, for your information (in the\ncase you do not know), it is a little bit too formal. ("sinceres\nsalutions" is better to end unformal messages).\n\n(my english is poor as my taylor, but your french is perfect : )\n\nSincerely yours, : )\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I.Vecchi wrote:
> > Have you got some data concerning the "no-recoil" assumption?
>
> I am not sure I understand the question. Do you expect me to provide
> data falsifying Newton's third law?
: ))) no.
> If you need a reference where the "no-recoil" assumption is introduced
> explicitly I suggest Joos' article in the classic "Decoherence and the
> Appearance of a Classical World in Quantum Theory". Joos is a believer
> in decoherence, but he writes and argues with remarkable clarity,
> making it easy to spot DT's hidden assumptions.
>
Thanks a lot. I will recheck Joos paper again (I have missed this part
when I have read it : ).
> Cheers, or even better, je vous prie d'accepter, Monsieur Seratend,
> l'expression sinc=E8re de mes sentiments les plus distingu=E9s.=20
>
> IV
Waow. I am impressed. : )))). However, for your information (in the
case you do not know), it is a little bit too formal. ("sinceres
salutions" is better to end unformal messages).
(my english is poor as my taylor, but your french is perfect : )
Sincerely yours, : )
Seratend.
joe@alpha.to
Jun7-05, 02:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in\nmessage news:42A05FE1.2090109@univie.ac.at...\n> Joe Rongen wrote:\n>\n> >>Arnold Neumaier wrote:\n> >>\n> >>>I am looking for an explanation why a particular detector coupled\n> >>>to a particular quantum system produces the observed erratic but\n> >>>objective record of individual results that can be analyzed\n> >>>statistically and quoted in a physics journal.\n> >\n> > Some detector systems employ photomultiplier tube(s).\n> >\n> > The ideal photomultiplier tube is a detector that basically\n> > absorbs (photo-electric effect) one photon and internally\n> > converts/produces** due to an electron cascade/amplifier\n> > effect, one measurable event.\n> >\n> > ** Lawrence and Beams showed in 1928 that photo-electrons are\n> > sometimes emitted less than 3 *10^(-9) sec after initial illumination.\n>\n> Could you please explain how this relates to my statement?\n\nI took the liberty to understand your "particular quantum system"\nas a photon producing system. The photomultiplier tube (PMT)\nis also a quantum device; the difference being that the output\nenergy is measurable in electron-volts. The PMT is in theory,\nand experimentally a well understood device and as such follows\nthis (circular) suggestion closely:\n\n"Theory is meant to be substantiated by appeal to the\nobservable facts, while at the same time the observable\nfacts can only be justified by appeal to theory."\n\n> Even a photomultiplier tube will trigger an erratic response\n> following a Poisson process when fed with a low intensity coherent\n> laser beam.\n\nPrecisely, the PMT is a quantum (detector) system and due to its very\nhigh gain 10^(6) or more, is also very sensitive to its environment.\n\nExperiments have shown that one can eliminate a lot of random PMT\ncounts, like dark current, etc.. by cooling the PMT and adjusting the\nHigh Voltage. And the PMT output energy level can be pre-set, by\nan electronic window, for instance, between 5 and 8 eV and thereby\neliminating unwanted input - output energies. However, some\nunwanted random counts may still arrive at the PMT\'s output due to\nthe PMT\'s design, or could be caused by a number of events including\ncosmic particles or the disintegration of a radioactive particle buried\n\nsomewhere in the PMT\'s environment. Even those counts can be mostly\neliminated by modern electronics - the PMT\'s output must match an\nknown EPROM signature measurement or it will not be measured\nas a valid count.\n\nAfter a proper setup, the PMT (a quantum system), will measure an\nobjective record of individual results that can be analyzed\nstatistically\nand quoted in a physics journal.\n\nBest regards Joe Rongen 6/3/05/4:14 pm.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in
message news:42A05FE1.2090109@univie.ac.at...
> Joe Rongen wrote:
>
> >>Arnold Neumaier wrote:
> >>
> >>>I am looking for an explanation why a particular detector coupled
> >>>to a particular quantum system produces the observed erratic but
> >>>objective record of individual results that can be analyzed
> >>>statistically and quoted in a physics journal.
> >
> > Some detector systems employ photomultiplier tube(s).
> >
> > The ideal photomultiplier tube is a detector that basically
> > absorbs (photo-electric effect) one photon and internally
> > converts/produces** due to an electron cascade/amplifier
> > effect, one measurable event.
> >
> > ** Lawrence and Beams showed in 1928 that photo-electrons are
> > sometimes emitted less than 3 *10^(-9) sec after initial illumination.
>
> Could you please explain how this relates to my statement?
I took the liberty to understand your "particular quantum system"
as a photon producing system. The photomultiplier tube (PMT)
is also a quantum device; the difference being that the output
energy is measurable in electron-volts. The PMT is in theory,
and experimentally a well understood device and as such follows
this (circular) suggestion closely:
"Theory is meant to be substantiated by appeal to the
observable facts, while at the same time the observable
facts can only be justified by appeal to theory."
> Even a photomultiplier tube will trigger an erratic response
> following a Poisson process when fed with a low intensity coherent
> laser beam.
Precisely, the PMT is a quantum (detector) system and due to its very
high gain 10^(6) or more, is also very sensitive to its environment.
Experiments have shown that one can eliminate a lot of random PMT
counts, like dark current, etc.. by cooling the PMT and adjusting the
High Voltage. And the PMT output energy level can be pre-set, by
an electronic window, for instance, between 5 and 8 eV and thereby
eliminating unwanted input - output energies. However, some
unwanted random counts may still arrive at the PMT's output due to
the PMT's design, or could be caused by a number of events including
cosmic particles or the disintegration of a radioactive particle buried
somewhere in the PMT's environment. Even those counts can be mostly
eliminated by modern electronics - the PMT's output must match an
known EPROM signature measurement or it will not be measured
as a valid count.
After a proper setup, the PMT (a quantum system), will measure an
objective record of individual results that can be analyzed
statistically
and quoted in a physics journal.
Best regards Joe Rongen 6/3/05/4:14 pm.
Joe Rongen
Jun7-05, 02:30 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in\nmessage news:42A05FE1.2090109@univie.ac.at...\n> Joe Rongen wrote:\n>\n> >>Arnold Neumaier wrote:\n> >>\n> >>>I am looking for an explanation why a particular detector coupled\n> >>>to a particular quantum system produces the observed erratic but\n> >>>objective record of individual results that can be analyzed\n> >>>statistically and quoted in a physics journal.\n> >\n> > Some detector systems employ photomultiplier tube(s).\n> >\n> > The ideal photomultiplier tube is a detector that basically\n> > absorbs (photo-electric effect) one photon and internally\n> > converts/produces** due to an electron cascade/amplifier\n> > effect, one measurable event.\n> >\n> > ** Lawrence and Beams showed in 1928 that photo-electrons are\n> > sometimes emitted less than 3 *10^(-9) sec after initial illumination.\n>\n> Could you please explain how this relates to my statement?\n\nI took the liberty to understand your "particular quantum system"\nas a photon producing system. The photomultiplier tube (PMT)\nis also a quantum device; the difference being that the output\nenergy is measurable in electron-volts. The PMT is in theory,\nand experimentally a well understood device and as such follows\nthis (circular) suggestion closely:\n\n"Theory is meant to be substantiated by appeal to the\nobservable facts, while at the same time the observable\nfacts can only be justified by appeal to theory."\n\n> Even a photomultiplier tube will trigger an erratic response\n> following a Poisson process when fed with a low intensity coherent\n> laser beam.\n\nPrecisely, the PMT is a quantum (detector) system and due to its very\nhigh gain 10^(6) or more, is also very sensitive to its environment.\n\nExperiments have shown that one can eliminate a lot of random PMT\ncounts, like dark current, etc.. by cooling the PMT and adjusting the\nHigh Voltage. And the PMT output energy level can be pre-set, by\nan electronic window, for instance, between 5 and 8 eV and thereby\neliminating unwanted input - output energies. However, some\nunwanted random counts may still arrive at the PMT\'s output due to\nthe PMT\'s design, or could be caused by a number of events including\ncosmic particles or the disintegration of a radioactive particle buried\nsomewhere in the PMT\'s environment. Even those counts can be mostly\neliminated by modern electronics - the PMT\'s output must match an\nknown EPROM signature measurement or it will not be measured\nas a valid count.\n\nAfter a proper setup, the PMT (a quantum system), will measure an\nobjective record of individual results that can be analyzed statistically\nand quoted in a physics journal.\n\nBest regards Joe\n\n\n--\nNo virus found in this outgoing message.\nChecked by AVG Anti-Virus.\nVersion: 7.0.323 / Virus Database: 267.6.2 - Release Date: 6/4/05\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in
message news:42A05FE1.2090109@univie.ac.at...
> Joe Rongen wrote:
>
> >>Arnold Neumaier wrote:
> >>
> >>>I am looking for an explanation why a particular detector coupled
> >>>to a particular quantum system produces the observed erratic but
> >>>objective record of individual results that can be analyzed
> >>>statistically and quoted in a physics journal.
> >
> > Some detector systems employ photomultiplier tube(s).
> >
> > The ideal photomultiplier tube is a detector that basically
> > absorbs (photo-electric effect) one photon and internally
> > converts/produces** due to an electron cascade/amplifier
> > effect, one measurable event.
> >
> > ** Lawrence and Beams showed in 1928 that photo-electrons are
> > sometimes emitted less than 3 *10^(-9) sec after initial illumination.
>
> Could you please explain how this relates to my statement?
I took the liberty to understand your "particular quantum system"
as a photon producing system. The photomultiplier tube (PMT)
is also a quantum device; the difference being that the output
energy is measurable in electron-volts. The PMT is in theory,
and experimentally a well understood device and as such follows
this (circular) suggestion closely:
"Theory is meant to be substantiated by appeal to the
observable facts, while at the same time the observable
facts can only be justified by appeal to theory."
> Even a photomultiplier tube will trigger an erratic response
> following a Poisson process when fed with a low intensity coherent
> laser beam.
Precisely, the PMT is a quantum (detector) system and due to its very
high gain 10^(6) or more, is also very sensitive to its environment.
Experiments have shown that one can eliminate a lot of random PMT
counts, like dark current, etc.. by cooling the PMT and adjusting the
High Voltage. And the PMT output energy level can be pre-set, by
an electronic window, for instance, between 5 and 8 eV and thereby
eliminating unwanted input - output energies. However, some
unwanted random counts may still arrive at the PMT's output due to
the PMT's design, or could be caused by a number of events including
cosmic particles or the disintegration of a radioactive particle buried
somewhere in the PMT's environment. Even those counts can be mostly
eliminated by modern electronics - the PMT's output must match an
known EPROM signature measurement or it will not be measured
as a valid count.
After a proper setup, the PMT (a quantum system), will measure an
objective record of individual results that can be analyzed statistically
and quoted in a physics journal.
Best regards Joe
--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7..323 / Virus Database: 267.6.2 - Release Date: 6/4/05
Take this example : "It is\nhelpful to remember that the quantum state is just an expectation\ncatalog.\nIts purpose is to make predictions about possible measurement results a\nspecific observer does not know yet" ([1]).\n\n> Physicists dislike knowledge because\n> knowledge is subjective, and subjective things are bad.\n\nThe point is that the belief in an objective, inherently existing\nuniverse is unfounded.
The problem with that view is that it doesn't allow you to apply any great principle to "nature" which doesn't exist. Why should there be lorentz invariance, then ? What laws does a catalog of possible measurements (of what?) have to obey ? If you do not give any ontological status to the wavefunction, and deny any objective world to exist (even if it is not the world that is subjectively OBSERVED!) then how can you expect a non-existant world to obey any laws of a non-existant nature ?
If that non-existant nature constantly gives rise to subjective experiences AS IF there were an underlying reality, then isn't it more fruitful to assume that such a reality exists ? That doesn't mean one has to subscribe to any physical collapse: unitary evolution is ok, as long as subjective experiences are extracted from it using the Born rule (and which are, of course, subjective, and "observer" dependent). But I find it hard to at the same time assume that there are laws of nature and deny any existance of said nature :-) For instance, what does "locality" mean to a non-existing world ? Is "locality" then a law of non-nature ?
cheers,
Patrick.
No. Only a closed system evolves unitarily, and of course it cannot
be observed and hence does not produce outcomes.
How can you exclude that internal parts of the closed system have observational subjective experiences which they would qualify as "measurements" ?
cheers,
Patrick.
This is where I disagree. There's a fundamental _physical_ question:
whether or not the wavefunction collapses or not. This is (in principle)
experimentally verifiable. It's not philosophy; it's a question about
the real world.
The only thing that is experimentally verifiable is whether there is quantum interference or not. I don't see how you are going to verify the collapse itself.
Now, a more philosophical question that is, I think, informed by all of
this is why do we not perceive superpositions (which, even in the
presence of decoherence, still exist)? Or, in other words, why do we
only perceive one branch of the wavefunction. I'd like to think that
this has some real, physical answer, but maybe it's all just ephemeral.
I think that this must somehow be postulated and cannot be derived "from within" QM. I wrote a small paper on that: quant-ph/0505059.
It just happens that our subjective experience follows the Born rule while "riding on the unitary wave function". What's wrong with such a postulate ?
cheers,
Patrick.
Aaron Bergman
Jun7-05, 09:31 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <d81sfe09ee@drn.newsguy.com>,\nstevendaryl3016@yah oo.com (Daryl McCullough) wrote:\n\n> Aaron Bergman says...\n>\n> >I\'m a frequentist. In statistical mechanics, you assume that you fully\n> >sample the phase space and the probabilities fall out.\n>\n> Do they? It seems to me that the usual development of classical\n> statistical mechanics depends crucially on the assumption that\n> all microstates that are consistent with a given macrostate are\n> equally likely.\n\nSure. That\'s what I meant by the poorly phrased \'fully sample the phase\nspace\'.\n\n> That allows us to use density of states as a\n> stand-in for probability density. But why should all microstates\n> be equally likely?\n>\n> In certain special cases, it is possible to prove (terminology: is\n> this ergodicity?) that the trajectory through phase space comes\n> arbitrarily close to every point consistent with the macroscopic\n> variables (energy, volume, number of particles, etc.) In this case,\n> the statistical assumption of equal likelihood will be true, *provided*\n> that the system has been in equilibrium long enough to "sample" all\n> of the allowed phase space, which in practice is never true, since\n> phase space is so huge.\n\nAs I remember it (and I very well could be wrong here), it is possible\nto prove such a thing, but most of the proofs involve time scales way,\nway too long to be physically relevant, ie, on the order of the\nrecurrence time.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <d81sfe09ee@drn.newsguy.com>,
stevendaryl3016@yahoo.com (Daryl McCullough) wrote:
> Aaron Bergman says...
>
> >I'm a frequentist. In statistical mechanics, you assume that you fully
> >sample the phase space and the probabilities fall out.
>
> Do they? It seems to me that the usual development of classical
> statistical mechanics depends crucially on the assumption that
> all microstates that are consistent with a given macrostate are
> equally likely.
Sure. That's what I meant by the poorly phrased 'fully sample the phase
space'.
> That allows us to use density of states as a
> stand-in for probability density. But why should all microstates
> be equally likely?
>
> In certain special cases, it is possible to prove (terminology: is
> this ergodicity?) that the trajectory through phase space comes
> arbitrarily close to every point consistent with the macroscopic
> variables (energy, volume, number of particles, etc.) In this case,
> the statistical assumption of equal likelihood will be true, *provided*
> that the system has been in equilibrium long enough to "sample" all
> of the allowed phase space, which in practice is never true, since
> phase space is so huge.
As I remember it (and I very well could be wrong here), it is possible
to prove such a thing, but most of the proofs involve time scales way,
way too long to be physically relevant, ie, on the order of the
recurrence time.
Aaron
Arnold Neumaier
Jun7-05, 09:31 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n>>>I hope you also consider the statistics of statistical classical\n>>>mechanics as pragmatic procedures. If this is the case, you are simply\n>>>looking for the deterministic evolution of individual outcomes from a\n>>>given initial condition:\n>>>Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).\n>>>If it is what you are looking for, general unitary evolution tells you\n>>>that it is most of the time impossible:\n>>\n>>No. Only a closed system evolves unitarily, and of course it cannot\n>>be observed and hence does not produce outcomes.\n>>\n> The state of a closed system evolves unitary and the above text does\n> not say the contrary.\n\nYes. This was just an introduction to the second half of my statement.\n\n> However, the sentence "the closed system cannot\n> be observed and hence cannot produce outcomes" is already an\n> interpretation of the measurement formalism [of QM axiomatic theory].\n\nNo. How could a closed system be possibly observed from the outside???\nIf the observer sits in a different system then, because the first\nsystem is closed, it cannot have any interactions. Thus the observer\'s\ndynamics will be completely unaffected by the system. Thus the observer\nwill not be able to collect any information about the system.\nThus the observer cannot claim convincingly to have observed the system.\n\nObservability by an external observer therefore demands openness of the\nsystem. At least under conventional assumptions about what the terms\nclosed, interaction, observation mean.\n\nFor the universe as a whole, the situation is different since it is\nobserved by an observer _within_ the system. While this is not\nanalyzed in the trasditional setting, it can be analyzed within the\nconsistent experiment interpretation.\n\n\n>>This even holds in the traditional Copenhagen interpretation.\n>>The view is that the system is closed most of the time and then\n>>evolves unitarity. At certain very short moments, it is assumed\n>>to be in contact with a detector for measurement - then the\n>>system is open and evolves nonunitarily, by collapse.\n>>\n> This is interpretation,\n\nOf course, I didn\'t claim otherwise.\nIt is the Copenhagen _interpretation_.\n\n\n> Note, in the QM formalism, there is no classical/quantum boundary (only\n> in the interpretations of QM). Just postulates that may be applied,\n> hopefully (for the consistence of the theory) on closed systems as well\n> as opened ones.\n\nBut there are different postulates for\n\n- closed systems (unitarity),\n- systems open just at some instant (collpse), and\n- continuously open systems (Lindblad type dissipative dynamics,\nor corresponding stochastic quantum processes).\n\nAll of these are needed and heavily used to account forthe current\nway to successfully apply QM to the myriad of problems it can handle.\n\n\nWill respond to the remainder of your mail separately.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
>>>I hope you also consider the statistics of statistical classical
>>>mechanics as pragmatic procedures. If this is the case, you are simply
>>>looking for the deterministic evolution of individual outcomes from a
>>>given initial condition:
>>>Outcome_i(t)= f(outcome_1(to), outcome_n(to),t).
>>>If it is what you are looking for, general unitary evolution tells you
>>>that it is most of the time impossible:
>>
>>No. Only a closed system evolves unitarily, and of course it cannot
>>be observed and hence does not produce outcomes.
>>
> The state of a closed system evolves unitary and the above text does
> not say the contrary.
Yes. This was just an introduction to the second half of my statement.
> However, the sentence "the closed system cannot
> be observed and hence cannot produce outcomes" is already an
> interpretation of the measurement formalism [of QM axiomatic theory].
No. How could a closed system be possibly observed from the outside???
If the observer sits in a different system then, because the first
system is closed, it cannot have any interactions. Thus the observer's
dynamics will be completely unaffected by the system. Thus the observer
will not be able to collect any information about the system.
Thus the observer cannot claim convincingly to have observed the system.
Observability by an external observer therefore demands openness of the
system. At least under conventional assumptions about what the terms
closed, interaction, observation mean.
For the universe as a whole, the situation is different since it is
observed by an observer _within_ the system. While this is not
analyzed in the trasditional setting, it can be analyzed within the
consistent experiment interpretation.
>>This even holds in the traditional Copenhagen interpretation.
>>The view is that the system is closed most of the time and then
>>evolves unitarity. At certain very short moments, it is assumed
>>to be in contact with a detector for measurement - then the
>>system is open and evolves nonunitarily, by collapse.
>>
> This is interpretation,
Of course, I didn't claim otherwise.
It is the Copenhagen _interpretation_.
> Note, in the QM formalism, there is no classical/quantum boundary (only
> in the interpretations of QM). Just postulates that may be applied,
> hopefully (for the consistence of the theory) on closed systems as well
> as opened ones.
But there are different postulates for
- closed systems (unitarity),
- systems open just at some instant (collpse), and
- continuously open systems (Lindblad type dissipative dynamics,
or corresponding stochastic quantum processes).
All of these are needed and heavily used to account forthe current
way to successfully apply QM to the myriad of problems it can handle.
Will respond to the remainder of your mail separately.
Arnold Neumaier
I.Vecchi
Jun7-05, 01:28 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> As I understand it, it\'s more than just not seeing macroscopic\n> superpositions; the actual process of decoherence has been observed.\n>\n\nWhat has been observed (see e.g. [1]) is interference patterns being\nblurred as the system\' s dynamics perturbs them, putting them beyond\nthe observer\'s grasp. It should be noted, first, that this process is\nsystem-specific, second, that , if this is decoherence, by the same\ntoken a rabbit disappearing into the stage-magician\'s hat is\n"decohering".\n\nIV\n\n[1] http://physicsweb.org/articles/news/8/2/9\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> As I understand it, it's more than just not seeing macroscopic
> superpositions; the actual process of decoherence has been observed.
>
What has been observed (see e.g. [1]) is interference patterns being
blurred as the system' s dynamics perturbs them, putting them beyond
the observer's grasp. It should be noted, first, that this process is
system-specific, second, that , if this is decoherence, by the same
token a rabbit disappearing into the stage-magician's hat is
"decohering".
IV
[1] http://physicsweb.org/articles/news/8/2/9
Hendrik van Hees
Jun7-05, 05:47 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n\n> For example, an ion trap models a single, well-defined quantum\n> system over time. Experiments routinely get measurable time series\n> that define the detector\'s response to this single quantum system.\n> Each time series is a realization of a stochastic process.\n> But its time correlation functions computed from a _single_\n> realization are in accordance with quantum mechanics.\n> Thus these are quantum predictions about single quantum systems\n> observed over time.\n\nCan you give a reference to such an experiment or describe what was\nreally measured?\n\n\n--\nHendrik van Hees Texas A&M University\nPhone: +1 979/845-1411 Cyclotron Institute, MS-3366\nFax: +1 979/845-1899 College Station, TX 77843-3366\nhttp://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> For example, an ion trap models a single, well-defined quantum
> system over time. Experiments routinely get measurable time series
> that define the detector's response to this single quantum system.
> Each time series is a realization of a stochastic process.
> But its time correlation functions computed from a _single_
> realization are in accordance with quantum mechanics.
> Thus these are quantum predictions about single quantum systems
> observed over time.
Can you give a reference to such an experiment or describe what was
really measured?
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu
Seratend
Jun7-05, 05:47 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Seratend wrote:\n>\n> > Arnold Neumaier wrote:\n> >\n> >>Seratend wrote:\n> > However, the sentence "the closed system cannot\n> > be observed and hence cannot produce outcomes" is already an\n> > interpretation of the measurement formalism [of QM axiomatic theory].\n>\n> No. How could a closed system be possibly observed from the outside???\n> If the observer sits in a different system then, because the first\n> system is closed, it cannot have any interactions. Thus the observer\'s\n> dynamics will be completely unaffected by the system. Thus the observer\n> will not be able to collect any information about the system.\n\nWe are at the heart of the problem between the formalism of the theory\nand the interpretation.\nPlease note that the measurement part of the theory does not require\nany interaction. The observer outside or inside the system has no\nmeaning in the QM formalism (only in the interpretations).\nThe collapse postulate is just the *acknowledgement* of a property of a\nsystem (the outcome of the observable A is a), an outcome of the one\ninstance of the system (among all the possible instances of these\nsystems). It is not an interaction at all.\nThis is why it important to separate in the "real" measurement\ntools/observers, the interactions with the system (described by the\nHamiltonians) from the collapse, at least formally. The whole system\nalways evolve unitary in the QM formalism while a particular instance\nof this system [in the "reality"] has the property of the collapse\n(outcome of A is a).\n\nMoreover, an opened system is a closed system when we consider the rest\nof the world (formal). We have the collapse postulate on the local\nstate (given by the highly degenerated projector |a><a|(x)Id, where Id\napplies to the rest of the world, for the outcome a). Nothing prevents\n(in the QM formalism) an instance of such a system to get this\nproperty.\n\n> Thus the observer cannot claim convincingly to have observed the system.\n>\nI hope you understand better why this sentence has no meaning in the QM\ntheory formalism (in my opinion : ).\n\n> Observability by an external observer therefore demands openness of the\n> system. At least under conventional assumptions about what the terms\n> closed, interaction, observation mean.\n>\nH= sum_i Hi => unitary evolution, including the interactions of the\nobserver object.\n+ collapse postulate: property of an instance of a system governed by H\n(including the observer object).\nIf I say, I have a system [including the observer object] with a given\nproperty => I have the associated collapse. There is no "observer"\nin the sentence "I have a system [including the observer object] with\na given property", just the logic affirmation of this property.\n\n> For the universe as a whole, the situation is different since it is\n> observed by an observer _within_ the system. While this is not\n> analyzed in the trasditional setting, it can be analyzed within the\n> consistent experiment interpretation.\n>\nI am still working on your post reply dealing with the "consistent\nexperiment interpretation". I hope soon I will be able to give you\nsome feedbacks.\n>\n> >>This even holds in the traditional Copenhagen interpretation.\n> >>The view is that the system is closed most of the time and then\n> >>evolves unitarity. At certain very short moments, it is assumed\n> >>to be in contact with a detector for measurement - then the\n> >>system is open and evolves nonunitarily, by collapse.\n> >>\n> > This is interpretation,\n>\n> Of course, I didn\'t claim otherwise.\n> It is the Copenhagen _interpretation_.\n>\nWell, as I have said before, I will not question the interpretation as\nlong as it does not change the QM theory formalism. In this\ninterpretation context, I do not know what you intend by collapse (you\nseem to have studied deeper the CI than I : )). All what I know is the\nlogical meaning of the label "collapse" in the QM formalism and\ndefinitively it does not say it is a non unitary evolution of the\nsystem. Only the interpretation of the words "before" and\n"after" may lead to such a conclusion (hence an interpretation).\n>\n> > Note, in the QM formalism, there is no classical/quantum boundary (only\n> > in the interpretations of QM). Just postulates that may be applied,\n> > hopefully (for the consistence of the theory) on closed systems as well\n> > as opened ones.\n>\n> But there are different postulates for\n>\n> - closed systems (unitarity),\n> - systems open just at some instant (collpse), and\n> - continuously open systems (Lindblad type dissipative dynamics,\n> or corresponding stochastic quantum processes).\n>\nI hope that no!\n\nYou have the unitary evolution and the measurement postulates: An Open\nsystem is always a part of a closed system (otherwise, the unitary\nevolution postulate is not true => problem with the consistence of the\nQM theory). The collapse postulate always applies to the whole system\ndescription.\n\nStarting from this point you may derive the results on the description\nof open systems (your above list), with local collapse (i.e. with\nglobal projectors acting on the local space). However, you still apply\nthe same postulates of the QM theory (you derive the results form the\ninitial postulates).\n\n> All of these are needed and heavily used to account for the current\n> way to successfully apply QM to the myriad of problems it can handle.\n>\nIn my understanding, all the results prove the successful application\nof the QM formalism. Only the interpretations have to be adapted in\norder to keep in pace with the formalism and its surprising results.\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Seratend wrote:
>
> > Arnold Neumaier wrote:
> >
> >>Seratend wrote:
> > However, the sentence "the closed system cannot
> > be observed and hence cannot produce outcomes" is already an
> > interpretation of the measurement formalism [of QM axiomatic theory].
>
> No. How could a closed system be possibly observed from the outside???
> If the observer sits in a different system then, because the first
> system is closed, it cannot have any interactions. Thus the observer's
> dynamics will be completely unaffected by the system. Thus the observer
> will not be able to collect any information about the system.
We are at the heart of the problem between the formalism of the theory
and the interpretation.
Please note that the measurement part of the theory does not require
any interaction. The observer outside or inside the system has no
meaning in the QM formalism (only in the interpretations).
The collapse postulate is just the *acknowledgement* of a property of a
system (the outcome of the observable A is a), an outcome of the one
instance of the system (among all the possible instances of these
systems). It is not an interaction at all.
This is why it important to separate in the "real" measurement
tools/observers, the interactions with the system (described by the
Hamiltonians) from the collapse, at least formally. The whole system
always evolve unitary in the QM formalism while a particular instance
of this system [in the "reality"] has the property of the collapse
(outcome of A is a).
Moreover, an opened system is a closed system when we consider the rest
of the world (formal). We have the collapse postulate on the local
state (given by the highly degenerated projector |a><a|(x)Id, where Id
applies to the rest of the world, for the outcome a). Nothing prevents
(in the QM formalism) an instance of such a system to get this
property.
> Thus the observer cannot claim convincingly to have observed the system.
>
I hope you understand better why this sentence has no meaning in the QM
theory formalism (in my opinion : ).
> Observability by an external observer therefore demands openness of the
> system. At least under conventional assumptions about what the terms
> closed, interaction, observation mean.
>
H= sum_i Hi => unitary evolution, including the interactions of the
observer object.
+ collapse postulate: property of an instance of a system governed by H
(including the observer object).
If I say, I have a system [including the observer object] with a given
property => I have the associated collapse. There is no "observer"
in the sentence "I have a system [including the observer object] with
a given property", just the logic affirmation of this property.
> For the universe as a whole, the situation is different since it is
> observed by an observer _within_ the system. While this is not
> analyzed in the trasditional setting, it can be analyzed within the
> consistent experiment interpretation.
>
I am still working on your post reply dealing with the "consistent
experiment interpretation". I hope soon I will be able to give you
some feedbacks.
>
> >>This even holds in the traditional Copenhagen interpretation.
> >>The view is that the system is closed most of the time and then
> >>evolves unitarity. At certain very short moments, it is assumed
> >>to be in contact with a detector for measurement - then the
> >>system is open and evolves nonunitarily, by collapse.
> >>
> > This is interpretation,
>
> Of course, I didn't claim otherwise.
> It is the Copenhagen _interpretation_.
>
Well, as I have said before, I will not question the interpretation as
long as it does not change the QM theory formalism. In this
interpretation context, I do not know what you intend by collapse (you
seem to have studied deeper the CI than I : )). All what I know is the
logical meaning of the label "collapse" in the QM formalism and
definitively it does not say it is a non unitary evolution of the
system. Only the interpretation of the words "before" and
"after" may lead to such a conclusion (hence an interpretation).
>
> > Note, in the QM formalism, there is no classical/quantum boundary (only
> > in the interpretations of QM). Just postulates that may be applied,
> > hopefully (for the consistence of the theory) on closed systems as well
> > as opened ones.
>
> But there are different postulates for
>
> - closed systems (unitarity),
> - systems open just at some instant (collpse), and
> - continuously open systems (Lindblad type dissipative dynamics,
> or corresponding stochastic quantum processes).
>
I hope that no!
You have the unitary evolution and the measurement postulates: An Open
system is always a part of a closed system (otherwise, the unitary
evolution postulate is not true => problem with the consistence of the
QM theory). The collapse postulate always applies to the whole system
description.
Starting from this point you may derive the results on the description
of open systems (your above list), with local collapse (i.e. with
global projectors acting on the local space). However, you still apply
the same postulates of the QM theory (you derive the results form the
initial postulates).
> All of these are needed and heavily used to account for the current
> way to successfully apply QM to the myriad of problems it can handle.
>
In my understanding, all the results prove the successful application
of the QM formalism. Only the interpretations have to be adapted in
order to keep in pace with the formalism and its surprising results.
Seratend.
Aaron Bergman
Jun8-05, 01:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1118070553.900097.186040@g49g2000cwa.googlegroups .com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> I accept the results of decoherence, how the entanglement transforms\n> the evolution of macroscopic states. I just do not understand (the\n> logic behind such an affirmation) on how it can solve the preferred\n> basis prediction (ab initio).\n\nOK. Let\'s try to work from this.\n\nYou accept the results of decoherence and you accept that they can (in\nprinciple) be derived from the law of unitary evolution, right? If so,\nthen implicit in this statement is that you believe in the existence of\nthe basis selected by decoherence. (I\'m going to avoid \'preferred\'\nbecause you seem to want to impart some ontological baggage there that I\ndon\'t want.)\n\nI didn\'t think I was making any controversial statements here. This same\nidea appears in III.E (.3 in particular) of the paper that was referred\nto earlier on this thread, quant-ph/0312059.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1118070553.900097.186040@g49g2000cwa.googlegroups. com>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> I accept the results of decoherence, how the entanglement transforms
> the evolution of macroscopic states. I just do not understand (the
> logic behind such an affirmation) on how it can solve the preferred
> basis prediction (ab initio).
OK. Let's try to work from this.
You accept the results of decoherence and you accept that they can (in
principle) be derived from the law of unitary evolution, right? If so,
then implicit in this statement is that you believe in the existence of
the basis selected by decoherence. (I'm going to avoid 'preferred'
because you seem to want to impart some ontological baggage there that I
don't want.)
I didn't think I was making any controversial statements here. This same
idea appears in III.E (.3 in particular) of the paper that was referred
to earlier on this thread, http://www.arxiv.org/abs/quant-ph/0312059.
Aaron
Arnold Neumaier
Jun8-05, 01:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n> The formal measurement (collapse and born rules) are just the\n> statistical description of experiments:\n>\n> a) The collapse postulate describes 2 topics, a property of the system\n> (Outcome a of a given observable A is true) and the state of the system\n> if this property is true (stability of the property: the "true\n> remains true").\n> b) the born rules: a state and an observable define the probability law\n> of the outcomes of the observable.\n>\n> Therefore, the probability law of the outcomes (the statistics) of an\n> experiment is completely defined by the couple (|psi>, A). However to\n> calculate the statistics on experiments (the mapping), we need the\n> collapse: the formal mapping between the experiment outcomes and the\n> statistics simply expressed by the collapse property: the outcome\n> "a" for this experiment trial is true.\n> Note that in order to recover the probability law in the frequency of\n> outcomes we must have the independence of identical systems (hence, we\n> need a "preparation" to select the systems).\n\nBut this is not satisfied in many experiments analyzed by quantum\nmechanics. For example, in an ion trap, one has the continuous\nmeasurement of a single system, in which the observation at different\ntimes can by no means considered to be obervations of independent\nsystems.\n\nThus your conceptual framework for interpreting quantum mechanical\nexperiments is too restrictive.\n\n\n> A physical theory is mainly a choice of description (formally, we are\n> free to choose what we want)\n\n...but only if we don\'t care about the quality of our predictions.\nIf we want to have good predictions, we must choose what quantum\nmechanics tells us to choose.\n\n\n> and the prediction (the useful content\n> imposed by the "reality") in the context of this choice of\n> description.\n>\n> Usually (my knowledge : ), we use 2 logical type of descriptions in\n> physical theories: the "determinist" (i.e. the description of a\n> function) and the statistical description of a system (i.e. the\n> statistics induced by the function). QM and Statistical classical\n> mechanics are both based on the use of the formal statistical\n> description of a system; therefore, I will describe what I mean (the\n> logic) by the logical content of a statistical description (the\n> mathematics).\n>\n> a) Math: A function is a collection of true propositions, by the\n> logical mapping a=f(e) <=> if e then a.\n> b) Math: giving a function f or a set F= {(a,e), for all e in the\n> domain of the function} is equivalent.\n> c) statistical description:\n>\n> Statistical description is a very pragmatic description choice (and not\n> a mysterious physical process). With QM or with a basic coin flipping\n> experiment we always do the same thing: we label the experimental\n> trials and compute the frequencies of the outcomes:\n\nWhat is a true outcome in a world described by quantum mechanics/\n\n\n> 1) We have an implicitly defined random variable, an abstract function\n> f, which expresses the experiment logic results: for the trial labelled\n> e, we associate the result a (logic true): "if e then result a".\n> The function/random variable is defined by the set {(e, a), for all e}\n> is equivalent to a=f(e) (i.e. the proposition "the result of the\n> experiment trial label e is a" is true).\n\nEven classical statistics is surrounded by a foundational mystery,\ncausing as heated debates as in QM.\n\nYour description is by no means universally accepted. The frequentist\napproach you favor here has severe problems in that the predicted\nprobabilities and the observed frequencies only match approximately.\nOne can encounter long strings of heads although the probability\nof a head is 1/2.\n\nYou can read about my view of probability theory in my theoretical\nphysics FAQ at\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\n\nWhat I want as a basis of physics is a mathematically defined\nmodel of the world in which one can give unambiguous descriptions\nof all that matters in physics - physical systems, detectors, observers,\nindividual observations, statistics about these observations,\nerror analysis, etc. in such a way that it mirrors reality.\nJust as in matheamtical logic, one models the whole logical process\nin a concise mathematical framework.\n\n\n\n>>Although not very clearly separated in many discussions,\n>>these two processes happen never simultaneously but context\n>>dependent, and are of course only approximations to more\n>>realistic measurement situations.\n>>\n>>For example, in a Stern-Gerlach experiment, the system (silver atom)\n>>moves from the source along the magnet towards the screen with very\n>>good accuracy in a unitary (and indeed reversible) way. But a few\n>>split moments before it hits the screen it feels its interactions,\n>>and describing it as a closed system becomes hopelessly inaccurate.\n>>Instead, since the interaction time is very short, it can be\n>>described very accurately by an instantaneous collapse.\n>>\n> Why do you say it becomes hopelessly inaccurate?\n\nBecause the closed system in this setting contains >10^20 degrees of\nfreedom, and we cannot model such systems accurately. We need the\nthermodynamic approximation, and with it an unavoidable inaccuracy\nin the response to the microscopic particle state.\n\n\n> And How can you really\n> apply a collapse to a non closed system? In this case, don\'t you\n> think the collapse result (the outcome) should be independent of the\n> partial system description versus the whole system (including the\n> universe if necessary)?\n\nLook at the corresponding classical situation. A classical particle\nencounters a classical screen (say, a thin foil through which\nthe particle will most likely escape) involving a huge number\nof classical particles bound by (and interacting with the\nincident particle) by empirical forces. It ends up in some state\nthat is determined only probablilistically, once you ignore the\ndetailed structure of the screen. But it ends up in a _definite_\nstate. To describe it, however, without reference to the state of\nthe screen, necessitaties a probabilistic description and a collapse.\n\nThe quantum system is - in the consistent experiment interpretation -\ncompletely analogous, except that the dynamics differs in detail\nsignificantly from the classical dynamics.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
> The formal measurement (collapse and born rules) are just the
> statistical description of experiments:
>
> a) The collapse postulate describes 2 topics, a property of the system
> (Outcome a of a given observable A is true) and the state of the system
> if this property is true (stability of the property: the "true
> remains true").
> b) the born rules: a state and an observable define the probability law
> of the outcomes of the observable.
>
> Therefore, the probability law of the outcomes (the statistics) of an
> experiment is completely defined by the couple (|\psi>, A). However to
> calculate the statistics on experiments (the mapping), we need the
> collapse: the formal mapping between the experiment outcomes and the
> statistics simply expressed by the collapse property: the outcome
> "a" for this experiment trial is true.
> Note that in order to recover the probability law in the frequency of
> outcomes we must have the independence of identical systems (hence, we
> need a "preparation" to select the systems).
But this is not satisfied in many experiments analyzed by quantum
mechanics. For example, in an ion trap, one has the continuous
measurement of a single system, in which the observation at different
times can by no means considered to be obervations of independent
systems.
Thus your conceptual framework for interpreting quantum mechanical
experiments is too restrictive.
> A physical theory is mainly a choice of description (formally, we are
> free to choose what we want)
...but only if we don't care about the quality of our predictions.
If we want to have good predictions, we must choose what quantum
mechanics tells us to choose.
> and the prediction (the useful content
> imposed by the "reality") in the context of this choice of
> description.
>
> Usually (my knowledge : ), we use 2 logical type of descriptions in
> physical theories: the "determinist" (i.e. the description of a
> function) and the statistical description of a system (i.e. the
> statistics induced by the function). QM and Statistical classical
> mechanics are both based on the use of the formal statistical
> description of a system; therefore, I will describe what I mean (the
> logic) by the logical content of a statistical description (the
> mathematics).
>
> a) Math: A function is a collection of true propositions, by the
> logical mapping a=f(e) <=> if e then a.
> b) Math: giving a function f or a set F= {(a,e), for all e in the
> domain of the function} is equivalent.
> c) statistical description:
>
> Statistical description is a very pragmatic description choice (and not
> a mysterious physical process). With QM or with a basic coin flipping
> experiment we always do the same thing: we label the experimental
> trials and compute the frequencies of the outcomes:
What is a true outcome in a world described by quantum mechanics/
> 1) We have an implicitly defined random variable, an abstract function
> f, which expresses the experiment logic results: for the trial labelled
> e, we associate the result a (logic true): "if e then result a".
> The function/random variable is defined by the set {(e, a), for all e}
> is equivalent to a=f(e) (i.e. the proposition "the result of the
> experiment trial label e is a" is true).
Even classical statistics is surrounded by a foundational mystery,
causing as heated debates as in QM.
Your description is by no means universally accepted. The frequentist
approach you favor here has severe problems in that the predicted
probabilities and the observed frequencies only match approximately.
One can encounter long strings of heads although the probability
of a head is 1/2.
You can read about my view of probability theory in my theoretical
physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
What I want as a basis of physics is a mathematically defined
model of the world in which one can give unambiguous descriptions
of all that matters in physics - physical systems, detectors, observers,
individual observations, statistics about these observations,
error analysis, etc. in such a way that it mirrors reality.
Just as in matheamtical logic, one models the whole logical process
in a concise mathematical framework.
>>Although not very clearly separated in many discussions,
>>these two processes happen never simultaneously but context
>>dependent, and are of course only approximations to more
>>realistic measurement situations.
>>
>>For example, in a Stern-Gerlach experiment, the system (silver atom)
>>moves from the source along the magnet towards the screen with very
>>good accuracy in a unitary (and indeed reversible) way. But a few
>>split moments before it hits the screen it feels its interactions,
>>and describing it as a closed system becomes hopelessly inaccurate.
>>Instead, since the interaction time is very short, it can be
>>described very accurately by an instantaneous collapse.
>>
> Why do you say it becomes hopelessly inaccurate?
Because the closed system in this setting contains >10^20 degrees of
freedom, and we cannot model such systems accurately. We need the
thermodynamic approximation, and with it an unavoidable inaccuracy
in the response to the microscopic particle state.
> And How can you really
> apply a collapse to a non closed system? In this case, don't you
> think the collapse result (the outcome) should be independent of the
> partial system description versus the whole system (including the
> universe if necessary)?
Look at the corresponding classical situation. A classical particle
encounters a classical screen (say, a thin foil through which
the particle will most likely escape) involving a huge number
of classical particles bound by (and interacting with the
incident particle) by empirical forces. It ends up in some state
that is determined only probablilistically, once you ignore the
detailed structure of the screen. But it ends up in a _definite_
state. To describe it, however, without reference to the state of
the screen, necessitaties a probabilistic description and a collapse.
The quantum system is - in the consistent experiment interpretation -
completely analogous, except that the dynamics differs in detail
significantly from the classical dynamics.
Arnold Neumaier
Arnold Neumaier
Jun8-05, 01:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>>>>a) what is the initial state of the photon (assuming a wave packet) :\n>>>>>|psi>= |path1>+|path2> with <path1|path2>=0?\n>>>>\n>>>>Not quite. Roughly,\n>>>> |psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>\n>>>>with spatial coherent states |pathi(t)> (i=1,2) moving at the\n>>>>velocity of light and monochromatic 1-Photon Fock states |1>, say.\n>>>\n>>>Ok, usually when I write a state |path1>, this state may be the tensor\n>>>product of whatever we want (we may expand it when it is required).\n>>>Therefore, you seem to require the detail of this state:\n>>>\n>>>|psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?\n>>\n>>No; there is no need for orthogonality. Indeed, coherent states are\n>>not quite orthogonal, although their overlap is small if the paths are\n>>far away.\n>>\n>\n> Ok. However, this is not important as long as we can introduce later\n> the specificities we want. We use the linearity of the states to add,\n> later, additional features when we think they are really required for\n> the current study.\n> General wave packets and free propagation between local interactions\n> are almost always sufficient to describe the behaviour of the\n> experiments, once we know the behaviour of the interactions on the\n> states (screen with slits etc ...).\n> There is no need to detail precisely the wave packet as long as we\n> consider only coarse localizations, etc ...\n\nThe standard descriptions of quantum optical experiments treat\nthe path classically, which means, in a less sloppy formulation,\nas coherent states. This is reflected in my formulation.\nThere is no virtue in being more inaccurate; it only clouds the\nissues.\n\n\n> Let\'s assume we have the orthogonality, or if you prefer the\n> approximated orthogonality (strong separation in space of the 2\n> states).\n\nOnly the second is appropriate.\n\n\n> Sometimes, I prefer to take well known particles with simple\n> interactions (independent of spin) in order to verify some descriptions\n> behaviour with well known experiments.\n> Ok for spin 0 or with spin but without spin interaction (no polarizer\n> for photons, etc ...).\n\nOK, so let us talk of massive spin 0 particles that we call photons.\n\n\n>>Yes please. I haven\'t read the initial description of your setting\n>>(and my remarks below might reflect musunderstanding because of that).\n>>\n> Ok, we have an initial state |psi(0)>|screen1>|screen2>.\n>\n> With |psi(0)>= [|path1(0)>+|path2(0)>](x)|1>.\n>\n> Where |path1(t)> and |path2(t)> are partially localised wave packets\n> ((x,y) plane), propagating along the z direction at the same speed.\n>\n> We assume (we choose), the interactions of the screen 1 and screen 2 to\n> be:\n> H_int1= |screen1><screen1|(x)V1(r)\n> H_int2= |screen2><screen2|(x)V2(r)\n>\n> V1(r) is a reflective potential (a quantum wall potential) localized\n> with the screen1 area. This potential vanishes within the hole of\n> screen 1. let\'s call A this hole area.\n>\n> V2(r) is a reflective potential (a quantum wall potential) localized\n> with the screen2 area.\n>\n> We assume <r|path1(t)>=0 for r in the area A, for any t. (the path 1\n> fully interacts with screen 1)\n>\n> We assume <r|path2(t)>= 0 for r *not* in the area A, for any t. (the\n> path 2 is located in the hole of the potential of screen 1).\n>\n> We have the global Hamiltonian (photons or electrons, screen 1 and\n> screen 2):\n>\n> H_tot=Ho + H_oscreen1+ H_oscreen2 + H_int1+ H_int2\n>\n> Where:\n>\n> a) Ho, H_oscreen1, H_oscreen2 are the free Hamiltonians of the\n> particle, screen1 and screen2.\n> b) |screen1> and |screen2> are eigenstates of the free scren\n> Hamiltonians.\n>\n> -------------------------------------------------------> z\n> \\ screen1 \\screen2\n>\n> \\ \\\n> [source]+----1-----\\ \\\n> | / \\ \\\n> +----2---/------------------\\\n> / \\ / \\\n> / \\ / \\\n> / \\ / \\\n> V V\n> (reflected wavepackets when the screen\n> planes are not orthogonal to the z propagation direction)\n\nOK. This is a good setting.\n\n\n>>If the dynamics is unitary, how do you get the permanent record (the\n>>definite click or macroscopic spot) that constitutes a measurement?\n>>\n> This is what I want to show. The figure above shows that the screens\n> modify the wave packets and that this modification is described by a\n> unitary evolution.\n>\n> QM formalism does not describe the occurrence of clicks. The clicks are\n> the observed properties on the experimental trials (in this case\n> "reflection by a screen" or "click by a distant detector").\n> If a property is true (e.g. the reflection by screen2), the associated\n> formal collapse is also true. If the property is false the collapse is\n> also false.\n\nSo you assume the collapse rather than deriving it.\nYou postulate the existence of objective hidden variables\n(the observable clicks) that follow an uncontrolled, unmodelled\ndynamics correlated to the wave function according to the postulated\nBorn rule. This is a cheap way out.\n\nI want _better_ foundations. The clicks are not things unrelated to\nquantum mechanics, but they are macroscopic pressure distributions\nin the air surrounding the ear that hears the click. No pressure\ndistribution characteristic of a click implies no click to be heard.\n\nThe collapse challenge is to demonstrate the emergence of this\nparticular pressure distribution at the time it is observed,\nby considering the air as the quantum system which statistical\nmechanics claims it to be.\n\n\n\n> In any case, we have for a given instance of this system a property\n> false that becomes true. This has no meaning in this formalism.\n\nThen your formalism is severely deficient, not consistent with\nwhat textbooks assert.\n\nThe objective change of pressure distribution has a well-defined\nmeaning in the statistical mechanics description of the system\n(particle + air).\n\n\n\n> I hope you better understand, my meaning of the formal collapse: I do\n> not say more than the formalism of the theory does.\n\nI understand it, but regard it as empty talk.\n\nThe formalism of quantum statistical mechanics says more.\nIt says that a macroscopic quantum system has definite macroscopic\nobservables such as the pressure distribution of the air,\ngiven by the usual thermodynamical formalism.\n\n\n>>>I like this toy model where we force no entanglement between the\n>>>photons states and the screens and where we have the simple unitary\n>>>evolution of the initial state. It reflects perfectly what we do on an\n>>>experiment that reflects this unitary evolution:\n>>>a) we have to choose between all the photons, the one with the initial\n>>>state (hence an initial measurement result)\n>>\n>>How do we choose that?\n>>\n> This is the recursivity of statistical description model. By another\n> measurement (the preparation) that defines the properties we observe,\n> we use to say a given experiment trial is the good one (it is in the\n> good state).\n> This preparation can be as simple as a lamp with a slit plate. We know\n> that at a long distances of the slit plate, if we do a measurement\n> (the thought measurement), we recover wavepackets (approximation).\n> Therefore, we can say, from the formalism point of view, that the lamp+\n> slit plate is a measurement that gives as an output state wave packets.\n> Now, to understand better the recursivity, you can ask, how we know it\n> is a lamp with a screen? Etc ...\n\nThis is like a circular argument. It levaes everything undetermined...\nWhile traditionally accepted out of despair, it doesn\'t make for\ngood foundations.\n\n\n>>In my terminology, this would be a preparation, not a measurement,\n>>since measurement is _acquiring_ new information or _confirming/testing_\n>>old information, while preparation is _assuming_ information based on\n>>past experience with one\'s equipment.\n>>\n> Yes, this is the usual preparation of the Copenhagen interpretation if\n> I am correct. However, the preparation interpretation means you known\n> the state with 100% confidence. It is therefore undistinguishable from\n\n... what would have happened in ...\n\n> a collapse with the same state (note on how the correct description of\n> this property may require, the time, the space, etc ...).\n\n> For me it is logic to say: I have an instance of a system with a given\n> property. The preparation word is in this sense redundant with the\n> collapse word of the QM formalism.\n\nNo. It is important conceptually to distinguish the two.\nSomething different happens; only the prepared state is the same\nas that in a von_Neumann measurement.\n\n\n> In this section of your post, it is interesting to see the mixture of\n> interpretation with the QM formal results.\n> I say, formally, in a given experiment, we have properties (the results\n> of experiments, expressed by the collapse postulate). I do not specify,\n> if we learn or not this information as it is completely out of scope of\n> the formalism (the description choice).\n> In other words, assuming or not the acquisition of new information does\n> not change the properties of the system in this formalism.\n\nOf course, if you keep events outside the formalism, then only unitarity\nis left. But then nothing is to be explained anyway...\n\nYou solve the problem by banning everything that comes in the way of\nunitarity to be outside the theory. This completely removes the theory\nfrom experiment.\n\n\n>>>Assuming this, we can say (interpretation) that the screens do not\n>>>collapse the wave function if we have no detectors, while if we put the\n>>>detectors we can say that the screen collapses the wave function.\n>>\n>>Anything which is part of the system modelled unitarily does not\n>>produce collapse, while anything does that isn\'t modelled in full\n>>detail but whose interaction with the unmodelled dof\'s is nontrival.\n>>\n> I am not saying that a mysterious physical process defines the\n> collapse.\n\nThere is no mysterious physical process defining the collapse.\nThe interaction with anything outside the collapsing system is\nresponsible for the collapse, and such an interaction is\nnot mysterious at all, but common knowledge.\n\n\n> I just say, that in the statistical description choice of the\n> QM theory formalism, the collapse is just the notification of the\n> results of experimental trials (a property is true). Saying more than\n> that is interpreting the theory with the risk of modifying the theory.\n\nIn the statistical interpretation, the collapse is just the change\nof description caused by taking conditional expectations under a\nchage of the condition. Nothing needs to be explained on that level.\n\nWhat needs explanation is how the individual system is related to\nthe statistical description.\n\nIf we increase the size of the quantum system it becomes more and more\nunique. If the system is large enough (e.g. the Moon), the system\nis an individual, and it is no longer possible to prepare identically\ndisstributed copies of the Moon. But we still can observe it, and we\nstill believe it is governed by quantum mechanics, since no one can\npoint at any size where quantum mechanics starts to be inapplicable.\n\nHere is the need for explanation!\n\n\n\n>>>>That something remains to be explained even from the Copenhagen\n>>>>point of view (some version of which you seem to adhere to)\n>>>>is discussed in Section 3.\n>>>>\n>>>Copenhagen interpretation does not assume the "reality" of the\n>>>wavefunction.\n>>\n>>But it assumes the reality of the classical equipment, which\n>>therefore gives an N-particle system with large N an ontological\n>>status different from one with small N. It forgets to say at which\n>>value of N one is entitled to swich from one status to the other.\n>>\n> This is where Copenhagen interpretation may limit the validity of QM\n> theory, depending on how we interpret the words of the Copenhagen\n> interpretation. This is questionable.\n\nThe statistical interpretation has a similar conflict; it assumes\nthe reality of the objective event, the measurement result,\nand forgets to say which macroscopic observations are entitled to\nbe taken as objective events. This is questionable.\n\n\n\n> It is why I prefer to apply the "shut up and calculate" point of\n> view,\n\nThis is why most physicists shut up and calculate.\n\nThis is a sensible point of view, but not one that could claim to\nsolve the foundational riddles.\n\n\n> with the formal mapping of collapse with the experiments results\n> (the statistical description). It avoids to say more than the formalism\n> of the theory says.\n\nRather, it avoids to specify the precise meaning of what the formalism\nof quantum mechanics says. It just says, if you don\'t look too closely\nat the meaning, you can apply it very successfully...\n\n\n>>>>>At the end, I must apply the born\n>>>>>rules to get the statistics (what I see in the experiment).\n>>>>\n>>>>This is the informal prescription that is used to apply single-particle\n>>>>reasoning to a complex multiparticle experiment. It successfully\n>>>>avoids looking at the physics happening at the screen, replacing it\n>>>>by simply assuming the collapse, i.e., the emergence of an objective\n>>>>record according to the probabilities from the Born rule.\n>>>>While this is an acceptable attitude it is obviously not the whole\n>>>>story.\n>>>>\n>>>This is what I call the statistical description of the physical\n>>>phenomena (we do not explain the outcomes, we just measure their\n>>>frequency and their evolution in the space time).\n>>\n>>Yes.\n>>\n> So, why are you searching a physical meaning of to the collapse?\n\nBecause I think it has a physical meaning.\n\nI reject the statistical interpretation as being the fundamental\ndescription of nature. It cannot be consistently applied to the\nmany situations where quantum mechnaics is applied routinely\nalthough no two identically distributed realizations can be produced.\n\n\n> Here, I want to understand what you really mean by physical collapse.\n\nThe physical collapse is the response of a small quantum system\nto interactions of very short duration with a detector not modelled\nin detail.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>>>>a) what is the initial state of the photon (assuming a wave packet) :
>>>>>|\psi>= |path1>+|path2> with <path1|path2>=0?
>>>>
>>>>Not quite. Roughly,
>>>> |\psi(t)> = |path1(t)> tensor |1> + |path2(t)> tensor |1>
>>>>with spatial coherent states |pathi(t)> (i=1,2) moving at the
>>>>velocity of light and monochromatic 1-Photon Fock states |1>, say.
>>>
>>>Ok, usually when I write a state |path1>, this state may be the tensor
>>>product of whatever we want (we may expand it when it is required).
>>>Therefore, you seem to require the detail of this state:
>>>
>>>|\psi(t)>= [|path1(t)>+|path2(t)>](x)|1> with <path1|path2>=0?
>>
>>No; there is no need for orthogonality. Indeed, coherent states are
>>not quite orthogonal, although their overlap is small if the paths are
>>far away.
>>
>
> Ok. However, this is not important as long as we can introduce later
> the specificities we want. We use the linearity of the states to add,
> later, additional features when we think they are really required for
> the current study.
> General wave packets and free propagation between local interactions
> are almost always sufficient to describe the behaviour of the
> experiments, once we know the behaviour of the interactions on the
> states (screen with slits etc ...).
> There is no need to detail precisely the wave packet as long as we
> consider only coarse localizations, etc ...
The standard descriptions of quantum optical experiments treat
the path classically, which means, in a less sloppy formulation,
as coherent states. This is reflected in my formulation.
There is no virtue in being more inaccurate; it only clouds the
issues.
> Let's assume we have the orthogonality, or if you prefer the
> approximated orthogonality (strong separation in space of the 2
> states).
Only the second is appropriate.
> Sometimes, I prefer to take well known particles with simple
> interactions (independent of spin) in order to verify some descriptions
> behaviour with well known experiments.
> Ok for spin or with spin but without spin interaction (no polarizer
> for photons, etc ...).
OK, so let us talk of massive spin particles that we call photons.
>>Yes please. I haven't read the initial description of your setting
>>(and my remarks below might reflect musunderstanding because of that).
>>
> Ok, we have an initial state |\psi(0)>|screen1>|screen2>.
>
> With |\psi(0)>= [|path1(0)>+|path2(0)>](x)|1>.
>
> Where |path1(t)> and |path2(t)> are partially localised wave packets
> ((x,y) plane), propagating along the z direction at the same speed.
>
> We assume (we choose), the interactions of the screen 1 and screen 2 to
> be:
> H_{int1}= |screen1><screen1|(x)V1(r)
> H_{int2}= |screen2><screen2|(x)V2(r)
>
> V1(r) is a reflective potential (a quantum wall potential) localized
> with the screen1 area. This potential vanishes within the hole of
> screen 1. let's call A this hole area.
>
> V2(r) is a reflective potential (a quantum wall potential) localized
> with the screen2 area.
>
> We assume <r|path1(t)>=0 for r in the area A, for any t. (the path 1
> fully interacts with screen 1)
>
> We assume <r|path2(t)>= for r *not* in the area A, for any t. (the
> path 2 is located in the hole of the potential of screen 1).
>
> We have the global Hamiltonian (photons or electrons, screen 1 and
> screen 2):
>
> H_{tot}=Ho + H_{oscreen1}+ H_{oscreen2} + H_{int1}+ H_{int2}
>
> Where:
>
> a) Ho, H_{oscreen1}, H_{oscreen2} are the free Hamiltonians of the
> particle, screen1 and screen2.
> b) |screen1> and |screen2> are eigenstates of the free scren
> Hamiltonians.
>
> -------------------------------------------------------> z
> \ screen1 \screen2
>
> \ \
> [source]+----1-----\ \
> | / \ \
> +----2---/------------------\
> / \ / \
> / \ / \
> / \ / \
> V V
> (reflected wavepackets when the screen
> planes are not orthogonal to the z propagation direction)
OK. This is a good setting.
>>If the dynamics is unitary, how do you get the permanent record (the
>>definite click or macroscopic spot) that constitutes a measurement?
>>
> This is what I want to show. The figure above shows that the screens
> modify the wave packets and that this modification is described by a
> unitary evolution.
>
> QM formalism does not describe the occurrence of clicks. The clicks are
> the observed properties on the experimental trials (in this case
> "reflection by a screen" or "click by a distant detector").
> If a property is true (e.g. the reflection by screen2), the associated
> formal collapse is also true. If the property is false the collapse is
> also false.
So you assume the collapse rather than deriving it.
You postulate the existence of objective hidden variables
(the observable clicks) that follow an uncontrolled, unmodelled
dynamics correlated to the wave function according to the postulated
Born rule. This is a cheap way out.
I want _better_ foundations. The clicks are not things unrelated to
quantum mechanics, but they are macroscopic pressure distributions
in the air surrounding the ear that hears the click. No pressure
distribution characteristic of a click implies no click to be heard.
The collapse challenge is to demonstrate the emergence of this
particular pressure distribution at the time it is observed,
by considering the air as the quantum system which statistical
mechanics claims it to be.
> In any case, we have for a given instance of this system a property
> false that becomes true. This has no meaning in this formalism.
Then your formalism is severely deficient, not consistent with
what textbooks assert.
The objective change of pressure distribution has a well-defined
meaning in the statistical mechanics description of the system
(particle + air).
> I hope you better understand, my meaning of the formal collapse: I do
> not say more than the formalism of the theory does.
I understand it, but regard it as empty talk.
The formalism of quantum statistical mechanics says more.
It says that a macroscopic quantum system has definite macroscopic
observables such as the pressure distribution of the air,
given by the usual thermodynamical formalism.
>>>I like this toy model where we force no entanglement between the
>>>photons states and the screens and where we have the simple unitary
>>>evolution of the initial state. It reflects perfectly what we do on an
>>>experiment that reflects this unitary evolution:
>>>a) we have to choose between all the photons, the one with the initial
>>>state (hence an initial measurement result)
>>
>>How do we choose that?
>>
> This is the recursivity of statistical description model. By another
> measurement (the preparation) that defines the properties we observe,
> we use to say a given experiment trial is the good one (it is in the
> good state).
> This preparation can be as simple as a lamp with a slit plate. We know
> that at a long distances of the slit plate, if we do a measurement
> (the thought measurement), we recover wavepackets (approximation).
> Therefore, we can say, from the formalism point of view, that the lamp+
> slit plate is a measurement that gives as an output state wave packets.
> Now, to understand better the recursivity, you can ask, how we know it
> is a lamp with a screen? Etc ...
This is like a circular argument. It levaes everything undetermined...
While traditionally accepted out of despair, it doesn't make for
good foundations.
>>In my terminology, this would be a preparation, not a measurement,
>>since measurement is _acquiring_ new information or _confirming/testing_
>>old information, while preparation is _assuming_ information based on
>>past experience with one's equipment.
>>
> Yes, this is the usual preparation of the Copenhagen interpretation if
> I am correct. However, the preparation interpretation means you known
> the state with 100% confidence. It is therefore undistinguishable from
... what would have happened in ...
> a collapse with the same state (note on how the correct description of
> this property may require, the time, the space, etc ...).
> For me it is logic to say: I have an instance of a system with a given
> property. The preparation word is in this sense redundant with the
> collapse word of the QM formalism.
No. It is important conceptually to distinguish the two.
Something different happens; only the prepared state is the same
as that in a von_Neumann measurement.
> In this section of your post, it is interesting to see the mixture of
> interpretation with the QM formal results.
> I say, formally, in a given experiment, we have properties (the results
> of experiments, expressed by the collapse postulate). I do not specify,
> if we learn or not this information as it is completely out of scope of
> the formalism (the description choice).
> In other words, assuming or not the acquisition of new information does
> not change the properties of the system in this formalism.
Of course, if you keep events outside the formalism, then only unitarity
is left. But then nothing is to be explained anyway...
You solve the problem by banning everything that comes in the way of
unitarity to be outside the theory. This completely removes the theory
from experiment.
>>>Assuming this, we can say (interpretation) that the screens do not
>>>collapse the wave function if we have no detectors, while if we put the
>>>detectors we can say that the screen collapses the wave function.
>>
>>Anything which is part of the system modelled unitarily does not
>>produce collapse, while anything does that isn't modelled in full
>>detail but whose interaction with the unmodelled dof's is nontrival.
>>
> I am not saying that a mysterious physical process defines the
> collapse.
There is no mysterious physical process defining the collapse.
The interaction with anything outside the collapsing system is
responsible for the collapse, and such an interaction is
not mysterious at all, but common knowledge.
> I just say, that in the statistical description choice of the
> QM theory formalism, the collapse is just the notification of the
> results of experimental trials (a property is true). Saying more than
> that is interpreting the theory with the risk of modifying the theory.
In the statistical interpretation, the collapse is just the change
of description caused by taking conditional expectations under a
chage of the condition. Nothing needs to be explained on that level.
What needs explanation is how the individual system is related to
the statistical description.
If we increase the size of the quantum system it becomes more and more
unique. If the system is large enough (e.g. the Moon), the system
is an individual, and it is no longer possible to prepare identically
disstributed copies of the Moon. But we still can observe it, and we
still believe it is governed by quantum mechanics, since no one can
point at any size where quantum mechanics starts to be inapplicable.
Here is the need for explanation!
>>>>That something remains to be explained even from the Copenhagen
>>>>point of view (some version of which you seem to adhere to)
>>>>is discussed in Section 3.
>>>>
>>>Copenhagen interpretation does not assume the "reality" of the
>>>wavefunction.
>>
>>But it assumes the reality of the classical equipment, which
>>therefore gives an N-particle system with large N an ontological
>>status different from one with small N. It forgets to say at which
>>value of N one is entitled to swich from one status to the other.
>>
> This is where Copenhagen interpretation may limit the validity of QM
> theory, depending on how we interpret the words of the Copenhagen
> interpretation. This is questionable.
The statistical interpretation has a similar conflict; it assumes
the reality of the objective event, the measurement result,
and forgets to say which macroscopic observations are entitled to
be taken as objective events. This is questionable.
> It is why I prefer to apply the "shut up and calculate" point of
> view,
This is why most physicists shut up and calculate.
This is a sensible point of view, but not one that could claim to
solve the foundational riddles.
> with the formal mapping of collapse with the experiments results
> (the statistical description). It avoids to say more than the formalism
> of the theory says.
Rather, it avoids to specify the precise meaning of what the formalism
of quantum mechanics says. It just says, if you don't look too closely
at the meaning, you can apply it very successfully...
>>>>>At the end, I must apply the born
>>>>>rules to get the statistics (what I see in the experiment).
>>>>
>>>>This is the informal prescription that is used to apply single-particle
>>>>reasoning to a complex multiparticle experiment. It successfully
>>>>avoids looking at the physics happening at the screen, replacing it
>>>>by simply assuming the collapse, i.e., the emergence of an objective
>>>>record according to the probabilities from the Born rule.
>>>>While this is an acceptable attitude it is obviously not the whole
>>>>story.
>>>>
>>>This is what I call the statistical description of the physical
>>>phenomena (we do not explain the outcomes, we just measure their
>>>frequency and their evolution in the space time).
>>
>>Yes.
>>
> So, why are you searching a physical meaning of to the collapse?
Because I think it has a physical meaning.
I reject the statistical interpretation as being the fundamental
description of nature. It cannot be consistently applied to the
many situations where quantum mechnaics is applied routinely
although no two identically distributed realizations can be produced.
> Here, I want to understand what you really mean by physical collapse.
The physical collapse is the response of a small quantum system
to interactions of very short duration with a detector not modelled
in detail.
Arnold Neumaier
Arnold Neumaier
Jun8-05, 01:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>joe@alpha.to wrote:\n\n> "Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in\n> message news:42A05FE1.2090109@univie.ac.at...\n>\n>>Joe Rongen wrote:\n>>\n>>>>Arnold Neumaier wrote:\n>>>>\n>>>>I am looking for an explanation why a particular detector coupled\n>>>>>to a particular quantum system produces the observed erratic but\n>>>>>objective record of individual results that can be analyzed\n>>>>>statistically and quoted in a physics journal.\n>>>\n>>>Some detector systems employ photomultiplier tube(s).\n>>>\n>>>The ideal photomultiplier tube is a detector that basically\n>>>absorbs (photo-electric effect) one photon and internally\n>>>converts/produces** due to an electron cascade/amplifier\n>>>effect, one measurable event.\n>>>\n>>>** Lawrence and Beams showed in 1928 that photo-electrons are\n>>>sometimes emitted less than 3 *10^(-9) sec after initial illumination.\n>>\n>>Could you please explain how this relates to my statement?\n>\n>\n> I took the liberty to understand your "particular quantum system"\n> as a photon producing system. The photomultiplier tube (PMT)\n> is also a quantum device; the difference being that the output\n> energy is measurable in electron-volts. The PMT is in theory,\n> and experimentally a well understood device and as such follows\n> this (circular) suggestion closely:\n>\n> "Theory is meant to be substantiated by appeal to the\n> observable facts, while at the same time the observable\n> facts can only be justified by appeal to theory."\n\nCircular statements of this nature have a noncircular formulation\nthat makes them amenable to analysis: To find a selfconsistent\ndescription in which both sides of the statement are faithfully\nrepresented.\n\n\n>>Even a photomultiplier tube will trigger an erratic response\n>>following a Poisson process when fed with a low intensity coherent\n>>laser beam.\n>\n> Precisely, the PMT is a quantum (detector) system and due to its very\n> high gain 10^(6) or more, is also very sensitive to its environment.\n>\n> Experiments have shown that one can eliminate a lot of random PMT\n> counts [...]\n> After a proper setup, the PMT (a quantum system), will measure an\n> objective record of individual results that can be analyzed\n> statistically and quoted in a physics journal.\n\nYes. I agree fully to that.\n\nTo repeat my quest,\nI am looking for an explanation why this particular detector coupled\nto a particular quantum system produces the observed erratic but\nobjective record of individual results.\n\nTradition shows how to predict the properties of the resulting\ndistribution, but not how individual macroscopic results (mean\nvalues of certain microscpoic current operators) are produced.\nWe observe _bursts_ of <j(x,t)> at certain times t but not at others.\nWhy?\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>joe@\alpha.to wrote:
> "Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in
> message news:42A05FE1.2090109@univie.ac.at...
>
>>Joe Rongen wrote:
>>
>>>>Arnold Neumaier wrote:
>>>>
>>>>I am looking for an explanation why a particular detector coupled
>>>>>to a particular quantum system produces the observed erratic but
>>>>>objective record of individual results that can be analyzed
>>>>>statistically and quoted in a physics journal.
>>>
>>>Some detector systems employ photomultiplier tube(s).
>>>
>>>The ideal photomultiplier tube is a detector that basically
>>>absorbs (photo-electric effect) one photon and internally
>>>converts/produces** due to an electron cascade/amplifier
>>>effect, one measurable event.
>>>
>>>** Lawrence and Beams showed in 1928 that photo-electrons are
>>>sometimes emitted less than 3 *10^(-9) sec after initial illumination.
>>
>>Could you please explain how this relates to my statement?
>
>
> I took the liberty to understand your "particular quantum system"
> as a photon producing system. The photomultiplier tube (PMT)
> is also a quantum device; the difference being that the output
> energy is measurable in electron-volts. The PMT is in theory,
> and experimentally a well understood device and as such follows
> this (circular) suggestion closely:
>
> "Theory is meant to be substantiated by appeal to the
> observable facts, while at the same time the observable
> facts can only be justified by appeal to theory."
Circular statements of this nature have a noncircular formulation
that makes them amenable to analysis: To find a selfconsistent
description in which both sides of the statement are faithfully
represented.
>>Even a photomultiplier tube will trigger an erratic response
>>following a Poisson process when fed with a low intensity coherent
>>laser beam.
>
> Precisely, the PMT is a quantum (detector) system and due to its very
> high gain 10^(6) or more, is also very sensitive to its environment.
>
> Experiments have shown that one can eliminate a lot of random PMT
> counts [...]
> After a proper setup, the PMT (a quantum system), will measure an
> objective record of individual results that can be analyzed
> statistically and quoted in a physics journal.
Yes. I agree fully to that.
To repeat my quest,
I am looking for an explanation why this particular detector coupled
to a particular quantum system produces the observed erratic but
objective record of individual results.
Tradition shows how to predict the properties of the resulting
distribution, but not how individual macroscopic results (mean
values of certain microscpoic current operators) are produced.
We observe _bursts_ of <j(x,t)> at certain times t but not at others.
Why?
Arnold Neumaier
Arnold Neumaier
Jun8-05, 01:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Daryl McCullough wrote:\n\n> Aaron Bergman says...\n>\n>>I\'m a frequentist. In statistical mechanics, you assume that you fully\n>>sample the phase space and the probabilities fall out.\n>\n> Do they? It seems to me that the usual development of classical\n> statistical mechanics depends crucially on the assumption that\n> all microstates that are consistent with a given macrostate are\n> equally likely. That allows us to use density of states as a\n> stand-in for probability density. But why should all microstates\n> be equally likely?\n\nThey aren\'t. They are only in a microcanonical ensemble which is\nnearly impossilbe to prepare.\n\nIn Bayesian terminology, the microcanonical ensemble simply serves\nas noninformative prior...\n\nBut of course Bayesian reasoning doesn\'t make sense here; we cannot\nhope to predict well with the microcanonical ensemble, independent of\nhow much or how little we know.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Daryl McCullough wrote:
> Aaron Bergman says...
>
>>I'm a frequentist. In statistical mechanics, you assume that you fully
>>sample the phase space and the probabilities fall out.
>
> Do they? It seems to me that the usual development of classical
> statistical mechanics depends crucially on the assumption that
> all microstates that are consistent with a given macrostate are
> equally likely. That allows us to use density of states as a
> stand-in for probability density. But why should all microstates
> be equally likely?
They aren't. They are only in a microcanonical ensemble which is
nearly impossilbe to prepare.
In Bayesian terminology, the microcanonical ensemble simply serves
as noninformative prior...
But of course Bayesian reasoning doesn't make sense here; we cannot
hope to predict well with the microcanonical ensemble, independent of
how much or how little we know.
Arnold Neumaier
Arnold Neumaier
Jun8-05, 10:50 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n>>>However, the sentence "the closed system cannot\n>>>be observed and hence cannot produce outcomes" is already an\n>>>interpretation of the measurement formalism [of QM axiomatic theory].\n>>\n>>No. How could a closed system be possibly observed from the outside???\n>>If the observer sits in a different system then, because the first\n>>system is closed, it cannot have any interactions. Thus the observer\'s\n>>dynamics will be completely unaffected by the system. Thus the observer\n>>will not be able to collect any information about the system.\n>\n> We are at the heart of the problem between the formalism of the theory\n> and the interpretation.\n> Please note that the measurement part of the theory does not require\n> any interaction.\n\nThe formalism itself has nothing to do with the real world, unless\nit is given _some_ interpretation.\n\nReal measurement requires real interactions.\nThe theory models these by assuming collapse under measurement,\nno matter whether in the eyes of the observer or whether objective.\nAt least this is the traditional way of viewing the formalism.\n\n\n> The observer outside or inside the system has no\n> meaning in the QM formalism (only in the interpretations).\n\nThe QM formalism is about closed systems in which no measurements\nhappen by definition of what it means to be closed. There are no\nmeasurements in the formalism.\n\nIf measurements are discussed within the formalism (as\nmeasurement theory), they have to be _defined_, and they _are_\ndefined via an interaction. But the measurements as happening within\nthe formalism alone cannot be related to actual measurements\nwithout an interpretation of what the formalism means in the real\nworld. Without an interpretation no relation between formalism and\nreality.\n\n\n> Moreover, an opened system is a closed system when we consider the rest\n> of the world (formal).\n\nBut then one needs an interpretation of what it means for one subsystem\nof the closed world to measure another subsystem, and for lack of a\nprobabilistic interpretation in our unique world this hasn\'t been given\nin _any_ of the current interpretations.\n\n\n>>Thus the observer cannot claim convincingly to have observed the system.\n>>\n> I hope you understand better why this sentence has no meaning in the QM\n> theory formalism (in my opinion : ).\n\nI understand better why it has no meaning for you.\nBut I don\'t accept your arguments as being valid for the QM formalism\n(which includes the Born rule, which makes sense only together with\nthe collapse).\n\n\n>>Observability by an external observer therefore demands openness of the\n>>system. At least under conventional assumptions about what the terms\n>>closed, interaction, observation mean.\n>>\n> H= sum_i Hi => unitary evolution, including the interactions of the\n> observer object.\n> + collapse postulate: property of an instance of a system governed by H\n> (including the observer object).\n> If I say, I have a system [including the observer object] with a given\n> property => I have the associated collapse. There is no "observer"\n> in the sentence "I have a system [including the observer object] with\n> a given property", just the logic affirmation of this property.\n\nI don\'t understand you. If there are interactions we have\nH= sum_i Hi + sum_ij V_ij.\nAnd I don\'t understand what a \'property\' is; the traditional QM\nformalism has no place for it. If you want to stay on the formal\nside you are only allowed to talk about operators, states, Hilbert\nspaces and other on the formal level well-defined concepts.\n\n\n>>For the universe as a whole, the situation is different since it is\n>>observed by an observer _within_ the system. While this is not\n>>analyzed in the trasditional setting, it can be analyzed within the\n>>consistent experiment interpretation.\n>>\n> I am still working on your post reply dealing with the "consistent\n> experiment interpretation". I hope soon I will be able to give you\n> some feedbacks.\n\nI am looking forward to this discussion.\n\n\n>>>>This even holds in the traditional Copenhagen interpretation.\n>>>>The view is that the system is closed most of the time and then\n>>>>evolves unitarity. At certain very short moments, it is assumed\n>>>>to be in contact with a detector for measurement - then the\n>>>>system is open and evolves nonunitarily, by collapse.\n>>>>\n>>>This is interpretation,\n>>\n>>Of course, I didn\'t claim otherwise.\n>>It is the Copenhagen _interpretation_.\n>>\n> Well, as I have said before, I will not question the interpretation as\n> long as it does not change the QM theory formalism.\n\nI do not change the formal side of quantum mechanics.\nBut it is meaningless without an interpretation in terms of the\nreal world.\n\n\n> In this\n> interpretation context, I do not know what you intend by collapse (you\n> seem to have studied deeper the CI than I : )). All what I know is the\n> logical meaning of the label "collapse" in the QM formalism and\n> definitively it does not say it is a non unitary evolution of the\n> system. Only the interpretation of the words "before" and\n> "after" may lead to such a conclusion (hence an interpretation).\n\nIt would be good if you could give a concise formal definition of\nwhat you consider to be _the_ QM formalism. One can state everything\nin a few axioms, but it seems that your set of axioms is different from\nwhat I hold to be the common view.\n\n\n>>>Note, in the QM formalism, there is no classical/quantum boundary (only\n>>>in the interpretations of QM). Just postulates that may be applied,\n>>>hopefully (for the consistence of the theory) on closed systems as well\n>>>as opened ones.\n>>\n>>But there are different postulates for\n>>\n>>- closed systems (unitarity),\n>>- systems open just at some instant (collpse), and\n>>- continuously open systems (Lindblad type dissipative dynamics,\n>>or corresponding stochastic quantum processes).\n>>\n> I hope that no!\n\nMy statement is based on assessing the heap of papers on QM that\nI read among the flood of papers published in the last 10 years,\nsay. In particular, most realistic experimental analysis requires\nthe open systems view in which energy is _not_ conserved but\ndissipates into unmodelled degrees of freedom. These systems are\nnot unitary, but are as quantum mechanical as one could wish.\n\nVon Neumann\'s 1932 postulates are no longer believed to be valid\nfor small systems since it is well recognized that these are\nnecessarily open.\n\nThese postulates are only believed to govern a very large system\n(small system plus detector plus environment), from which a\nstatistical mechanics type analysis (heat bath etc.) produces\nthe reduced open description.\n\nAt least that\'s the conclusion one gets when looking at how\npeople who analyze nontrivial experiments actually use quantum\nmechanics. (There is of course lip service to tradition, though,\nbut one should measure people by what they do rather than what\nthey say.)\n\n\n> You have the unitary evolution and the measurement postulates: An Open\n> system is always a part of a closed system (otherwise, the unitary\n> evolution postulate is not true => problem with the consistence of the\n> QM theory). The collapse postulate always applies to the whole system\n> description.\n\nThe closed system is always the whole universe. Since this cannot\nbe observed from the outside, von Neumann\'s measurement theory does\nnot apply there. It is never in the factorized state assumed to\nprevail before the beginning of a measurement. Interactions cannot\nbe switched on and off to restrict the measurement to a short duration.\nThus assuming the state of the universe to collapse has no basis in\neither theory or empirical observation.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
>>>However, the sentence "the closed system cannot
>>>be observed and hence cannot produce outcomes" is already an
>>>interpretation of the measurement formalism [of QM axiomatic theory].
>>
>>No. How could a closed system be possibly observed from the outside???
>>If the observer sits in a different system then, because the first
>>system is closed, it cannot have any interactions. Thus the observer's
>>dynamics will be completely unaffected by the system. Thus the observer
>>will not be able to collect any information about the system.
>
> We are at the heart of the problem between the formalism of the theory
> and the interpretation.
> Please note that the measurement part of the theory does not require
> any interaction.
The formalism itself has nothing to do with the real world, unless
it is given _some_ interpretation.
Real measurement requires real interactions.
The theory models these by assuming collapse under measurement,
no matter whether in the eyes of the observer or whether objective.
At least this is the traditional way of viewing the formalism.
> The observer outside or inside the system has no
> meaning in the QM formalism (only in the interpretations).
The QM formalism is about closed systems in which no measurements
happen by definition of what it means to be closed. There are no
measurements in the formalism.
If measurements are discussed within the formalism (as
measurement theory), they have to be _defined_, and they _are_
defined via an interaction. But the measurements as happening within
the formalism alone cannot be related to actual measurements
without an interpretation of what the formalism means in the real
world. Without an interpretation no relation between formalism and
reality.
> Moreover, an opened system is a closed system when we consider the rest
> of the world (formal).
But then one needs an interpretation of what it means for one subsystem
of the closed world to measure another subsystem, and for lack of a
probabilistic interpretation in our unique world this hasn't been given
in _any_ of the current interpretations.
>>Thus the observer cannot claim convincingly to have observed the system.
>>
> I hope you understand better why this sentence has no meaning in the QM
> theory formalism (in my opinion : ).
I understand better why it has no meaning for you.
But I don't accept your arguments as being valid for the QM formalism
(which includes the Born rule, which makes sense only together with
the collapse).
>>Observability by an external observer therefore demands openness of the
>>system. At least under conventional assumptions about what the terms
>>closed, interaction, observation mean.
>>
> H= sum_i Hi => unitary evolution, including the interactions of the
> observer object.
> + collapse postulate: property of an instance of a system governed by H
> (including the observer object).
> If I say, I have a system [including the observer object] with a given
> property => I have the associated collapse. There is no "observer"
> in the sentence "I have a system [including the observer object] with
> a given property", just the logic affirmation of this property.
I don't understand you. If there are interactions we have
H= sum_i Hi + sum_ij V_{ij}.
And I don't understand what a 'property' is; the traditional QM
formalism has no place for it. If you want to stay on the formal
side you are only allowed to talk about operators, states, Hilbert
spaces and other on the formal level well-defined concepts.
>>For the universe as a whole, the situation is different since it is
>>observed by an observer _within_ the system. While this is not
>>analyzed in the trasditional setting, it can be analyzed within the
>>consistent experiment interpretation.
>>
> I am still working on your post reply dealing with the "consistent
> experiment interpretation". I hope soon I will be able to give you
> some feedbacks.
I am looking forward to this discussion.
>>>>This even holds in the traditional Copenhagen interpretation.
>>>>The view is that the system is closed most of the time and then
>>>>evolves unitarity. At certain very short moments, it is assumed
>>>>to be in contact with a detector for measurement - then the
>>>>system is open and evolves nonunitarily, by collapse.
>>>>
>>>This is interpretation,
>>
>>Of course, I didn't claim otherwise.
>>It is the Copenhagen _interpretation_.
>>
> Well, as I have said before, I will not question the interpretation as
> long as it does not change the QM theory formalism.
I do not change the formal side of quantum mechanics.
But it is meaningless without an interpretation in terms of the
real world.
> In this
> interpretation context, I do not know what you intend by collapse (you
> seem to have studied deeper the CI than I : )). All what I know is the
> logical meaning of the label "collapse" in the QM formalism and
> definitively it does not say it is a non unitary evolution of the
> system. Only the interpretation of the words "before" and
> "after" may lead to such a conclusion (hence an interpretation).
It would be good if you could give a concise formal definition of
what you consider to be _the_ QM formalism. One can state everything
in a few axioms, but it seems that your set of axioms is different from
what I hold to be the common view.
>>>Note, in the QM formalism, there is no classical/quantum boundary (only
>>>in the interpretations of QM). Just postulates that may be applied,
>>>hopefully (for the consistence of the theory) on closed systems as well
>>>as opened ones.
>>
>>But there are different postulates for
>>
>>- closed systems (unitarity),
>>- systems open just at some instant (collpse), and
>>- continuously open systems (Lindblad type dissipative dynamics,
>>or corresponding stochastic quantum processes).
>>
> I hope that no!
My statement is based on assessing the heap of papers on QM that
I read among the flood of papers published in the last 10 years,
say. In particular, most realistic experimental analysis requires
the open systems view in which energy is _not_ conserved but
dissipates into unmodelled degrees of freedom. These systems are
not unitary, but are as quantum mechanical as one could wish.
Von Neumann's 1932 postulates are no longer believed to be valid
for small systems since it is well recognized that these are
necessarily open.
These postulates are only believed to govern a very large system
(small system plus detector plus environment), from which a
statistical mechanics type analysis (heat bath etc.) produces
the reduced open description.
At least that's the conclusion one gets when looking at how
people who analyze nontrivial experiments actually use quantum
mechanics. (There is of course lip service to tradition, though,
but one should measure people by what they do rather than what
they say.)
> You have the unitary evolution and the measurement postulates: An Open
> system is always a part of a closed system (otherwise, the unitary
> evolution postulate is not true => problem with the consistence of the
> QM theory). The collapse postulate always applies to the whole system
> description.
The closed system is always the whole universe. Since this cannot
be observed from the outside, von Neumann's measurement theory does
not apply there. It is never in the factorized state assumed to
prevail before the beginning of a measurement. Interactions cannot
be switched on and off to restrict the measurement to a short duration.
Thus assuming the state of the universe to collapse has no basis in
either theory or empirical observation.
Arnold Neumaier
Seratend
Jun9-05, 06:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Seratend wrote:\n>\n> > Arnold Neumaier wrote:\n> >\n> >>Seratend wrote:\n> >>\n> > The formal measurement (collapse and born rules) are just the\n> > statistical description of experiments:\n> >\n> > a) The collapse postulate describes 2 topics, a property of the system\n> > (Outcome a of a given observable A is true) and the state of the system\n> > if this property is true (stability of the property: the "true\n> > remains true").\n> > b) the born rules: a state and an observable define the probability law\n> > of the outcomes of the observable.\n> >\n> > Therefore, the probability law of the outcomes (the statistics) of an\n> > experiment is completely defined by the couple (|psi>, A). However to\n> > calculate the statistics on experiments (the mapping), we need the\n> > collapse: the formal mapping between the experiment outcomes and the\n> > statistics simply expressed by the collapse property: the outcome\n> > "a" for this experiment trial is true.\n> > Note that in order to recover the probability law in the frequency of\n> > outcomes we must have the independence of identical systems (hence, we\n> > need a "preparation" to select the systems).\n>\n> But this is not satisfied in many experiments analyzed by quantum\n> mechanics. For example, in an ion trap, one has the continuous\n> measurement of a single system, in which the observation at different\n> times can by no means considered to be observations of independent\n> systems.\n>\nWhere is the problem (logically)? (I may miss something). Do you mean\nthe collapse postulate is not satisfied in continuous measurements?\n\nPlease note that when you say a continuous measurement over time of a\nsingle system, you mean a single measurement that spans over time of\none instance of this system (the measurement has to be specified over\ntime and space or the equivalent observables to have a meaning). The\n"continuous measurement" in the QM formalism helps one to\nunderstand the logical meaning of "before" and "after" of the\ncollapse postulate: It is "an acknowledgement" of the property of a\ngiven system, the property may be related to time or independent of\ntime.\n\nFor an example of what I mean, please see "When the unitary evolution\nis derived from the collapse postulate in QM" in\nhttp://www.physicsforums.com/showthread.php?t=72181\n\n>\n> Thus your conceptual framework for interpreting quantum mechanical\n> experiments is too restrictive.\n>\nI do not understand on how it is too restrictive.\nI am using the "chut up and calculate" view.\nWhen we just have a single experiment trial in all the universe, we\njust have the only interesting result: the unique set of results of\nthis experiment. There is no way to make predictions (this is also true\nfor CM). However, if this experiment belongs to the set of experiments\nwhere we know, with P~100%, the ion is trapped, we have a direct\nprediction of what will occur with such a single experiment (the\nresults where P~100%).\n\nIn addition, it raises an interesting question when we consider the\ncontinuous measurement (we suppose all the interactions may be modelled\ninto interaction Hamiltonians, including the interactions of the\nmeasurement apparatus):\nIs it the state of the system that changes upon measurement due to the\ncollapse ("action" of the collapse) or is it the measured values\nthat change continuously upon time ("acknowledgement" of the\ncollapse)?\n\n>\n> > A physical theory is mainly a choice of description (formally, we are\n> > free to choose what we want)\n>\n> ..but only if we don\'t care about the quality of our predictions.\n> If we want to have good predictions, we must choose what quantum\n> mechanics tells us to choose.\n>\nEvery physical theory is a description choice. Good predictions is\nsomewhat a matter of taste (i.e. a practical choice).\nFor example, take My god determinist theory: the collection of all the\n"measurable" properties of the universe we may ever know. I call it\ndeterminist because, labelling all the properties (and assuming the\ncollection of labels and properties is a ZF set: the only restiction),\nit defines an implicit function. Does it make good predictions?\n>\n> > Statistical description is a very pragmatic description choice (and not\n> > a mysterious physical process). With QM or with a basic coin flipping\n> > experiment we always do the same thing: we label the experimental\n> > trials and compute the frequencies of the outcomes:\n>\n> What is a true outcome in a world described by quantum mechanics/\n>\nI have outcomes, hence they are true otherwise I cannot say (logical\nmeaning) I have outcomes (I assume you understand that QM does not\nexplain the outcomes, just their probability, i.e. their occurrence),\nthis is a circular reasoning. In QM theory, the outcomes are\nexternally given by the experimental realisation (when "we"\nassociate/map the experimental realisations to the formal outcomes of\nthe collapse postulate). When we have thought experiments, the outcomes\nare externally given (by saying the "outcome a of A" is true): they\nare the properties of the considered system.\n\nNote we have an analogue problem in classical mechanics. How can we say\nthe proposition "a particle at position q at time t" is true? The\ntheory does not explain that, it uses it as QM does.\n\nHowever, the main difference between classical mechanics and QM comes\nfrom the preferred basis of the outcomes. In CM we assume it is the\nposition while in QM it may be any basis (position, energy momentum).\n>\n> > 1) We have an implicitly defined random variable, an abstract function\n> > f, which expresses the experiment logic results: for the trial labelled\n> > e, we associate the result a (logic true): "if e then result a".\n> > The function/random variable is defined by the set {(e, a), for all e}\n> > is equivalent to a=f(e) (i.e. the proposition "the result of the\n> > experiment trial label e is a" is true).\n>\n> Even classical statistics is surrounded by a foundational mystery,\n> causing as heated debates as in QM.\n>\n> Your description is by no means universally accepted. The frequentist\n> approach you favor here has severe problems in that the predicted\n> probabilities and the observed frequencies only match approximately.\n\nHowever, we only need this to describe what we ever see. This is the\nrestriction choice of the frequentist approach.\nIt is not a question of acceptation, it is a question of the\nmathematical objects we choose (not an obligation) to describe the\n"reality". The theorems are always true, we choose to apply them or\nnot.\n\nIn other words, I may choose to view the "reality" by different\nmathematical concepts, this does not change the reality, just the\ndescription of the reality. The only required property is the\nconservation of the logic (as I do not know what to take to replace the\nusual logic).\n\n> One can encounter long strings of heads although the probability\n> of a head is 1/2.\n\nAnd one can choose the set of these trials and define the associated\nprobability law assuming the independence of the trials. She/He will\nobtain a different probability law (i.e. p(heads)=/=1/2).\nWhere is the problem, once we select these set of trials with this new\nprobability law? (if you prefer the context of the experiment). This is\nthe logic and the description choices.\n\nQuestion, why does the computed frequency of head/tails of a coin\nflipping is 50/50?\nIs it due to a mysterious ontic property, or is it due to the coin\nflipping experiment and its description choice (by saying p= n(a)/N)?\n\nI am just trying to promote the epistemic view and the relativity of\ndescriptions.\n>\n> You can read about my view of probability theory in my theoretical\n> physics FAQ at\n> http://www.mat.univie.ac.at/~neum/physics-faq.txt\n>\nI am surprised because, we seem to say almost the same (math results)\n(except may be for your comments on Bayesian probability).\n(Note: I have implicitly selected my preferred interpretation of your\nwords : )).\n\nHowever, I have a suggestion: you should explicitly say that the sample\nspace of the sequence of trials of a random variable of more than one\nvalue (i.e. P=/=100%) is uncountable. This property explains most of\nthe problems with probabilities and the "uniqueness"\n(reproducibility) of each infinite sequence.\n\n> What I want as a basis of physics is a mathematically defined\n> model of the world in which one can give unambiguous descriptions\n> of all that matters in physics - physical systems, detectors, observers,\n> individual observations, statistics about these observations,\n> error analysis, etc. in such a way that it mirrors reality.\n\nI understand, however, there is more than one model. And, I think you\nshould also accept conceptually that the only unambiguous model should\nbe what I call the "god determinist theory" that is not very\ninteresting (the absolute knowledge) and not practical.\n> Just as in matheamtical logic, one models the whole logical process\n> in a concise mathematical framework.\n>\nThis is a sort of compression process of the "god determinist\ntheory". Therefore, I hope you should accept loss of information\n(description) in this process.\n\nI think the QM theory is a concise one (may be too). The main problem\nseems to be the preferred basis prediction. However, If we look at\ngeneral relativity we encounter an almost analogue problem: the\npreferred frame to describe the events.\n>\n> >>Although not very clearly separated in many discussions,\n> >>these two processes happen never simultaneously but context\n> >>dependent, and are of course only approximations to more\n> >>realistic measurement situations.\n> >>\n> >>For example, in a Stern-Gerlach experiment, the system (silver atom)\n> >>moves from the source along the magnet towards the screen with very\n> >>good accuracy in a unitary (and indeed reversible) way. But a few\n> >>split moments before it hits the screen it feels its interactions,\n> >>and describing it as a closed system becomes hopelessly inaccurate.\n> >>Instead, since the interaction time is very short, it can be\n> >>described very accurately by an instantaneous collapse.\n> >>\n> > Why do you say it becomes hopelessly inaccurate?\n>\n> Because the closed system in this setting contains >10^20 degrees of\n> freedom, and we cannot model such systems accurately. We need the\n> thermodynamic approximation, and with it an unavoidable inaccuracy\n> in the response to the microscopic particle state.\n>\nYou can describe the stern-gerlach experiment with an excellent\napproximation as a closed quantum system. The thermodynamic\napproximation will just define macroscopic variables compatible with\nsuch a closed description (it will show what a simple quantum toy model\nshows). The value of the macroscopic variable is a property and hence a\ncollapse for the considered system.\nOne remaining question is to know if the thermodynamic approximation is\nable to predict the preferred basis.\n\n>\n> > And How can you really\n> > apply a collapse to a non closed system? In this case, don\'t you\n> > think the collapse result (the outcome) should be independent of the\n> > partial system description versus the whole system (including the\n> > universe if necessary)?\n>\n> Look at the corresponding classical situation. A classical particle\n> encounters a classical screen (say, a thin foil through which\n> the particle will most likely escape) involving a huge number\n> of classical particles bound by (and interacting with the\n> incident particle) by empirical forces. It ends up in some state\n> that is determined only probablilistically, once you ignore the\n> detailed structure of the screen. But it ends up in a _definite_\n> state.\n\nIf you say it ends up in a _definite_ state you are implicitly\n_defining_ a true property for this system instance and hence a whole\ncollapse! Do you see what I mean? You have no choice, this is simple\nlogic, you can avoid it, otherwise you cannot assume the particle ends\nup in a _definite_ state. This is the formalism of QM.\n\nIf you prefer, we can use the Hilbert space formulation of classical\nstatistical mechanics, in order to view on the collapse is an\nacknowledgement of the property and not a physical evolution that is\ndescribed by the unitary evolution (of the whole interactions).\n\nQM formalism just says that there exist many other properties that may\nbe true (the different basis) respectively to the Classical mechanics\n(|q,p> seems the preferred basis: the superselection rule of CM).\n\n> To describe it, however, without reference to the state of\n> the screen, necessitates a probabilistic description and a collapse.\n>\nBut you have a property for the screen, otherwise you cannot apply the\ncollapse ("the don\'t care property or if you prefer, the Identity\nprojector).\n\nNote: for me P=100% is a probabilistic description (it means 100% of\nthe systems have the considered property).\n\n> The quantum system is - in the consistent experiment interpretation -\n> completely analogous, except that the dynamics differs in detail\n> significantly from the classical dynamics.\n>\nI am still working on this (I need to understand the logic).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Seratend wrote:
>
> > Arnold Neumaier wrote:
> >
> >>Seratend wrote:
> >>
> > The formal measurement (collapse and born rules) are just the
> > statistical description of experiments:
> >
> > a) The collapse postulate describes 2 topics, a property of the system
> > (Outcome a of a given observable A is true) and the state of the system
> > if this property is true (stability of the property: the "true
> > remains true").
> > b) the born rules: a state and an observable define the probability law
> > of the outcomes of the observable.
> >
> > Therefore, the probability law of the outcomes (the statistics) of an
> > experiment is completely defined by the couple (|\psi>, A). However to
> > calculate the statistics on experiments (the mapping), we need the
> > collapse: the formal mapping between the experiment outcomes and the
> > statistics simply expressed by the collapse property: the outcome
> > "a" for this experiment trial is true.
> > Note that in order to recover the probability law in the frequency of
> > outcomes we must have the independence of identical systems (hence, we
> > need a "preparation" to select the systems).
>
> But this is not satisfied in many experiments analyzed by quantum
> mechanics. For example, in an ion trap, one has the continuous
> measurement of a single system, in which the observation at different
> times can by no means considered to be observations of independent
> systems.
>
Where is the problem (logically)? (I may miss something). Do you mean
the collapse postulate is not satisfied in continuous measurements?
Please note that when you say a continuous measurement over time of a
single system, you mean a single measurement that spans over time of
one instance of this system (the measurement has to be specified over
time and space or the equivalent observables to have a meaning). The
"continuous measurement" in the QM formalism helps one to
understand the logical meaning of "before" and "after" of the
collapse postulate: It is "an acknowledgement" of the property of a
given system, the property may be related to time or independent of
time.
For an example of what I mean, please see "When the unitary evolution
is derived from the collapse postulate in QM" in
http://www.physicsforums.com/showthread.php?t=72181
>
> Thus your conceptual framework for interpreting quantum mechanical
> experiments is too restrictive.
>
I do not understand on how it is too restrictive.
I am using the "chut up and calculate" view.
When we just have a single experiment trial in all the universe, we
just have the only interesting result: the unique set of results of
this experiment. There is no way to make predictions (this is also true
for CM). However, if this experiment belongs to the set of experiments
where we know, with P~100%, the ion is trapped, we have a direct
prediction of what will occur with such a single experiment (the
results where P~100%).
In addition, it raises an interesting question when we consider the
continuous measurement (we suppose all the interactions may be modelled
into interaction Hamiltonians, including the interactions of the
measurement apparatus):
Is it the state of the system that changes upon measurement due to the
collapse ("action" of the collapse) or is it the measured values
that change continuously upon time ("acknowledgement" of the
collapse)?
>
> > A physical theory is mainly a choice of description (formally, we are
> > free to choose what we want)
>
> ..but only if we don't care about the quality of our predictions.
> If we want to have good predictions, we must choose what quantum
> mechanics tells us to choose.
>
Every physical theory is a description choice. Good predictions is
somewhat a matter of taste (i.e. a practical choice).
For example, take My god determinist theory: the collection of all the
"measurable" properties of the universe we may ever know. I call it
determinist because, labelling all the properties (and assuming the
collection of labels and properties is a ZF set: the only restiction),
it defines an implicit function. Does it make good predictions?
>
> > Statistical description is a very pragmatic description choice (and not
> > a mysterious physical process). With QM or with a basic coin flipping
> > experiment we always do the same thing: we label the experimental
> > trials and compute the frequencies of the outcomes:
>
> What is a true outcome in a world described by quantum mechanics/
>
I have outcomes, hence they are true otherwise I cannot say (logical
meaning) I have outcomes (I assume you understand that QM does not
explain the outcomes, just their probability, i.e. their occurrence),
this is a circular reasoning. In QM theory, the outcomes are
externally given by the experimental realisation (when "we"
associate/map the experimental realisations to the formal outcomes of
the collapse postulate). When we have thought experiments, the outcomes
are externally given (by saying the "outcome a of A" is true): they
are the properties of the considered system.
Note we have an analogue problem in classical mechanics. How can we say
the proposition "a particle at position q at time t" is true? The
theory does not explain that, it uses it as QM does.
However, the main difference between classical mechanics and QM comes
from the preferred basis of the outcomes. In CM we assume it is the
position while in QM it may be any basis (position, energy momentum).
>
> > 1) We have an implicitly defined random variable, an abstract function
> > f, which expresses the experiment logic results: for the trial labelled
> > e, we associate the result a (logic true): "if e then result a".
> > The function/random variable is defined by the set {(e, a), for all e}
> > is equivalent to a=f(e) (i.e. the proposition "the result of the
> > experiment trial label e is a" is true).
>
> Even classical statistics is surrounded by a foundational mystery,
> causing as heated debates as in QM.
>
> Your description is by no means universally accepted. The frequentist
> approach you favor here has severe problems in that the predicted
> probabilities and the observed frequencies only match approximately.
However, we only need this to describe what we ever see. This is the
restriction choice of the frequentist approach.
It is not a question of acceptation, it is a question of the
mathematical objects we choose (not an obligation) to describe the
"reality". The theorems are always true, we choose to apply them or
not.
In other words, I may choose to view the "reality" by different
mathematical concepts, this does not change the reality, just the
description of the reality. The only required property is the
conservation of the logic (as I do not know what to take to replace the
usual logic).
> One can encounter long strings of heads although the probability
> of a head is 1/2.
And one can choose the set of these trials and define the associated
probability law assuming the independence of the trials. She/He will
obtain a different probability law (i.e. p(heads)=/=1/2).
Where is the problem, once we select these set of trials with this new
probability law? (if you prefer the context of the experiment). This is
the logic and the description choices.
Question, why does the computed frequency of head/tails of a coin
flipping is 50/50?
Is it due to a mysterious ontic property, or is it due to the coin
flipping experiment and its description choice (by saying p= n(a)/N)?I am just trying to promote the epistemic view and the relativity of
descriptions.
>
> You can read about my view of probability theory in my theoretical
> physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>
I am surprised because, we seem to say almost the same (math results)
(except may be for your comments on Bayesian probability).
(Note: I have implicitly selected my preferred interpretation of your
words : )).
However, I have a suggestion: you should explicitly say that the sample
space of the sequence of trials of a random variable of more than one
value (i.e. P=/=100%) is uncountable. This property explains most of
the problems with probabilities and the "uniqueness"
(reproducibility) of each infinite sequence.
> What I want as a basis of physics is a mathematically defined
> model of the world in which one can give unambiguous descriptions
> of all that matters in physics - physical systems, detectors, observers,
> individual observations, statistics about these observations,
> error analysis, etc. in such a way that it mirrors reality.
I understand, however, there is more than one model. And, I think you
should also accept conceptually that the only unambiguous model should
be what I call the "god determinist theory" that is not very
interesting (the absolute knowledge) and not practical.
> Just as in matheamtical logic, one models the whole logical process
> in a concise mathematical framework.
>
This is a sort of compression process of the "god determinist
theory". Therefore, I hope you should accept loss of information
(description) in this process.
I think the QM theory is a concise one (may be too). The main problem
seems to be the preferred basis prediction. However, If we look at
general relativity we encounter an almost analogue problem: the
preferred frame to describe the events.
>
> >>Although not very clearly separated in many discussions,
> >>these two processes happen never simultaneously but context
> >>dependent, and are of course only approximations to more
> >>realistic measurement situations.
> >>
> >>For example, in a Stern-Gerlach experiment, the system (silver atom)
> >>moves from the source along the magnet towards the screen with very
> >>good accuracy in a unitary (and indeed reversible) way. But a few
> >>split moments before it hits the screen it feels its interactions,
> >>and describing it as a closed system becomes hopelessly inaccurate.
> >>Instead, since the interaction time is very short, it can be
> >>described very accurately by an instantaneous collapse.
> >>
> > Why do you say it becomes hopelessly inaccurate?
>
> Because the closed system in this setting contains >10^20 degrees of
> freedom, and we cannot model such systems accurately. We need the
> thermodynamic approximation, and with it an unavoidable inaccuracy
> in the response to the microscopic particle state.
>
You can describe the stern-gerlach experiment with an excellent
approximation as a closed quantum system. The thermodynamic
approximation will just define macroscopic variables compatible with
such a closed description (it will show what a simple quantum toy model
shows). The value of the macroscopic variable is a property and hence a
collapse for the considered system.
One remaining question is to know if the thermodynamic approximation is
able to predict the preferred basis.
>
> > And How can you really
> > apply a collapse to a non closed system? In this case, don't you
> > think the collapse result (the outcome) should be independent of the
> > partial system description versus the whole system (including the
> > universe if necessary)?
>
> Look at the corresponding classical situation. A classical particle
> encounters a classical screen (say, a thin foil through which
> the particle will most likely escape) involving a huge number
> of classical particles bound by (and interacting with the
> incident particle) by empirical forces. It ends up in some state
> that is determined only probablilistically, once you ignore the
> detailed structure of the screen. But it ends up in a _definite_
> state.
If you say it ends up in a _definite_ state you are implicitly
_defining_ a true property for this system instance and hence a whole
collapse! Do you see what I mean? You have no choice, this is simple
logic, you can avoid it, otherwise you cannot assume the particle ends
up in a _definite_ state. This is the formalism of QM.
If you prefer, we can use the Hilbert space formulation of classical
statistical mechanics, in order to view on the collapse is an
acknowledgement of the property and not a physical evolution that is
described by the unitary evolution (of the whole interactions).
QM formalism just says that there exist many other properties that may
be true (the different basis) respectively to the Classical mechanics
(|q,p> seems the preferred basis: the superselection rule of CM).
> To describe it, however, without reference to the state of
> the screen, necessitates a probabilistic description and a collapse.
>
But you have a property for the screen, otherwise you cannot apply the
collapse ("the don't care property or if you prefer, the Identity
projector).
Note: for me P=100% is a probabilistic description (it means 100% of
the systems have the considered property).
> The quantum system is - in the consistent experiment interpretation -
> completely analogous, except that the dynamics differs in detail
> significantly from the classical dynamics.
>
I am still working on this (I need to understand the logic).
Seratend.
Seratend
Jun9-05, 06:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Seratend wrote:\n>\n> > Arnold Neumaier wrote:\n> >\n> >>Seratend wrote:\n> >>\n> > We are at the heart of the problem between the formalism of the theory\n> > and the interpretation.\n> > Please note that the measurement part of the theory does not require\n> > any interaction.\n>\n> The formalism itself has nothing to do with the real world, unless\n> it is given _some_ interpretation.\n>\n> Real measurement requires real interactions.\n>\nQM formalism does not say what is a real measurement. QM formalism\nspeaks about the collapse postulate and the born rules and the unitary\nevolution. That\'s all.\n\nI need quantum interactions to describe the whole unitary evolution of\nthe system and the measurement apparatus object. Unitary evolutions\nintroduce statistical correlations between the system and the\nmeasurement apparatus object (including the environment if necessary to\ndescribe the evolution).\nWe use these statistical correlations on the statistics of formal\nmeasurement results of this whole system (including the "measurement\napparatus" that has not to be confused with the formal measurement\nresult). That\'s what the formalism allows one to say (hence the\nrequirement of interactions to correlate the measurement apparatus to\nthe system). All the rest is interpretation. Saying the measurement\napparatus does a formal measurement is interpretation (completely out\nof the scope of the QM formalism). I do not refute the interpretation,\nnor I can\'t as long as it is consistent with the formalism.\n\n> The theory models these by assuming collapse under measurement,\n> no matter whether in the eyes of the observer or whether objective.\n> At least this is the traditional way of viewing the formalism.\n>\nThis is the traditional *interpretation* of the formalism.\nI am just using the logic in the context of the formalism: I do not\nexplain why I observe a result, just that when this result is true, I\nhave a collapse. No interaction is involved in this logical\naffirmation.\nThe formal measurement does not have "hidden" interactions. It is\nnot the measurement apparatus (its interactions).\n\nThe usual interpretation is "interpreted measurement result" =\n{system, apparatus, all the interations with a global unitary evolution\nand the formal measurement result}.\n\nI do not question this label. However, I cannot subscribe to deductions\nmade on the interpretation that are out of scope of the theory\nformalism.\n\n>\n> > The observer outside or inside the system has no\n> > meaning in the QM formalism (only in the interpretations).\n>\n> The QM formalism is about closed systems in which no measurements\n> happen by definition of what it means to be closed. There are no\n> measurements in the formalism.\n>\nSo, Do you claim the measurement postulates of QM formalism are wrong\nin some obscure cases?\nWhere have you seen such a definition in the 6 postulates of QM theory?\n\n(Note: I interpret the word closed system, as a system where the state\nevolution on time follows the usual unitary evolution).\n\nNow, if what you call "measurement" is an interpretation\nmeasurement, I have nothing to say.\n\n> If measurements are discussed within the formalism (as\n> measurement theory), they have to be _defined_, and they _are_\n> defined via an interaction. But the measurements as happening within\n> the formalism alone cannot be related to actual measurements\n> without an interpretation of what the formalism means in the real\n> world. Without an interpretation no relation between formalism and\n> reality.\n>\nThis is the mapping between the outcomes of formal observables and the\noutcomes of the reality. It is the common denominator of all the\ninterpretations (I know). Hence no other interpretation is required.\nWe can say that the QM formalism with the mapping of outcomes is the\nminimum set to describe the reality: what I call the QM formalism.\nHence, any interpretation validates this formalism.\n>\n> > Moreover, an opened system is a closed system when we consider the rest\n> > of the world (formal).\n>\n> But then one needs an interpretation of what it means for one subsystem\n> of the closed world to measure another subsystem, and for lack of a\n> probabilistic interpretation in our unique world this hasn\'t been given\n> in _any_ of the current interpretations.\n>\nI need no interpretation (see above) I just need projectors and formal\nhypotheses (e.g. the independence of systems, the low impact of\nenvironment etc ...) and the final verification on a "real" system.\nI have not a system that measures (in the sense of the postulates)\nanother system (no meaning), just a global measurement and its results.\n>\n> >>Thus the observer cannot claim convincingly to have observed the system.\n> >>\n> > I hope you understand better why this sentence has no meaning in the QM\n> > theory formalism (in my opinion : ).\n>\n> I understand better why it has no meaning for you.\n> But I don\'t accept your arguments as being valid for the QM formalism\n> (which includes the Born rule, which makes sense only together with\n> the collapse).\n>\nSee above. I am just using the logical meaning of the QM formalism +\nthe mapping of the observables outcome to the real outcomes taht make\nsense for any experiment we may think. I assume that whatever\ninterpretation you assume, my logical set is always valid, hence you\nshould logically accept my results.\n\nThe main difference is on the collapse of the word meanings: what you\ncall measurement is not the measurement described in QM formalism.\nHence, you should change this word in order to avoid confusions.\n\n>\n> >>Observability by an external observer therefore demands openness of the\n> >>system. At least under conventional assumptions about what the terms\n> >>closed, interaction, observation mean.\n> >>\n> > H= sum_i Hi => unitary evolution, including the interactions of the\n> > observer object.\n> > + collapse postulate: property of an instance of a system governed by H\n> > (including the observer object).\n> > If I say, I have a system [including the observer object] with a given\n> > property => I have the associated collapse. There is no "observer"\n> > in the sentence "I have a system [including the observer object] with\n> > a given property", just the logic affirmation of this property.\n>\n> I don\'t understand you. If there are interactions we have\n> H= sum_i Hi + sum_ij V_ij.\n\nRe-label the set of labels i,j by a new label i and call V_ij=H_inew =>\nwe recover the previous general relation.\n\n> And I don\'t understand what a \'property\' is; the traditional QM\n> formalism has no place for it. If you want to stay on the formal\n> side you are only allowed to talk about operators, states, Hilbert\n> spaces and other on the formal level well-defined concepts.\n>\nWith the outcomes mapping with the "reality", the property\n"outcome of A is a" has both a signification in a real object as\nwell as in a symbolic one.\n(here property: the mathematical signification. You can use proposition\nif you it is more adequate).\nIn the traditional formalism of QM, when the collapse postulate is\ntrue, the property "outcome of A is a" is true. This is a property\nof the considered system (logic).If this property is false the\ncorresponding collapse postulate is also false => the collapse of a\nsystem is a property of the system (QM formalism).\n\nI am not inventing new words, I am just using mathematical results of\nthe QM formalism.\n\n> >>\n> > Well, as I have said before, I will not question the interpretation as\n> > long as it does not change the QM theory formalism.\n>\n> I do not change the formal side of quantum mechanics.\n> But it is meaningless without an interpretation in terms of the\n> real world.\n>\nI think this post underlines that you may have at least given a\nsignification to the word measurement of the QM formalism that may be\nnot compatible with the formalism (If I have understood what you have\nsaid).\n>\n> It would be good if you could give a concise formal definition of\n> what you consider to be _the_ QM formalism. One can state everything\n> in a few axioms, but it seems that your set of axioms is different from\n> what I hold to be the common view.\n>\nThe 6 usual postulates + the mapping of the observables outcomes\n(defined by the collapse postulate) to the outcomes of real systems.\nThat\'s all.\n>\n> >>>Note, in the QM formalism, there is no classical/quantum boundary (only\n> >>>in the interpretations of QM). Just postulates that may be applied,\n> >>>hopefully (for the consistence of the theory) on closed systems as well\n> >>>as opened ones.\n> >>\n> >>But there are different postulates for\n> >>\n> >>- closed systems (unitarity),\n> >>- systems open just at some instant (collapse), and\n> >>- continuously open systems (Lindblad type dissipative dynamics,\n> >>or corresponding stochastic quantum processes).\n> >>\n> > I hope that no!\n>\n> My statement is based on assessing the heap of papers on QM that\n> I read among the flood of papers published in the last 10 years,\n> say. In particular, most realistic experimental analysis requires\n> the open systems view in which energy is _not_ conserved but\n> dissipates into unmodelled degrees of freedom. These systems are\n> not unitary, but are as quantum mechanical as one could wish.\n>\nI understand that your statements as most of the written papers are\nbased on a mix of interpretation and formalism. I do not question the\neffective results. Each time I read a new paper, I try to remove all\nthe interpretation stuff from the real logic content.\nWhat you say is true: the local state of an opened system does not\nevolve unitary. This is a result of QM formalism. No need to interpret\nthis result. The coupling of theses open systems define a global\nunitary evolution and hence a local non unitary evolution that may have\nsome interesting properties (localisation of the state on a subset of\npossible outcomes in a give basis, etc ...). This again is given by the\nQM formalism.\n\nTherefore, strictly speaking, you can only say that the evolution of a\nlocal state of a given system is non unitary. However, in a more\ncommon language you can say the system does not evolve unitary,\nassuming implicitly you are speaking of the local state.\n\nHowever, strictly speaking, a local outcome of a system is a global\noutcome of the whole system (including the universe) in the QM\nformalism: we always apply a projector\nP=|local><local|(x)Id_restoftheworld when we say we have a peculiar\noutcome. The property applies to the whole universe, strictly speaking.\n\n> Von Neumann\'s 1932 postulates are no longer believed to be valid\n> for small systems since it is well recognized that these are\n> necessarily open.\n>\nThis is a matter of words. What you say is that you always have\ninteractions with other parts of the world, even for a small system.\nThis in no case refutes the fundamental postulates.\n\n> These postulates are only believed to govern a very large system\n> (small system plus detector plus environment), from which a\n> statistical mechanics type analysis (heat bath etc.) produces\n> the reduced open description.\n>\nAgain, QM formalism does not refute such a result. The probability\nP~100% of some outcomes are possible.\nNote this is the same thing in CM: we do not know no real system\nwithout dissipation (in the absolute) however, the laws assume the\nenergy momentum conservation.\n\n\n>\n> > You have the unitary evolution and the measurement postulates: An Open\n> > system is always a part of a closed system (otherwise, the unitary\n> > evolution postulate is not true => problem with the consistence of the\n> > QM theory). The collapse postulate always applies to the whole system\n> > description.\n>\n> The closed system is always the whole universe.\nIn the absolute, yes as in the CM formalism.\n> Since this cannot be observed from the outside, von Neumann\'s measurement theory > does not apply there.\nOnce again you are mixing the measurement formalism with your\nmeasurement interpretation.\n\n> It is never in the factorized state assumed to\n> prevail before the beginning of a measurement. Interactions cannot\n> be switched on and off to restrict the measurement to a short duration.\n\nInteractions has not to be switched on/off in a formal measurement:\n\nA formal measurement is the acknowledgement of a property (the\n"outcome a") of an instance of a given system. There is not any\ninteraction in this acknowledgement. There is not any interaction\ninvolved in a formal measurement.\nThink on the god theory of the previous post: we just have properties\nthat are established once. Formal measurement is just the aknowlegement\nof some of these properties and not the modification of these\nproperties, it does not change the system.\n\nWe use to mix in the word measurement, the interactions added by the\nmeasurement apparatus and the formal measurement (the acknowledgement).\nIf you follow rigorously the QM formalism, you have to separate these 2\nmeanings: the apparatus (and hence its interactions) and the formal\nmeasurement (no interaction at all, does not modified the considered\ninstance of the system+apparatus+ ...).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Seratend wrote:
>
> > Arnold Neumaier wrote:
> >
> >>Seratend wrote:
> >>
> > We are at the heart of the problem between the formalism of the theory
> > and the interpretation.
> > Please note that the measurement part of the theory does not require
> > any interaction.
>
> The formalism itself has nothing to do with the real world, unless
> it is given _some_ interpretation.
>
> Real measurement requires real interactions.
>
QM formalism does not say what is a real measurement. QM formalism
speaks about the collapse postulate and the born rules and the unitary
evolution. That's all.
I need quantum interactions to describe the whole unitary evolution of
the system and the measurement apparatus object. Unitary evolutions
introduce statistical correlations between the system and the
measurement apparatus object (including the environment if necessary to
describe the evolution).
We use these statistical correlations on the statistics of formal
measurement results of this whole system (including the "measurement
apparatus" that has not to be confused with the formal measurement
result). That's what the formalism allows one to say (hence the
requirement of interactions to correlate the measurement apparatus to
the system). All the rest is interpretation. Saying the measurement
apparatus does a formal measurement is interpretation (completely out
of the scope of the QM formalism). I do not refute the interpretation,
nor I can't as long as it is consistent with the formalism.
> The theory models these by assuming collapse under measurement,
> no matter whether in the eyes of the observer or whether objective.
> At least this is the traditional way of viewing the formalism.
>
This is the traditional *interpretation* of the formalism.
I am just using the logic in the context of the formalism: I do not
explain why I observe a result, just that when this result is true, I
have a collapse. No interaction is involved in this logical
affirmation.
The formal measurement does not have "hidden" interactions. It is
not the measurement apparatus (its interactions).
The usual interpretation is "interpreted measurement result" =
{system, apparatus, all the interations with a global unitary evolution
and the formal measurement result}.
I do not question this label. However, I cannot subscribe to deductions
made on the interpretation that are out of scope of the theory
formalism.
>
> > The observer outside or inside the system has no
> > meaning in the QM formalism (only in the interpretations).
>
> The QM formalism is about closed systems in which no measurements
> happen by definition of what it means to be closed. There are no
> measurements in the formalism.
>
So, Do you claim the measurement postulates of QM formalism are wrong
in some obscure cases?
Where have you seen such a definition in the 6 postulates of QM theory?
(Note: I interpret the word closed system, as a system where the state
evolution on time follows the usual unitary evolution).
Now, if what you call "measurement" is an interpretation
measurement, I have nothing to say.
> If measurements are discussed within the formalism (as
> measurement theory), they have to be _defined_, and they _are_
> defined via an interaction. But the measurements as happening within
> the formalism alone cannot be related to actual measurements
> without an interpretation of what the formalism means in the real
> world. Without an interpretation no relation between formalism and
> reality.
>
This is the mapping between the outcomes of formal observables and the
outcomes of the reality. It is the common denominator of all the
interpretations (I know). Hence no other interpretation is required.
We can say that the QM formalism with the mapping of outcomes is the
minimum set to describe the reality: what I call the QM formalism.
Hence, any interpretation validates this formalism.
>
> > Moreover, an opened system is a closed system when we consider the rest
> > of the world (formal).
>
> But then one needs an interpretation of what it means for one subsystem
> of the closed world to measure another subsystem, and for lack of a
> probabilistic interpretation in our unique world this hasn't been given
> in _any_ of the current interpretations.
>
I need no interpretation (see above) I just need projectors and formal
hypotheses (e.g. the independence of systems, the low impact of
environment etc ...) and the final verification on a "real" system.
I have not a system that measures (in the sense of the postulates)
another system (no meaning), just a global measurement and its results.
>
> >>Thus the observer cannot claim convincingly to have observed the system.
> >>
> > I hope you understand better why this sentence has no meaning in the QM
> > theory formalism (in my opinion : ).
>
> I understand better why it has no meaning for you.
> But I don't accept your arguments as being valid for the QM formalism
> (which includes the Born rule, which makes sense only together with
> the collapse).
>
See above. I am just using the logical meaning of the QM formalism +
the mapping of the observables outcome to the real outcomes taht make
sense for any experiment we may think. I assume that whatever
interpretation you assume, my logical set is always valid, hence you
should logically accept my results.
The main difference is on the collapse of the word meanings: what you
call measurement is not the measurement described in QM formalism.
Hence, you should change this word in order to avoid confusions.
>
> >>Observability by an external observer therefore demands openness of the
> >>system. At least under conventional assumptions about what the terms
> >>closed, interaction, observation mean.
> >>
> > H= sum_i Hi => unitary evolution, including the interactions of the
> > observer object.
> > + collapse postulate: property of an instance of a system governed by H
> > (including the observer object).
> > If I say, I have a system [including the observer object] with a given
> > property => I have the associated collapse. There is no "observer"
> > in the sentence "I have a system [including the observer object] with
> > a given property", just the logic affirmation of this property.
>
> I don't understand you. If there are interactions we have
> H= sum_i Hi + sum_ij V_{ij}.
Re-label the set of labels i,j by a new label i and call V_{ij}=H_{inew} =>
we recover the previous general relation.
> And I don't understand what a 'property' is; the traditional QM
> formalism has no place for it. If you want to stay on the formal
> side you are only allowed to talk about operators, states, Hilbert
> spaces and other on the formal level well-defined concepts.
>
With the outcomes mapping with the "reality", the property
"outcome of A is a" has both a signification in a real object as
well as in a symbolic one.
(here property: the mathematical signification. You can use proposition
if you it is more adequate).
In the traditional formalism of QM, when the collapse postulate is
true, the property "outcome of A is a" is true. This is a property
of the considered system (logic).If this property is false the
corresponding collapse postulate is also false => the collapse of a
system is a property of the system (QM formalism).
I am not inventing new words, I am just using mathematical results of
the QM formalism.
> >>
> > Well, as I have said before, I will not question the interpretation as
> > long as it does not change the QM theory formalism.
>
> I do not change the formal side of quantum mechanics.
> But it is meaningless without an interpretation in terms of the
> real world.
>
I think this post underlines that you may have at least given a
signification to the word measurement of the QM formalism that may be
not compatible with the formalism (If I have understood what you have
said).
>
> It would be good if you could give a concise formal definition of
> what you consider to be _the_ QM formalism. One can state everything
> in a few axioms, but it seems that your set of axioms is different from
> what I hold to be the common view.
>
The 6 usual postulates + the mapping of the observables outcomes
(defined by the collapse postulate) to the outcomes of real systems.
That's all.
>
> >>>Note, in the QM formalism, there is no classical/quantum boundary (only
> >>>in the interpretations of QM). Just postulates that may be applied,
> >>>hopefully (for the consistence of the theory) on closed systems as well
> >>>as opened ones.
> >>
> >>But there are different postulates for
> >>
> >>- closed systems (unitarity),
> >>- systems open just at some instant (collapse), and
> >>- continuously open systems (Lindblad type dissipative dynamics,
> >>or corresponding stochastic quantum processes).
> >>
> > I hope that no!
>
> My statement is based on assessing the heap of papers on QM that
> I read among the flood of papers published in the last 10 years,
> say. In particular, most realistic experimental analysis requires
> the open systems view in which energy is _not_ conserved but
> dissipates into unmodelled degrees of freedom. These systems are
> not unitary, but are as quantum mechanical as one could wish.
>
I understand that your statements as most of the written papers are
based on a mix of interpretation and formalism. I do not question the
effective results. Each time I read a new paper, I try to remove all
the interpretation stuff from the real logic content.
What you say is true: the local state of an opened system does not
evolve unitary. This is a result of QM formalism. No need to interpret
this result. The coupling of theses open systems define a global
unitary evolution and hence a local non unitary evolution that may have
some interesting properties (localisation of the state on a subset of
possible outcomes in a give basis, etc ...). This again is given by the
QM formalism.
Therefore, strictly speaking, you can only say that the evolution of a
local state of a given system is non unitary. However, in a more
common language you can say the system does not evolve unitary,
assuming implicitly you are speaking of the local state.
However, strictly speaking, a local outcome of a system is a global
outcome of the whole system (including the universe) in the QM
formalism: we always apply a projector
P=|local><local|(x)Id_restoftheworld when we say we have a peculiar
outcome. The property applies to the whole universe, strictly speaking.
> Von Neumann's 1932 postulates are no longer believed to be valid
> for small systems since it is well recognized that these are
> necessarily open.
>
This is a matter of words. What you say is that you always have
interactions with other parts of the world, even for a small system.
This in no case refutes the fundamental postulates.
> These postulates are only believed to govern a very large system
> (small system plus detector plus environment), from which a
> statistical mechanics type analysis (heat bath etc.) produces
> the reduced open description.
>
Again, QM formalism does not refute such a result. The probability
P~100% of some outcomes are possible.
Note this is the same thing in CM: we do not know no real system
without dissipation (in the absolute) however, the laws assume the
energy momentum conservation.
>
> > You have the unitary evolution and the measurement postulates: An Open
> > system is always a part of a closed system (otherwise, the unitary
> > evolution postulate is not true => problem with the consistence of the
> > QM theory). The collapse postulate always applies to the whole system
> > description.
>
> The closed system is always the whole universe.
In the absolute, yes as in the CM formalism.
> Since this cannot be observed from the outside, von Neumann's measurement theory > does not apply there.
Once again you are mixing the measurement formalism with your
measurement interpretation.
> It is never in the factorized state assumed to
> prevail before the beginning of a measurement. Interactions cannot
> be switched on and off to restrict the measurement to a short duration.
Interactions has not to be switched on/off in a formal measurement:
A formal measurement is the acknowledgement of a property (the
"outcome a") of an instance of a given system. There is not any
interaction in this acknowledgement. There is not any interaction
involved in a formal measurement.
Think on the god theory of the previous post: we just have properties
that are established once. Formal measurement is just the aknowlegement
of some of these properties and not the modification of these
properties, it does not change the system.
We use to mix in the word measurement, the interactions added by the
measurement apparatus and the formal measurement (the acknowledgement).
If you follow rigorously the QM formalism, you have to separate these 2
meanings: the apparatus (and hence its interactions) and the formal
measurement (no interaction at all, does not modified the considered
instance of the system+apparatus+ ...).
Seratend.
Seratend
Jun9-05, 06:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n>\n> So you assume the collapse rather than deriving it.\n> You postulate the existence of objective hidden variables\n> (the observable clicks) that follow an uncontrolled, unmodelled\n> dynamics correlated to the wave function according to the postulated\n> Born rule. This is a cheap way out.\n>\nI just say that the QM model does not describe the outcomes, but the\noccurrence of outcomes. I hope you understand what I mean (this is a\nchoice of description).\n\n> I want _better_ foundations. The clicks are not things unrelated to\n> quantum mechanics, but they are macroscopic pressure distributions\n> in the air surrounding the ear that hears the click. No pressure\n> distribution characteristic of a click implies no click to be heard.\n>\nThis is our problem of misunderstanding. By no way the QM formalism\nexplains the outcomes. So what you are looking for is:\n\na) a naïve prediction of the outcomes that may context dependent: it\ndepends on the experiment you choose. You already have bohmian\nmechanics, that has adds new equation: the bohmian path of a particle.\n\nSome analysis on this type of description allows on to conclude that,\nin general, the deterministic function will be known when all the\ntrials on the identical systems are done (known). Not very practical\nfor a prediction tool (the trials and the outcomes define the function:\na=f(e) <=> (e,a)).\n\nb) the time evolution of some configurations with the conservation the\nP~100% statistics of the outcomes. (may be better words could be use to\ndescribe what I mean)\n\nI think this is the last case you are looking for (using mainly the law\nof large numbers and ergodicity properties, etc ...). This is the\ninteresting one (the one you are interested).\n\nOnce you have identified/defined these systems with the 100%\nstatistics, you can define deterministic evolutions of instances of\nsuch systems by defining a formal collapse (the initial condition, or\nthe final or intermediate etc ...) => you cannot avoid the formal\ncollapse.\n\nThis is the formal content of the collapse postulate in the QM\nformalism. This is not cheap. Just the way we choose the physical\ndescriptions. If you prefer, the way we say the things are.\n\nTry to see the initial conditions (or final, or ...) of CM as the\nformal particular collapse of the considered system: you cannot avoid\nit. If you have problems with that, just use the hilbert space\nformalulation (H=Hq(x)Hp) of classical mechanics in order to view how\nthe collapse is just the acknowledgement of some properties (in this\ncase the initial conditions) and not the prediction.\n\n> The collapse challenge is to demonstrate the emergence of this\n> particular pressure distribution at the time it is observed,\n> by considering the air as the quantum system which statistical\n> mechanics claims it to be.\n>\nSo what you call "collapse challenge" is the description of some\nsystems with 100% statistics. As explained above, this has nothing to\ndo with the collapse (we need to apply).\n\nI you prefer, let\'s change, your system by a classical system\ndescribed by the Hilbert space formalism and the unitary evolution of\nthe liouvillian operator.\n\nSee for example: quant-ph/0301172: Topics in Koopman-von Neumann Theory\n\nDo you see we still have a collapse postulate? Even if we take an\ninitial dirac distribution for the 2 paths (the path 1 and path 2 are\nthe 2 possible paths of the particle) and that this collapse has\nnothing to do with the screens or whatever we want, just the\nacknowledgement of the outcomes of the experiment.\n\n>\n>\n> > In any case, we have for a given instance of this system a property\n> > false that becomes true. This has no meaning in this formalism.\n>\n> Then your formalism is severely deficient, not consistent with\n> what textbooks assert.\n>\nAll the textbooks, I known (may be not the best ones : ), that deal\nwith the formalism does not say more than what I say. We always have\nthe danger when reading a text to give more signification to the words\nthan they really mean. For example, the words interpretation of the\n"before" and the "after" in the collapse postulate. Adding an\nextra meaning to these words most of the time leads to incoherent\npropositions.\n\nThe QM formalism is not deficient. It is a *complete* description (the\n"ackwoledgement") and a prediction of the statistics. Understanding\nit\'s formal meaning is crucial.\n\n> The objective change of pressure distribution has a well-defined\n> meaning in the statistical mechanics description of the system\n> (particle + air).\n>\nIn QM also.\n>\n>\n> > I hope you better understand, my meaning of the formal collapse: I do\n> > not say more than the formalism of the theory does.\n>\n> I understand it, but regard it as empty talk.\n>\nI am not sure you understand it. It is not an empty talk at all if you\nreally take all its predictive power (except for the preferred basis :\n).\n\n> The formalism of quantum statistical mechanics says more.\n> It says that a macroscopic quantum system has definite macroscopic\n> observables such as the pressure distribution of the air,\n> given by the usual thermodynamical formalism.\n>\nQM formalism allows system to have macroscopic observables with ~100%\nstatistical distributions. However to say that a macroscopic observable\nhas a value, you need the collapse postulate. This is not strange.\nOnce you understand this point, the collapse is no more mysterious\nneither empty.\n\nExample:\nFor a given system instance: at time to, I have the outcome a(to) and\nat time t1, I have the outcome a(t1).\n\nThe collapse associate to this system is "Outcome a(to)@to and\nOutcome a(t1)@t1".\n\nIf the system is determinist, you have P ("Outcome a(to)@to and\nOutcome a(t1)@t1")=100% and P ("Outcome a(to)@to and Outcome\nb=/=a(t1)@t1")=0.\n\n>From this statistics, you can deduce the outcome @ t1 providing the\noutcome@to but it does not change the collapse of such systems where\nthis property is true (otherwise it not the same system).\n\nYou can\'t avoid such reasoning, in classical or in quantum mechanics.\nThis is very natural.\n\nIn addition, if you analyse better this case, you will see that only\nthe outcomes of commuting observables may be determinist in the above\nsense (existence of a function connecting the outcomes => commuting\nobservables). Hence all the nice commuting properties of determinist\nsystems.\n\n\n>\n> > I just say, that in the statistical description choice of the\n> > QM theory formalism, the collapse is just the notification of the\n> > results of experimental trials (a property is true). Saying more than\n> > that is interpreting the theory with the risk of modifying the theory.\n>\n> In the statistical interpretation, the collapse is just the change\n> of description caused by taking conditional expectations under a\n> change of the condition. Nothing needs to be explained on that level.\n>\n> What needs explanation is how the individual system is related to\n> the statistical description.\n>\n?\nI mean, It is related to the statistical description by its outcome.\n\n> If we increase the size of the quantum system it becomes more and more\n> unique. If the system is large enough (e.g. the Moon), the system\n> is an individual, and it is no longer possible to prepare identically\n> distributed copies of the Moon. But we still can observe it, and we\n> still believe it is governed by quantum mechanics, since no one can\n> point at any size where quantum mechanics starts to be inapplicable.\n>\n> Here is the need for explanation!\n>\nI do not understand you (I am trying).\n\nQM formalism says, e.g. decoherence, that there may exist macroscopic\nsystems with 100% statistical distribution (of a given set of outcomes\nat different times=> implicitly defines a path): for a given system\nwith an outcome at time to (a(to)), we are able to deduce values of the\noutcomes at other times (e.g. a(t)): for 100% of the systems with\noutcome a(to).\n\n(Note that I am using a statistical language to describe a\ndeterministic evolution).\n\nIt would be very interesting and instructive to get rigorous and good\ndeductive explanations on how we can get these results (thermodynamics,\netc ...) for simple and more complex objects such as moon, balls etc\n... I mean on how we obtain the 100% statistical distribution from the\npostulates of QM. Hence in this aspect, I understand your search (and I\nam very interested on such a good explaination.\n\nNow what I do not understand, is the connection of this statistical\nprediction with the formal problem of finding several identical\ninstances of the same object and the collapse (i.e. with the outcome\na(to)).\n\n>\n> The statistical interpretation has a similar conflict; it assumes\n> the reality of the objective event, the measurement result,\n> and forgets to say which macroscopic observations are entitled to\n> be taken as objective events. This is questionable.\n>\nYes, this is what I call the problem of the preferred basis prediction.\nThe QM formalism does not predict the basis of the statistics. Hence my\nquestion concerning this topic and if it can be solved with the\navailable observable of macroscopic systems (or whatever else).\n\nCurrently, with the QM formalism we have to choose the Hamiltonian for\nthe unitary evolution and basis where we have the measurement results.\nIt seems there is too many degrees of freedom to mach theoretical\nresults with reality (just by rotating the basis of a given observable,\nwe change the statistical behaviour in huge proportions).\n\n> > with the formal mapping of collapse with the experiments results\n> > (the statistical description). It avoids to say more than the formalism\n> > of the theory says.\n>\n> Rather, it avoids to specify the precise meaning of what the formalism\n> of quantum mechanics says. It just says, if you don\'t look too closely\n> at the meaning, you can apply it very successfully...\n>\n: ) I agree. This explains surely why QM is so successful in the\nexisting experimental descriptions: we must do the experiment before\nfinding the basis (if we do not know - case of a completly new\nexperiment) and after we give the explanation of the observed\nstatistics.\n>\n> >>>>>At the end, I must apply the born\n> > So, why are you searching a physical meaning of to the collapse?\n>\n> Because I think it has a physical meaning.\n>\n> I reject the statistical interpretation as being the fundamental\n> description of nature. It cannot be consistently applied to the\n> many situations where quantum mechnaics is applied routinely\n> although no two identically distributed realizations can be produced.\n>\nI think I have not understand what you mean by "statistical\ninterpretation".\n>\n> > Here, I want to understand what you really mean by physical collapse.\n>\n> The physical collapse is the response of a small quantum system\n> to interactions of very short duration with a detector not modelled\n> in detail.\n>\nDo you accept the formal mapping:\n\n"physical collapse " <=> {set of interactions modelling + formal\ncollapse including basis selection of the collapse}\n\n?\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
>
> So you assume the collapse rather than deriving it.
> You postulate the existence of objective hidden variables
> (the observable clicks) that follow an uncontrolled, unmodelled
> dynamics correlated to the wave function according to the postulated
> Born rule. This is a cheap way out.
>
I just say that the QM model does not describe the outcomes, but the
occurrence of outcomes. I hope you understand what I mean (this is a
choice of description).
> I want _better_ foundations. The clicks are not things unrelated to
> quantum mechanics, but they are macroscopic pressure distributions
> in the air surrounding the ear that hears the click. No pressure
> distribution characteristic of a click implies no click to be heard.
>
This is our problem of misunderstanding. By no way the QM formalism
explains the outcomes. So what you are looking for is:
a) a naïve prediction of the outcomes that may context dependent: it
depends on the experiment you choose. You already have bohmian
mechanics, that has adds new equation: the bohmian path of a particle.
Some analysis on this type of description allows on to conclude that,
in general, the deterministic function will be known when all the
trials on the identical systems are done (known). Not very practical
for a prediction tool (the trials and the outcomes define the function:
a=f(e) <=> (e,a)).
b) the time evolution of some configurations with the conservation the
P~100% statistics of the outcomes. (may be better words could be use to
describe what I mean)
I think this is the last case you are looking for (using mainly the law
of large numbers and ergodicity properties, etc ...). This is the
interesting one (the one you are interested).
Once you have identified/defined these systems with the 100%
statistics, you can define deterministic evolutions of instances of
such systems by defining a formal collapse (the initial condition, or
the final or intermediate etc ...) => you cannot avoid the formal
collapse.
This is the formal content of the collapse postulate in the QM
formalism. This is not cheap. Just the way we choose the physical
descriptions. If you prefer, the way we say the things are.
Try to see the initial conditions (or final, or ...) of CM as the
formal particular collapse of the considered system: you cannot avoid
it. If you have problems with that, just use the hilbert space
formalulation (H=Hq(x)Hp) of classical mechanics in order to view how
the collapse is just the acknowledgement of some properties (in this
case the initial conditions) and not the prediction.
> The collapse challenge is to demonstrate the emergence of this
> particular pressure distribution at the time it is observed,
> by considering the air as the quantum system which statistical
> mechanics claims it to be.
>
So what you call "collapse challenge" is the description of some
systems with 100% statistics. As explained above, this has nothing to
do with the collapse (we need to apply).
I you prefer, let's change, your system by a classical system
described by the Hilbert space formalism and the unitary evolution of
the liouvillian operator.
See for example: http://www.arxiv.org/abs/quant-ph/0301172: Topics in Koopman-von Neumann Theory
Do you see we still have a collapse postulate? Even if we take an
initial dirac distribution for the 2 paths (the path 1 and path 2 are
the 2 possible paths of the particle) and that this collapse has
nothing to do with the screens or whatever we want, just the
acknowledgement of the outcomes of the experiment.
>
>
> > In any case, we have for a given instance of this system a property
> > false that becomes true. This has no meaning in this formalism.
>
> Then your formalism is severely deficient, not consistent with
> what textbooks assert.
>
All the textbooks, I known (may be not the best ones : ), that deal
with the formalism does not say more than what I say. We always have
the danger when reading a text to give more signification to the words
than they really mean. For example, the words interpretation of the
"before" and the "after" in the collapse postulate. Adding an
extra meaning to these words most of the time leads to incoherent
propositions.
The QM formalism is not deficient. It is a *complete* description (the
"ackwoledgement") and a prediction of the statistics. Understanding
it's formal meaning is crucial.
> The objective change of pressure distribution has a well-defined
> meaning in the statistical mechanics description of the system
> (particle + air).
>
In QM also.
>
>
> > I hope you better understand, my meaning of the formal collapse: I do
> > not say more than the formalism of the theory does.
>
> I understand it, but regard it as empty talk.
>
I am not sure you understand it. It is not an empty talk at all if you
really take all its predictive power (except for the preferred basis :
).
> The formalism of quantum statistical mechanics says more.
> It says that a macroscopic quantum system has definite macroscopic
> observables such as the pressure distribution of the air,
> given by the usual thermodynamical formalism.
>
QM formalism allows system to have macroscopic observables with ~100%
statistical distributions. However to say that a macroscopic observable
has a value, you need the collapse postulate. This is not strange.
Once you understand this point, the collapse is no more mysterious
neither empty.
Example:
For a given system instance: at time to, I have the outcome a(to) and
at time t1, I have the outcome a(t1).
The collapse associate to this system is "Outcome a(to)@to and
Outcome a(t1)@t1".
If the system is determinist, you have P ("Outcome a(to)@to and
Outcome a(t1)@t1")=100% and P ("Outcome a(to)@to and Outcome
b=/=a(t1)@t1")=0.
>From this statistics, you can deduce the outcome @ t1 providing the
outcome@to but it does not change the collapse of such systems where
this property is true (otherwise it not the same system).
You can't avoid such reasoning, in classical or in quantum mechanics.
This is very natural.
In addition, if you analyse better this case, you will see that only
the outcomes of commuting observables may be determinist in the above
sense (existence of a function connecting the outcomes => commuting
observables). Hence all the nice commuting properties of determinist
systems.
>
> > I just say, that in the statistical description choice of the
> > QM theory formalism, the collapse is just the notification of the
> > results of experimental trials (a property is true). Saying more than
> > that is interpreting the theory with the risk of modifying the theory.
>
> In the statistical interpretation, the collapse is just the change
> of description caused by taking conditional expectations under a
> change of the condition. Nothing needs to be explained on that level.
>
> What needs explanation is how the individual system is related to
> the statistical description.
>
?
I mean, It is related to the statistical description by its outcome.
> If we increase the size of the quantum system it becomes more and more
> unique. If the system is large enough (e.g. the Moon), the system
> is an individual, and it is no longer possible to prepare identically
> distributed copies of the Moon. But we still can observe it, and we
> still believe it is governed by quantum mechanics, since no one can
> point at any size where quantum mechanics starts to be inapplicable.
>
> Here is the need for explanation!
>
I do not understand you (I am trying).
QM formalism says, e.g. decoherence, that there may exist macroscopic
systems with 100% statistical distribution (of a given set of outcomes
at different times=> implicitly defines a path): for a given system
with an outcome at time to (a(to)), we are able to deduce values of the
outcomes at other times (e.g. a(t)): for 100% of the systems with
outcome a(to).
(Note that I am using a statistical language to describe a
deterministic evolution).
It would be very interesting and instructive to get rigorous and good
deductive explanations on how we can get these results (thermodynamics,
etc ...) for simple and more complex objects such as moon, balls etc
... I mean on how we obtain the 100% statistical distribution from the
postulates of QM. Hence in this aspect, I understand your search (and I
am very interested on such a good explaination.
Now what I do not understand, is the connection of this statistical
prediction with the formal problem of finding several identical
instances of the same object and the collapse (i.e. with the outcome
a(to)).
>
> The statistical interpretation has a similar conflict; it assumes
> the reality of the objective event, the measurement result,
> and forgets to say which macroscopic observations are entitled to
> be taken as objective events. This is questionable.
>
Yes, this is what I call the problem of the preferred basis prediction.
The QM formalism does not predict the basis of the statistics. Hence my
question concerning this topic and if it can be solved with the
available observable of macroscopic systems (or whatever else).
Currently, with the QM formalism we have to choose the Hamiltonian for
the unitary evolution and basis where we have the measurement results.
It seems there is too many degrees of freedom to mach theoretical
results with reality (just by rotating the basis of a given observable,
we change the statistical behaviour in huge proportions).
> > with the formal mapping of collapse with the experiments results
> > (the statistical description). It avoids to say more than the formalism
> > of the theory says.
>
> Rather, it avoids to specify the precise meaning of what the formalism
> of quantum mechanics says. It just says, if you don't look too closely
> at the meaning, you can apply it very successfully...
>
: ) I agree. This explains surely why QM is so successful in the
existing experimental descriptions: we must do the experiment before
finding the basis (if we do not know - case of a completly new
experiment) and after we give the explanation of the observed
statistics.
>
> >>>>>At the end, I must apply the born
> > So, why are you searching a physical meaning of to the collapse?
>
> Because I think it has a physical meaning.
>
> I reject the statistical interpretation as being the fundamental
> description of nature. It cannot be consistently applied to the
> many situations where quantum mechnaics is applied routinely
> although no two identically distributed realizations can be produced.
>
I think I have not understand what you mean by "statistical
interpretation".
>
> > Here, I want to understand what you really mean by physical collapse.
>
> The physical collapse is the response of a small quantum system
> to interactions of very short duration with a detector not modelled
> in detail.
>
Do you accept the formal mapping:
"physical collapse " <=> {set of interactions modelling + formal
collapse including basis selection of the collapse}
?
Seratend.
Seratend
Jun10-05, 01:21 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1118070553.900097.186040@g49g2000cwa.googlegroups .com>,\n> "Seratend" <ser_monmail@yahoo.fr> wrote:\n>\n> You accept the results of decoherence and you accept that they can (in\n> principle) be derived from the law of unitary evolution, right?\n\nYes. I take the QM formalism for granted (otherwise it is no more QM).\n\n> If so,\n> then implicit in this statement is that you believe in the existence of\n> the basis selected by decoherence. (I\'m going to avoid \'preferred\'\n> because you seem to want to impart some ontological baggage there that I\n> don\'t want.)\n>\nWhat I call the preferred basis is the basis where we notice the\noutcomes of a QM experiment. Hence, I need to see if QM formalism\n(hence the decoherence application) is able to predict the basis of\noutcomes in some cases. We can remove the preferred attribute if you\nwant.\n\n> I didn\'t think I was making any controversial statements here. This same\n> idea appears in III.E (.3 in particular) of the paper that was referred\n> to earlier on this thread, quant-ph/0312059.\n>\nGood, this was a paper I have studied a long time ago.\n\nLet me quote the section F:\n\nPointer basis vs. instantaneous Schmidt states. The so-called\n"Schmidt basis", obtained by diagonalizing the (reduced) density\nmatrix of the system at each instant t, has been frequently studied\nwith respect to its ability to yield a preferred basis, having led some\nto consider the Schmidt basis states as describing "instantaneous\npointer states". However, as it has been emphasized, any density\nmatrix is diagonal in some basis, and this basis will in general not\nplay any special interpretive role.\nPointer states that are supposed to correspond to quasiclassical stable\nobservables must be derived from an explicit criterion for classicality\n(typically, the stability criterion); the simple mathematical\ndiagonalization procedure of the instantaneous density matrix will\ngenerally not suffice to determine a quasiclassical pointer basis.\n\n(this sectionf is against your schmidt basis claim)\n\nNow , take the formula (3.8) page 14 of the same document, change the\nbasis of the system, apparatus and environment and, apply the weak\nargument of the mean time orthogonality of the environment basis (what\nis done between 3.13 and 3.14 of section III.E => you end with the same\napproximated decomposition but with completely different basis, for the\nsystem and apparatus (eq. 3.14).\n\n=> We have different possible basis for the measurements QED.\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1118070553.900097.186040@g49g2000cwa.googlegroups. com>,
> "Seratend" <ser_monmail@yahoo.fr> wrote:
>
> You accept the results of decoherence and you accept that they can (in
> principle) be derived from the law of unitary evolution, right?
Yes. I take the QM formalism for granted (otherwise it is no more QM).
> If so,
> then implicit in this statement is that you believe in the existence of
> the basis selected by decoherence. (I'm going to avoid 'preferred'
> because you seem to want to impart some ontological baggage there that I
> don't want.)
>
What I call the preferred basis is the basis where we notice the
outcomes of a QM experiment. Hence, I need to see if QM formalism
(hence the decoherence application) is able to predict the basis of
outcomes in some cases. We can remove the preferred attribute if you
want.
> I didn't think I was making any controversial statements here. This same
> idea appears in III.E (.3 in particular) of the paper that was referred
> to earlier on this thread, http://www.arxiv.org/abs/quant-ph/0312059.
>
Good, this was a paper I have studied a long time ago.
Let me quote the section F:
Pointer basis vs. instantaneous Schmidt states. The so-called
"Schmidt basis", obtained by diagonalizing the (reduced) density
matrix of the system at each instant t, has been frequently studied
with respect to its ability to yield a preferred basis, having led some
to consider the Schmidt basis states as describing "instantaneous
pointer states". However, as it has been emphasized, any density
matrix is diagonal in some basis, and this basis will in general not
play any special interpretive role.
Pointer states that are supposed to correspond to quasiclassical stable
observables must be derived from an explicit criterion for classicality
(typically, the stability criterion); the simple mathematical
diagonalization procedure of the instantaneous density matrix will
generally not suffice to determine a quasiclassical pointer basis.
(this sectionf is against your schmidt basis claim)
Now , take the formula (3.8) page 14 of the same document, change the
basis of the system, apparatus and environment and, apply the weak
argument of the mean time orthogonality of the environment basis (what
is done between 3.13 and 3.14 of section III.E => you end with the same
approximated decomposition but with completely different basis, for the
system and apparatus (eq. 3.14).
=> We have different possible basis for the measurements QED.
Seratend.
Joe Rongen
Jun10-05, 01:22 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote\nin message news:42A57F0D.1080800@univie.ac.at...\n> joe@alpha.to wrote:\n\n[snip...]\n\n> > After a proper setup, the PMT (a quantum system), will measure\n> > an objective record of individual results that can be analyzed\n> > statistically and quoted in a physics journal.\n>\n> Yes. I agree fully to that.\n>\n> To repeat my quest,\n> I am looking for an explanation why this particular detector coupled\n> to a particular quantum system produces the observed erratic but\n> objective record of individual results.\n>\n> Tradition shows how to predict the properties of the resulting\n> distribution, but not how individual macroscopic results (mean\n> values of certain microscpoic current operators) are produced.\n> We observe _bursts_ of <j(x,t)> at certain times t but not at others.\n> Why?\n\n\nThis maybe grasping at straws but a 1/10 degree Kelvin change in\ntemperature can sometimes play havoc with very sensitive equipment.\n\nOtherwise, I can only suggest that: it may not be simple, but mirror\ncopies of nature will always give correct values. If environment and\ncalculations do not account for the odd bursts than it appears it is\ntime to have a closer look at nature. That would be the ideal place\nto start from....\n\nBest regards Joe 6/9/05\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote
in message news:42A57F0D.1080800@univie.ac.at...
> joe@\alpha.to wrote:
[snip...]
> > After a proper setup, the PMT (a quantum system), will measure
> > an objective record of individual results that can be analyzed
> > statistically and quoted in a physics journal.
>
> Yes. I agree fully to that.
>
> To repeat my quest,
> I am looking for an explanation why this particular detector coupled
> to a particular quantum system produces the observed erratic but
> objective record of individual results.
>
> Tradition shows how to predict the properties of the resulting
> distribution, but not how individual macroscopic results (mean
> values of certain microscpoic current operators) are produced.
> We observe _bursts_ of <j(x,t)> at certain times t but not at others.
> Why?
This maybe grasping at straws but a 1/10 degree Kelvin change in
temperature can sometimes play havoc with very sensitive equipment.
Otherwise, I can only suggest that: it may not be simple, but mirror
copies of nature will always give correct values. If environment and
calculations do not account for the odd bursts than it appears it is
time to have a closer look at nature. That would be the ideal place
to start from....
Best regards Joe 6/9/05
rof@maths.tcd.ie
Jun10-05, 01:22 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n>rof@maths.tcd.ie wrote:\n\n>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>\n>>>rof@maths.tcd.ie wrote:\n>>\n>> I may have confused the official Copenhagen interpretation with\n>> what Bohr, Heisenberg, von Neumann and so on believed. As Scerir\n>> pointed out in this thread, Heisenberg said "The discontinuous change\n>> in the probability function, however, takes place with the act\n>> of registration, because it is the discontinuous change\n>> of our knowledge in the instant of registration that has its\n>> image in the discontinuous change of the probability function.",\n>> Hiesenberg, "Physics and Philosophy", 1958\n\n>I commented that already. the \'acto of registration\' happens on the\n>photographic plate or in the eye, not in the mind, and is simply\n>the irreversible magnification due to dissipation by interaction with\n>a macroscopic detector. It is objective and has no connection to\n>any \'knowledge\'.\n\n>... only that your interpretation of what he said in terms of\n>knowledge is a postmodern interpretation, and either the\n>Copenhagen interpretation nor Heisenberg\'s intention.\n\nMy apologies for taking so long to reply. Various collegiate\nmatters have occupied my attention for the last week.\n\nAnyway, to summarize:\n\nHeisenberg said "it is the discontinuous change of our knowledge\nin the instant of registration that has its image in the discontinuous\nchange of the probability function."\n\nMy interpretation of this is: it is the discontinuous change of our\nknowledge in the instant of registration that has its image in the\ndiscontinuous change of the probability function.\n\nYour interpretation of it is: it is _not_ the discontinuous change\nof our knowledge in the instant of registration that has its image\nin the discontinuous change of the probability function. It has no\nconnection to any \'knowledge\'.\n\nThen you declare that your arguments are excellent, and\nthat my interpretation of what Heisenberg said is "a postmodern\ninterpretation".\n\nNow, what appears to me to be happening here is that your position,\nthat Heisenberg believed that collapse "is objective and has no\nconnection to any \'knowledge\'", is entirely incorrect, and that\nHeisenberg said so himself, and that when confronted with this fact,\nyou gave the impression that his statements required "interpretation".\nYou then "interpreted" his statement to mean exactly the opposite\nof what he said. Then you accused me of having a distorted\ninterpretation because I took Heisenberg at his word, and\nproceeded to insult me by calling my interpretation postmodern.\n\nHeisenberg was even more explicit about the connection to knowledge,\nwhich you deny he believed in:\n"This probability function represents a mixture of two things,\npartly a fact and partly our knowledge of a fact. It represents a\nfact in so far as it assigns at the initial time the probability\nunity (i.e., complete certainty) to the initial situation: the\nelectron moving with the observed velocity at the observed position;\n\'observed\' means observed within the accuracy of the experiment.\nIt represents our knowledge in so far as another observer could\nperhaps know the position of the electron more accurately. The error\nin the experiment does - at least to some extent - not represent a\nproperty of the electron but a deficiency in our knowledge of the\nelectron. Also this deficiency of knowledge is expressed in the\nprobability function." Heisenberg, Physics and Philosophy\n\nHe said this in chapter three, and goes on to say:\n"We can, for instance, predict the probability for finding the\nelectron at a later time at a given point in the cloud chamber. It\nshould be emphasised, however, that the probability function does\nnot in itself represent a course of events in the course of time.\nIt represents a tendency for events and our knowledge of events."\n\nA little further, he says:\n"The observation ... breaks the determined continuity of the\nprobability function by changing our knowledge of the system."\n\nYou will, of course, deny that you intended any insult when\nyou used the word postmodern, and you will claim that everything\nHeisenberg said above is completely consistent with your\ninterpretation, which is that the wavefunction has nothing\nat all to do with knowledge. Then you\'ll claim that your\nposition is not absurd, despite the fact that it obviously\nis. You will probably focus on the occurrence of the word\n"fact" in Heisenberg\'s quote above, and claim that its\nappearance demonstrates that you are right, while\nignoring the parts where he says things like "the probability\nfunction ... represents a tendency for events and our knowledge of\nevents."\n\nNow, I should point out here that your claim that your arguments\nare excellent is incorrect; that they are, as I said they would be,\nunconvincing even to yourself. You have adopted a position where\nyou interpret a statement to mean its opposite, and you have done\nthis not because you find that it is an excellent argument, but\nbecause you can\'t allow yourself to change your mind in public,\nbecause you fear that there is some humiliation associated with\nthat. Let me assure you that anybody whose respect for you drops\nwhen he sees you change your mind is a person whose respect is\nnot worth having. A reasonable person would have more respect\nfor you if you showed the ability to change your mind, and\ntherefore learn, rather than sticking to a position long\nafter it has become ridiculous.\n\nBy the way, when you claimed that Heisenberg didn\'t think the\n\'act of registration\' happened in the mind:\n>... the \'act of registration\' happens on the\n>photographic plate or in the eye, not in the mind, and is simply\n>the irreversible magnification due to dissipation by interaction with\n>a macroscopic detector.\nyou were wrong.\n\nHeisenberg agrees with me that the "act of registration"\ndoes indeed occur in the mind of the observer, and not on the\nphotographic plate:\n"Therefore, the transition from the \'possible\' to the \'actual\' takes\nplace during the act of observation. If we want to describe what\nhappens in an atomic event, we have to realize that the word \'happens\'\ncan apply only to the observation, not to the state of affairs\nbetween two observations. It applies to the physical, not the\npsychical act of observation, and we may say that the transition\nfrom the \'possible\' to the \'actual\' takes place as soon as the\ninteraction of the object with the measuring device, and thereby\nwith the rest of the world, has come into play; it is not connected\nwith the act of registration of the result by the mind of the\nobserver. The discontinuous change in the probability function,\nhowever, takes place with the act of registration, because it is\nthe discontinuous change of our knowledge in the instant of\nregistration that has its image in the discontinuous change of the\nprobability function."\n\nThe act which we are talking about is, according to Heisenberg,\n"the act of registration of the result by the mind of the observer",\nand it is this that corresponds to the "discontinuous change in the\nprobability function". What happens at the photographic plate is\nthe transition from \'possible\' to \'actual\'.\n\nSince this all happens in a chapter called "The Copenhagen\nInterpretation of Quantum Theory", and since Heisenberg is, I hope\nyou will agree, competent to tell us what the Copenhagen interpretation\nis, perhaps you would be kind enough to acknowledge that I have\ntold you something about the Copenhagen interpretation that you\ndidn\'t previously know, namely that according to that interpretation,\ncollapse is associated with the "act of registration of the result\nby the mind of the observer".\n\nYou can read the chapter online at:\nhttp://www.marxists.org/reference/subject/philosophy/works/ge/heisenb3.htm\n\n>> With due respect, and I sincerely mean no offense, I believe\n>> that you have been infected\n\n>Whatever I am infected with, I hope it is highly infectuous\n>and incurable, so that it spreads and has a lasting effect.\n\nYou have become infected with it precisely because it is\nhighly infectious, and because it has spread far and has\nhad a lasting effect.\n\nIt is, however, not incurable, although the patients\ncertainly don\'t like the medicine.\n\n>> with the mental disease that I\n>> ranted about in an earlier post:\n>> http://groups-beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source\n\n>This is a long post, I cannot recognize myself reflected in it.\n>Neither do I recognize signs of a mental disease in my behavior.\n\nIt is extremely rare that one spots a mental disease in oneself,\nbut let me assure you that you are a textbook case.\n\n>> My understanding is that this is why you react so negatively to the\n>> suggestion that the wavefunction describes knowledge.\n\n>I followed the historical development of the interpretations of QM\n>quite closely, reading hundreds of papers, to be able to make up my\n>own mind of how _I_ should interpret QM (and other physics).\n>In the discussions on s.p.r., I share my insights for those who might\n>wish to learn from it. I simply think that phrasing objective\n>descriptions in a psychological language, making them dependent on\n>mental processes, is neither necessary to understanding nor does it\n>serve any useful purpose. There is nothing inherently absurd about\n>this assessment.\n\nThese are your boasts about how well-read you are (despite your\nrather poor knowledge of the Copenhagen interpretation), your\nbeliefs and your opinions. You cannot claim that your interpretation\nwas shared by the founders of quantum mechanics. I will acknowledge\nthat you are a strict conformist, but what you are conforming to\nis the modern desire to rid physics of any reference to subjective\nexperience, and thereby achieve "purity". This desire spreads like\na disease, which comes complete with instructions to ridicule\nthose who insist, as did Heisenberg, Bohr and von Neumann, that\nsubjective experience must be considered carefully and not\nignored. Objectivity has become a religion, and those who\ninsist that physicists should completely ignore subjective\nexperience have become fanatical and have been allowed to take over.\n\n>>>>A definition\n>>>>of measurement isn\'t missing because measurement is the\n>>>>acquisition of new knowledge.\n>>\n>>>This is not a good definition since it is never specified what\n>>>constitutes acquisition of knowledge.\n>>\n>> Acquisition of knowledge is what happens when you look at the\n>> measuring device and see where the pointer is pointing. That\'s\n>> perfectly precise for a normal person, but it seems insufficient\n>> to somebody who wants to know about "the real objective world".\n\n>It seems that it is sufficient for you. But it is insufficient for me.\n\n>I want a mathematical model of reality within which one can clearly\n>say what exists, what is an experiment, an observer, a measurement,\n>a record, etc., in such a way that one can predict in principle which\n>experiments give outcomes with which accuracy.\n>Such arguments are common in qunatum mechanical foundations (e.g.\n>discussions of the Heisenberg microscope) but currently based on\n>informal notions of experiment, observer, measurement, record\n>only.\n\n>My goal is to put the foundations of physics on a basis similarly to\n>the foundations of mathematics, where the whole logical process of\n>coherent deduction can be modelled on a metalevel and gives clarity\n>to the foundations of mathematics that is missing in physics.\n\n>And I think that such foundations are possible and will provide the\n>same clarity for physics.\n\nWell, they are not possible. What you are looking for is an ontology.\nI will explain in the other thread, "Why physicists should pay\nattention to the mind", where it is that you can find the proof\nthat this task is hopeless. You will, however, have to pay attention\nto the mind to understand the proof.\n\n>> Of course, if this is pointed out to them, they\n>> deny it, saying "Why not at all - I am the most\n>> reasonable of fellows.\n\n>Everyone who has a sensible point of view argues that way,\n>including you.\n\nReasonableness is to be demonstrated in one\'s words\nand actions. One should not proclaim that one is great\nand reasonable, that one has read hundreds of papers\nand has excellent arguments. A person may seek to\nacquire credibility by stating that they deserve it,\nbut such a person actually deserves less credibility.\nOne should give one\'s arguments and let others judge\nif they are good or bad; if one has read many papers,\nit should be shown by giving knowledgeable answers.\n\n>Your argument sounds as if you are not claiming that the wave function\n>collapse is about the change of real knowledge of real minds,\n>but about how knowledge should change if someone observes something\n>and acts completely rational. But then it becomes a moral statement\n>completely outside science.\n\n>However, the collapse was formulated by the founders as a necessity to\n>make sense of quantum mechanics, and not as a postulate about moral\n>standards for maintaining knowledge in minds.\n\nNow, morality is about good and evil. The question of how one\nshould use the knowledge one has to make the best predictions\nabout the results of experiments is a strategic question, which\nhas nothing to do with good or evil, and hence has nothing\nto do with morality. You must have confused "What I have to do\nin order to accomplish task X" with "What it makes me a good person\nto do." It seems to me that it would require an almost\nsuperhuman ability to become confused, to make that mistake.\nIt is certainly not an excellent argument.\n\n>>>Furthermore, knowledge depends on subjective decisions to trust\n>>>a measurement. If we discard one as an artifact, there is no\n>>>collapse. How can the collapse depend on such subjective issues?\n>>\n>> In the "wavefunction represents knowledge" interpretation, the\n>> wavefunction is not an objective thing,\n\n>How then can a non-objective thing change in time in an objective way???\n>(Please don\'t be offended by the three ?s!)\n\nConsider, for example, a random walk in one dimension. Suppose I\nsee where the particle is at time 0 and you see where it is at\ntime 1. At time 10, we both look at where the particle is, but\ndon\'t look at it between the first time we see it and the final\ntime. We each use the same equation to describe the time-evolution\nof the probability distribution for the position of the\nparticle, and hence the probability distribution evolves in\nan objective way (recall - objective means the same for\neverybody, subjective means differs from person to person). The\nprobability distribution, however, is subjective, because\nyou use a different one to mine - yours is a delta function\nat time 1, while mine is a delta function at time 0 and is\nspread out at time 1. That is an example of how a non-objective\nthing can change in time in an objective way.\n\n>> but different observers\n>> will use different wavefunctions, depending on what knowledge they\n>> have about the system.\n\n>If I know nothing about an experiemnt, which wave function should I use?\n>Should I use instead of a pure state the microcanonical ensemble,\n>suggested by many statistical mechanics treatments as noninformative\n>prior? Then I make observations and find that they are not in accordance\n>with the predictions of my ensemble since it is born of ignorance\n>rather than knowledge...\n\nYou will use a density matrix if you know absolutely nothing about\nthe preparation of the system.\n\n>> The "collapse" is what happens when the\n>> observer receives new knowledge, and updates his mathematical\n>> representation of his knowledge to reflect the new knowledge that\n>> he has.\n\n>This must be a ficticious observer invented to suit your interpretation.\n\n>A real observer with a real mind has no wave function in his mind --\n>that changes unitarily according to a differential equation whose\n>solution requires a computing capacity much beyond the mind\'s power, and\n>once it sees a measurement (any look out of the window, or only a\n>careful look at the detector needle to be sure of the third decimal?)\n>it computes the solution of the corresponding eigenvalue problem to\n>find out how the wave functions must be collapsed to be consistent.\n\n>At least you won\'t find that when interrogating the most competent\n>experimental physicists who know how they update their knowledge.\n\nYour sneering isn\'t justified. The statement regarding collapse\nabove is exactly what the Copenhagen interpretation states. If\nyou claim that you weren\'t sneering, then you have to also claim\nthat you really thought I was suggesting that people solve\nSchrodinger\'s equation in their mind in the course of\neverday life. You did not really think that.\n\n>> Recall that subjective doesn\'t mean simply bad.\n\n>I never assumed that. But subjective means outside the realm of science,\n>unless that subjectivity can be explained and predicted by models of how\n>it arises from something objective, such as the subjective\n>observer-dependence in special and general relativity.\n\nSo you appear to be saying that you think the processes in\nthe brain provide a sufficient explanation of subjective\nexperience. If you do, then you cannot claim that von Neumann\nagrees with you:\n\n"It is inherenly entirely correct that the measurement or the related\nprocess of the subjective perception is a new entity relative to\nthe physical environment and is not reducible to the latter. Indeed,\nsubjective perception leads us into the intellectual inner life of\nthe individual, which is extra-observational by its very nature."\nvon Neumann, Mathematical Foundations of Quantum Mechanics, p. 418\n\n>>>At the time of Bohr, von Neumann and Wigner, the collapse meant\n>>>something objective, though it might have been related to the mind\n>>>in some unspecified way.\n>>\n>> I have to disagree with that, although I do not mean it in an\n>> adversarial way. The relation to the mind was perfectly clear and\n>> very specific for these people, at least by the \'50s. Also, since\n>> they understood that the wavefunction represented knowledge, the\n>> collapse wasn\'t an objective thing for them.\n\n>Please support your claims by solid evidence!\n\nI do support my claims with solid evidence, but you consistently\npretend that I haven\'t, which is a dishonest thing for you to\ndo. The quotations from Heisenberg above where he explicitly\nsays that collapse corresponds to the reception of knowledge\nby the observer, and von Neumann\'s statements about psycho-physical\nparallelism, are solid evidence.\n\n>>>>>Von Neumann takes the collapse as an axiom, hence also testifies to its\n>>>>>reality.\n>>>>\n>>>>He uses it as an axiom, but that doesn\'t mean that he claimed that\n>>>>the wavefunction didn\'t represent knowledge.\n>>\n>>>But he certainly didn\'t claim that the wavefunction does represent\n>>>knowledge.\n>>\n>> As I quoted before,\n>>\n>> "Let us assume that we do not know the state of a system, S, but\n>> that we have made certain measurements about the state of S and\n>> know their results. In reality, it always happens this way, because\n>> we can learn something about the state of S only from the results\n>> of measurements. More precisely, the states are only a theoretical\n>> construction, only the results of measurements are actually available,\n>> and the problem of physics is to furnish relationships between the\n>> results of past and future measurements." p. 337\n>>\n>> This is exactly a claim that the wavefunction represents\n>> knowledge.\n\n>I cannot understand how you can possibly arrive at this statement.\n>If your claim were true, what von Neumann actually said (first sentence)\n>would mean: \'\'Let us assume that we do not know what we know (the state\n>of S)\'\', and then he deduces correctly from this (obviously false)\n>premise everything he likes.\n\nNo; if my claim were true, what von Neumann said would not mean that.\nYou are using an argument of the form: "If what you said were true,\nthen X", where X is a contradiction. However, you didn\'t even attempt\nto show how X would follow from the antecedent. You merely stated\nthat X would follow, as though the fact that you stated it were\na sufficient proof.\n\n>>>No. A proposition is a statement that is true or false,\n>>>or undecidable. It has nothing to do with whether or not\n>>>anyone knows (or claims to know) its truth or falsehood.\n>>\n>> Logic, which includes the propositional calculus, is the formal\n>> science of inference, and inference can only be done by the mind.\n\n>No. It is routinely (and more reliably) done by computers.\n\n...\n\n>> The desire to assert that logic has nothing to do with the mind is,\n>> I believe, rooted in the primitive notion of nobility,\n\n>No. For example, it can be rooted in the fact that logic can\n>be performed by microchips, which have little to do with mind as\n>commonly understood.\n\nI previously said:\n>>I have to anticipate how somebody could reject something as\n>>simple as this. The only thing I can think of is that somebody\n>>might claim that, since computers can be programmed to do\n>>symbolic manipulation, logic has nothing to do with thinking.\n>>\n>>The problem with this argument is that the fact that computers\n>>can do the symbolic manipulation associated with formal logic\n>>indicates only that logic can be represented by symbolic\n>>manipulations, but establishes nothing about what those\n>>symbolic manipulations describe. Logic was established\n>>in its present form because those symbolic manipulations\n>>describe certain rules of correct thinking.\n\nNow, you did exactly what I predicted - said that logic can be done\nby computers and therefore has nothing to do with thinking. You\nignored the fact that I had anticipated this argument and explained\nwhy it is wrong. I will explain again, in more detail, why it is\nwrong, and I would ask that the next time you reply, you either\naddress the argument that I give, or admit that logic does have a\nconnection to the mind.\n\nThe more detailed version of the explanation is:\nYes, computers can do symbolic manipulation, and the\nrules of inference and deduction, by which we produce\nnew knowledge from existing knowledge, have been\ncharacterized accurately enough to be expressed\nsymbolically. However, the fact that computers can\nmanipulate symbols does not mean that logic is not\na characterization of inference as done by thinking\npeople.\n\nI said: The formal system X describes Y.\nYou said: The formal system X does not describe Y because X\ncan be implemented in a computer.\n\nIn the present case, X refers to symbolic logic and Y refers\nto inference, which is what happens when a person goes from\nthe knowledge that "All men are mortal" and the additional\nknowledge that "Socrates is a man" to the knowledge that\n"Socrates is mortal".\n\nWe could, however, replace X with "The Euler equations", and\nY with "Fluid dynamics", and your argument would just be\nas invalid:\n\nMe: The Euler equations describe fluid dynamics\nYou: The Euler equations don\'t describe fluid dynamics because the\nEuler equations can be implemented in a computer.\n\nIn fact, when we use computers to do symbolic logic, we program\nthem with rules which are specifically chosen because they\nmatch "natural inference", meaning inference done by humans\nin the course of their thinking. The rules of symbolic logic\nwere constructed to describe correct deductive thought, and\ncomputers can be used to manipulate the symbols to produce\nconclusions that we trust because we know that, if we carefully\nexamine each symbolic manipulation that the computer does,\nit will agree with a deduction that a human could have\nmade without the help of the computer.\n\nPlease let me know if you understand this, or if I have to\nexplain it in further detail.\n\n>> I was\n>> asserting that von Neumann was aware that we only know the results\n>> of measurements,\n\n>I agree with this assertion. It is in flat contradiction with your claim\n>that the wave function represents our knowledge. For a wave function\n>needs infinitely many bits to specify, while the results of measurements\n>(according to what you just stated, the _only_ thing we know about the\n>system) can be coded in the finite number of bits making up a protocol.\n\nAny wavefunction that can be written down by a human has a finite\nKolmogorov complexity, otherwise the human wouldn\'t be able to\nwrite it down. Finite Kolmogorov complexity means finite information.\n\n>> "More precisely, the states are only a theoretical construction,\n>> only the results of measurements are actually available, and the\n>> problem of physics is to furnish relationships between the results\n>> of past and future measurements. To be sure, this is always\n>> accomplished through the introduction of the auxilliary concept\n>> "state", but the physical theory must then tell us on the one hand\n>> how to make from past measurements inferences about the present\n>> state, and on the other hand, how to go from the present state to\n>> the results of future measurements." p. 337\n>>\n>> What he is saying is that, in quantum mechanics, what we call\n>> a "state" is actually a theoretical construction\n\n>but with the same objective status as mass, temperature, momentum,\n>charge distribution, etc. of an object. These are also theoretical\n>constructs used to organize our observations.\n\nAlmost, but not quite. Different observers will assign different\nstates to the same system, so it is not quite as objective\nas mass or temperature.\n\n>> Basically, you are saying that knowledge is a dirty thing,\n\n>No. You read this into my statements. Knowledge has nothing to\n>do with cleanliness. Dirty things can be washed; I wouldn\'t know\n>how to wash knowledge.\n\nBravo, Arnold. You truly are the master of the metaphor.\n\n>Knowledge is what we (think we) know. This may be a number of\n>experimental results to within some accuracy, an approximate\n>description of a quantum mechanical state, the rough\n>temperature distribution in a room, the behavior of a piece of\n>equipment according to the manufacturer\'s manual (perhaps\n>corrected by our own calibration experiments), the weight,\n>length and age of the persons working in a room, etc.\n>It is (in some idealization) something describable in a finite\n>string of symbols.\n\n>On the other hand, fundamental physics is about the mathematical\n>model of Nature resulting from such information. This model\n>(von Neumann\'s \'\'theoretical construction\'\') is inferred from\n>observations and contains more accurate parts, less accurate parts,\n>probably a few mistaken parts, and completely unknown parts -\n>it is like a 17th century world map, but instead for the\n>physical phenomenon under study. The objective state of the\n>system is one of the polethora of states compatible with the\n>asvailable information - which one, we don\'t know. But if we know\n>sufficiently much, all compatible states are approximately the same,\n>so working with any particular of them will give good predicitions.\n\n>Nothing here prevents one of taking the system to be the whole universe.\n>The state of the universe must simply be compatible with all details\n>we observed in the parts of the universe accessible to our experiments.\n\nIt would be helpful if you took care to distinguish between your\nown personal interpretation of quantum mechanics and the interpretation\nwhich you claim von Neumann had. Here, I will point out that while\nyou claim that "fundamental physics is about the mathematical model\nof Nature", von Neumann claims that "the problem of physics is\nto furnish relations between the results of past and future\nmeasurements." p.337\n\nYou will, mostly likely claim that these two positions are compatible,\nbut they indicate a completely different way of looking at the\ntask of physics. You want a mathematical model of nature itself,\nand think that measurements and their results should be a part\nof the model, and shouldn\'t have any privileged status within\nthe theory. You are demanding more from fundamental physics than\nvon Neumann did, who simply wanted relations between the\nresults of measurements.\n\n>> Also, when you say "I don\'t buy this," are you saying that\n>> you don\'t believe that von Neumann held this opinion,\n>> namely that the principle of psycho-physical parallelism\n>> tells us that we can consider what we are observing\n>> to be within our own bodies? Because he did:\n>>\n>> "We wish to measure a temperature. ... [we can] say: this\n>> temperature is measured by the thermometer. ... we can\n>> calculate the resultant length of the mercury column,\n>> and then say: this length is seen by the observer. Going\n>> still further, and taking the light source into consideration ...\n>> we would say: this image is registered by the retina of the\n>> observer. And were our physiological knowledge more precise\n>> than it is today, we could go still further, tracing the\n>> chemical reactions which produce the impression of this image on\n>> the retina, in the optic nerve tract and in the brain, and then in\n>> the end say: these chemical changes of his brain cells are\n>> perceived by the observer." p.419\n>>\n>> "That this boundary can be pushed arbitrarily into the interior\n>> of the body of the observer is the content of the principle\n>> of the psycho-physical parallelism." p.420\n\n>Von Neumann says that collapse happens in each particular physical\n>system (defined by its boundary), but that consistency requires that\n>if we regard a particular system as part of a bigger system then\n>the collapse of the larger system must give, for the smaller system,\n>results compatible with the collapse of the smaller system considered\n>by itself. This is nothing more than an obvious compatibility\n>condition. It has nothing to do with the nature of the two systems,\n\nThis is not correct. The boundary separates the observed system\nfrom the observer, and von Neumann is very clear about this:\n"We must always divide the world into two parts, the one being\nthe observed system, the other the observer." p.420\n\nPlease note that he says "must".\n\nPlease acknowledge that, according to von Neumann,\nthe boundary separates the observed system from the observer,\nand does not merely separate one physical system from another.\n\nPlease acknowledge that von Neumann\'s view, that the task of\nphysics is to provide relations between the results of\nexperiments, is crucial to understanding why the boundary,\nbetween the observer and the observed system, must be\nplaced somewhere. It is quite clearly the observer who\nhas access to the results of measurements, and who\nseeks the relations between them, and that is why there\nhas to be a boundary between the observer, who examines\nthe results, and the observed system, which furnishes\nthe observer with the results.\n\nIt is only if you reject von Neumann\'s view, that the task of physics\nis to provide relations between the results of experiments, and\nsuppose instead that the task of physics is to describe "what\'s really\ngoing on", that you can think that measurements and their results\ndon\'t have a privileged role within physics. It is only if you\nthink that measurements don\'t have a privileged role, that you\ncan drop the demand that the boundary be placed somewhere.\n\nNow you have done this - rejected von Neumann\'s view of\nphysics, and you demand an ontology, that is, a description\nof the world as it really is in itself and considered\nin isolation from the manner in which we know about it,\nnamely through the results of experiments. As I said\nearlier, I will tell you in the other thread where you\ncan find the proof that your dream is hopeless.\n\nFor the moment, please acknowledge that this is indeed what you are\ntrying to do, and that von Neumann didn\'t consider your task - a\ndescription of nature in which measurements and the observer have\nno privileged role - to be a part of physics.\n\n>You might care to notice that von Neumann carefully avoids to invoke\n>either the \'mind\' or the observer\'s \'knowledge\'.\n\nHe refers to the "process of the subjective perception" on page\n418, and, on page 421, divides the world into three parts:\n\'I [is] everything up to the retina of the observer, II his\nretina, nerve tracts and brain, III his abstract "ego."\'\n\nBy the \'abstract "ego"\' he refers to the mind of the observer.\n\nI recommend that you read the relevant parts of the book\nbefore making statements about what he doesn\'t refer to.\n\n>Von Neumann simply argues that the collapse is consistent with the\n>psycho-physical parallelism (to the extent that one can define the\n>latter by the assertion that the \'\'boundary can be pushed arbitrarily\n>into the interior of the body of the observer\'\').\n\nThat is not how he defines the principle of psycho-physical\nparallelism. He defines it, on page 419, as the principle\n"that it must be possible to describe the extra-physical\nprocess of the subjective perception as if it were in\nreality in the physical world - i.e., to assign to its\nparts equivalent physical processes in the objective\nenvironment, in ordinary space."\n\n\n>... argument does not require a body or a brain; it is true wherever\n>the boundary is placed, for example when the boundary is placed\n>between the exposed photographic plate and the process developing\n>the plate to see the picture.\n\n>Thus the psycho-physical parallelism is completely inessential for\n>the interpretation of the collapse.\n\nHe says, on page 418, that the principle of psycho-physical parallelism\n"is a fundamental requirement of the scientific viewpoint". On\npage 421, he says "The danger lies in the fact that the principle\nof the psycho-physical parallelism is violated, so long as it\nis not shown that the boundary between the observed system and\nthe observer can be displaced arbitrarily in the sense given\nabove."\n\nClearly, he doesn\'t want the principle to be violated, and regards\nit as rather important, unlike you. Your claim that he considered\nit "completely inessential for the interpretation of the collapse"\nis incorrect. In fact, he devotes the rest of the chapter, indeed\nthe rest of the book, to showing that the collapse postulate does\nnot in fact violate the principle of psycho-physical parallelism.\nIn doing so, he clearly separates the world into three parts -\none being everything outside the observer\'s brain, another\nbeing the observer\'s brain, and the third being the observer\nhimself, namely the observer\'s mind, or as he calls, it\nthe \'abstract "ego"\'. I highly recommend that physicists\nread this book. It\'s a very good book.\n\n>> He also didn\'t have the "subjective means bad" attitude of modern\n>> physicists, and was aware that what we deal with in physics is\n>> not "the real world", but rather with subjective observations:\n>> "Indeed experience only makes statements of this type: an observer\n>> has made a certain (subjective) observation; and never any like\n>> this: a physical quantity has a certain value." p.420\n\n>Von Neumann is more careful in his use of language than you in your\n>interpretation of his words.\n\n>There is a difference between \'experience\' and \'experiment\'.\n>The former is a psychological concept; the latter is a concept\n>of physics.\n\n>An experience produces subjective sensory perceptions;\n>an experiment produces recorded values of physical quantities.\n\nAnd the first is bad, and banned from discussion of physics,\nwhile the second is good, and may be talked about.\n\n>> For him, the distinction between the observer and the observed\n>> was of fundamental importance in quantum mechanics; this is\n>> the so-called quantum/classical boundary:\n>> "That is, we must always divide the world into two parts,\n>> the one being the observed system, the other the observer. ...\n>> The boundary between the two is arbitrary to a large extent. ...\n\n>.. to such an extent that his observer can be an inanimate object\n>like a camera or a thermometer.\n\nNo; he spends considerable time in chapter six explaining that the\nsubjective experience of the observer is very important and has to\nbe considered carefully, to avoid violating the principle of\npsycho-physical parallelism. You keep pretending that this is not\nthe case, claiming that he never mentions the mind, when in fact\nhe does, and claiming that he considered subjective experience\nunimportant, when he thinks it\'s important enough to devote an\nentire chapter to.\n\nYou want to give the impression that von Neumann agreed with your\ninterpretation, because you can thereby claim some credibility for\nyour personal views. However, von Neumann\'s interpretation of\nquantum mechanics was that it is there to furnish us with relations\nbetween the results of experiments, while your interpretation is\nthat measurements have no privileged role in physics, and that\nquantum mechanics is there to give us a description of the world\nas it really is. These viewpoints are in complete opposition.\n\n>> but this does not change the fact that in each method of description\n>> the boundary must be placed somewhere, if the method is not to\n>> proceed vacuously, i.e., if a comparison with experiment is to be\n>> possible." p.420\n>>\n>> So, from von Neumann\'s point of view, to use a "wavefunction of the\n>> universe" would be to proceed vacuously.\n\n>Only in this last statement I agree with your interpretation of\n>his position.\n\nAt last. I was beginning to think that you would continue to stick\nto the "von Neumann agrees with me" story until you found yourself\nsaying that true is false.\n\n>At this point my view of quantum mechanics differs from his.\n>And with good grounds.\n\nThe grounds are the following:\n\nYou want a description of the world in which the observer is just\nanother subsystem of the whole world, and in which measurement\nhas no privileged role.\n\nVon Neumann believed that the task of physics is to furnish\nrelations between the results of experiments, and so measurements\nand their results must have a privileged role in the formalism.\n\nVon Neumann\'s view is only consistent if there is a boundary\nbetween the observer and the observed system.\n\nYou do not recognise this boundary as important because you\nfundamentally disagree with von Neumann about what the\ntask of physics is. You believe that the task of physics\nis to describe the world as it really is, and so it should\nbe possible to describe the entire world as it really is,\nand hence have a "wavefunction of the universe."\n\nIs this accurate?\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>rof@maths.tcd.ie wrote:
>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>
>>>rof@maths.tcd.ie wrote:
>>
>> I may have confused the official Copenhagen interpretation with
>> what Bohr, Heisenberg, von Neumann and so on believed. As Scerir
>> pointed out in this thread, Heisenberg said "The discontinuous change
>> in the probability function, however, takes place with the act
>> of registration, because it is the discontinuous change
>> of our knowledge in the instant of registration that has its
>> image in the discontinuous change of the probability function.",
>> Hiesenberg, "Physics and Philosophy", 1958
>I commented that already. the 'acto of registration' happens on the
>photographic plate or in the eye, not in the mind, and is simply
>the irreversible magnification due to dissipation by interaction with
>a macroscopic detector. It is objective and has no connection to
>any 'knowledge'.
>... only that your interpretation of what he said in terms of
>knowledge is a postmodern interpretation, and either the
>Copenhagen interpretation nor Heisenberg's intention.
My apologies for taking so long to reply. Various collegiate
matters have occupied my attention for the last week.
Anyway, to summarize:
Heisenberg said "it is the discontinuous change of our knowledge
in the instant of registration that has its image in the discontinuous
change of the probability function."
My interpretation of this is: it is the discontinuous change of our
knowledge in the instant of registration that has its image in the
discontinuous change of the probability function.
Your interpretation of it is: it is _not_ the discontinuous change
of our knowledge in the instant of registration that has its image
in the discontinuous change of the probability function. It has no
connection to any 'knowledge'.
Then you declare that your arguments are excellent, and
that my interpretation of what Heisenberg said is "a postmodern
interpretation".
Now, what appears to me to be happening here is that your position,
that Heisenberg believed that collapse "is objective and has no
connection to any 'knowledge'", is entirely incorrect, and that
Heisenberg said so himself, and that when confronted with this fact,
you gave the impression that his statements required "interpretation".
You then "interpreted" his statement to mean exactly the opposite
of what he said. Then you accused me of having a distorted
interpretation because I took Heisenberg at his word, and
proceeded to insult me by calling my interpretation postmodern.
Heisenberg was even more explicit about the connection to knowledge,
which you deny he believed in:
"This probability function represents a mixture of two things,
partly a fact and partly our knowledge of a fact. It represents a
fact in so far as it assigns at the initial time the probability
unity (i.e., complete certainty) to the initial situation: the
electron moving with the observed velocity at the observed position;
'observed' means observed within the accuracy of the experiment.
It represents our knowledge in so far as another observer could
perhaps know the position of the electron more accurately. The error
in the experiment does - at least to some extent - not represent a
property of the electron but a deficiency in our knowledge of the
electron. Also this deficiency of knowledge is expressed in the
probability function." Heisenberg, Physics and Philosophy
He said this in chapter three, and goes on to say:
"We can, for instance, predict the probability for finding the
electron at a later time at a given point in the cloud chamber. It
should be emphasised, however, that the probability function does
not in itself represent a course of events in the course of time.
It represents a tendency for events and our knowledge of events."
A little further, he says:
"The observation ... breaks the determined continuity of the
probability function by changing our knowledge of the system."
You will, of course, deny that you intended any insult when
you used the word postmodern, and you will claim that everything
Heisenberg said above is completely consistent with your
interpretation, which is that the wavefunction has nothing
at all to do with knowledge. Then you'll claim that your
position is not absurd, despite the fact that it obviously
is. You will probably focus on the occurrence of the word
"fact" in Heisenberg's quote above, and claim that its
appearance demonstrates that you are right, while
ignoring the parts where he says things like "the probability
function ... represents a tendency for events and our knowledge of
events."
Now, I should point out here that your claim that your arguments
are excellent is incorrect; that they are, as I said they would be,
unconvincing even to yourself. You have adopted a position where
you interpret a statement to mean its opposite, and you have done
this not because you find that it is an excellent argument, but
because you can't allow yourself to change your mind in public,
because you fear that there is some humiliation associated with
that. Let me assure you that anybody whose respect for you drops
when he sees you change your mind is a person whose respect is
not worth having. A reasonable person would have more respect
for you if you showed the ability to change your mind, and
therefore learn, rather than sticking to a position long
after it has become ridiculous.
By the way, when you claimed that Heisenberg didn't think the
'act of registration' happened in the mind:
>... the 'act of registration' happens on the
>photographic plate or in the eye, not in the mind, and is simply
>the irreversible magnification due to dissipation by interaction with
>a macroscopic detector.
you were wrong.
Heisenberg agrees with me that the "act of registration"
does indeed occur in the mind of the observer, and not on the
photographic plate:
"Therefore, the transition from the 'possible' to the 'actual' takes
place during the act of observation. If we want to describe what
happens in an atomic event, we have to realize that the word 'happens'
can apply only to the observation, not to the state of affairs
between two observations. It applies to the physical, not the
psychical act of observation, and we may say that the transition
from the 'possible' to the 'actual' takes place as soon as the
interaction of the object with the measuring device, and thereby
with the rest of the world, has come into play; it is not connected
with the act of registration of the result by the mind of the
observer. The discontinuous change in the probability function,
however, takes place with the act of registration, because it is
the discontinuous change of our knowledge in the instant of
registration that has its image in the discontinuous change of the
probability function."
The act which we are talking about is, according to Heisenberg,
"the act of registration of the result by the mind of the observer",
and it is this that corresponds to the "discontinuous change in the
probability function". What happens at the photographic plate is
the transition from 'possible' to 'actual'.
Since this all happens in a chapter called "The Copenhagen
Interpretation of Quantum Theory", and since Heisenberg is, I hope
you will agree, competent to tell us what the Copenhagen interpretation
is, perhaps you would be kind enough to acknowledge that I have
told you something about the Copenhagen interpretation that you
didn't previously know, namely that according to that interpretation,
collapse is associated with the "act of registration of the result
by the mind of the observer".
You can read the chapter online at:
http://www.marxists.org/reference/subject/philosophy/works/ge/heisenb3.htm
>> With due respect, and I sincerely mean no offense, I believe
>> that you have been infected
>Whatever I am infected with, I hope it is highly infectuous
>and incurable, so that it spreads and has a lasting effect.
You have become infected with it precisely because it is
highly infectious, and because it has spread far and has
had a lasting effect.
It is, however, not incurable, although the patients
certainly don't like the medicine.
>> with the mental disease that I
>> ranted about in an earlier post:
>> http://groups-\beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source
>This is a long post, I cannot recognize myself reflected in it.
>Neither do I recognize signs of a mental disease in my behavior.
It is extremely rare that one spots a mental disease in oneself,
but let me assure you that you are a textbook case.
>> My understanding is that this is why you react so negatively to the
>> suggestion that the wavefunction describes knowledge.
>I followed the historical development of the interpretations of QM
>quite closely, reading hundreds of papers, to be able to make up my
>own mind of how _I_ should interpret QM (and other physics).
>In the discussions on s.p.r., I share my insights for those who might
>wish to learn from it. I simply think that phrasing objective
>descriptions in a psychological language, making them dependent on
>mental processes, is neither necessary to understanding nor does it
>serve any useful purpose. There is nothing inherently absurd about
>this assessment.
These are your boasts about how well-read you are (despite your
rather poor knowledge of the Copenhagen interpretation), your
beliefs and your opinions. You cannot claim that your interpretation
was shared by the founders of quantum mechanics. I will acknowledge
that you are a strict conformist, but what you are conforming to
is the modern desire to rid physics of any reference to subjective
experience, and thereby achieve "purity". This desire spreads like
a disease, which comes complete with instructions to ridicule
those who insist, as did Heisenberg, Bohr and von Neumann, that
subjective experience must be considered carefully and not
ignored. Objectivity has become a religion, and those who
insist that physicists should completely ignore subjective
experience have become fanatical and have been allowed to take over.
>>>>A definition
>>>>of measurement isn't missing because measurement is the
>>>>acquisition of new knowledge.
>>
>>>This is not a good definition since it is never specified what
>>>constitutes acquisition of knowledge.
>>
>> Acquisition of knowledge is what happens when you look at the
>> measuring device and see where the pointer is pointing. That's
>> perfectly precise for a normal person, but it seems insufficient
>> to somebody who wants to know about "the real objective world".
>It seems that it is sufficient for you. But it is insufficient for me.
>I want a mathematical model of reality within which one can clearly
>say what exists, what is an experiment, an observer, a measurement,
>a record, etc., in such a way that one can predict in principle which
>experiments give outcomes with which accuracy.
>Such arguments are common in qunatum mechanical foundations (e.g.
>discussions of the Heisenberg microscope) but currently based on
>informal notions of experiment, observer, measurement, record
>only.
>My goal is to put the foundations of physics on a basis similarly to
>the foundations of mathematics, where the whole logical process of
>coherent deduction can be modelled on a metalevel and gives clarity
>to the foundations of mathematics that is missing in physics.
>And I think that such foundations are possible and will provide the
>same clarity for physics.
Well, they are not possible. What you are looking for is an ontology.
I will explain in the other thread, "Why physicists should pay
attention to the mind", where it is that you can find the proof
that this task is hopeless. You will, however, have to pay attention
to the mind to understand the proof.
>> Of course, if this is pointed out to them, they
>> deny it, saying "Why not at all - I am the most
>> reasonable of fellows.
>Everyone who has a sensible point of view argues that way,
>including you.
Reasonableness is to be demonstrated in one's words
and actions. One should not proclaim that one is great
and reasonable, that one has read hundreds of papers
and has excellent arguments. A person may seek to
acquire credibility by stating that they deserve it,
but such a person actually deserves less credibility.
One should give one's arguments and let others judge
if they are good or bad; if one has read many papers,
it should be shown by giving knowledgeable answers.
>Your argument sounds as if you are not claiming that the wave function
>collapse is about the change of real knowledge of real minds,
>but about how knowledge should change if someone observes something
>and acts completely rational. But then it becomes a moral statement
>completely outside science.
>However, the collapse was formulated by the founders as a necessity to
>make sense of quantum mechanics, and not as a postulate about moral
>standards for maintaining knowledge in minds.
Now, morality is about good and evil. The question of how one
should use the knowledge one has to make the best predictions
about the results of experiments is a strategic question, which
has nothing to do with good or evil, and hence has nothing
to do with morality. You must have confused "What I have to do
in order to accomplish task X" with "What it makes me a good person
to do." It seems to me that it would require an almost
superhuman ability to become confused, to make that mistake.
It is certainly not an excellent argument.
>>>Furthermore, knowledge depends on subjective decisions to trust
>>>a measurement. If we discard one as an artifact, there is no
>>>collapse. How can the collapse depend on such subjective issues?
>>
>> In the "wavefunction represents knowledge" interpretation, the
>> wavefunction is not an objective thing,
>How then can a non-objective thing change in time in an objective way???
>(Please don't be offended by the three ?s!)
Consider, for example, a random walk in one dimension. Suppose I
see where the particle is at time and you see where it is at
time 1. At time 10, we both look at where the particle is, but
don't look at it between the first time we see it and the final
time. We each use the same equation to describe the time-evolution
of the probability distribution for the position of the
particle, and hence the probability distribution evolves in
an objective way (recall - objective means the same for
everybody, subjective means differs from person to person). The
probability distribution, however, is subjective, because
you use a different one to mine - yours is a \delta function
at time 1, while mine is a \delta function at time and is
spread out at time 1. That is an example of how a non-objective
thing can change in time in an objective way.
>> but different observers
>> will use different wavefunctions, depending on what knowledge they
>> have about the system.
>If I know nothing about an experiemnt, which wave function should I use?
>Should I use instead of a pure state the microcanonical ensemble,
>suggested by many statistical mechanics treatments as noninformative
>prior? Then I make observations and find that they are not in accordance
>with the predictions of my ensemble since it is born of ignorance
>rather than knowledge...
You will use a density matrix if you know absolutely nothing about
the preparation of the system.
>> The "collapse" is what happens when the
>> observer receives new knowledge, and updates his mathematical
>> representation of his knowledge to reflect the new knowledge that
>> he has.
>This must be a ficticious observer invented to suit your interpretation.
>A real observer with a real mind has no wave function in his mind --
>that changes unitarily according to a differential equation whose
>solution requires a computing capacity much beyond the mind's power, and
>once it sees a measurement (any look out of the window, or only a
>careful look at the detector needle to be sure of the third decimal?)
>it computes the solution of the corresponding eigenvalue problem to
>find out how the wave functions must be collapsed to be consistent.
>At least you won't find that when interrogating the most competent
>experimental physicists who know how they update their knowledge.
Your sneering isn't justified. The statement regarding collapse
above is exactly what the Copenhagen interpretation states. If
you claim that you weren't sneering, then you have to also claim
that you really thought I was suggesting that people solve
Schrodinger's equation in their mind in the course of
everday life. You did not really think that.
>> Recall that subjective doesn't mean simply bad.
>I never assumed that. But subjective means outside the realm of science,
>unless that subjectivity can be explained and predicted by models of how
>it arises from something objective, such as the subjective
>observer-dependence in special and general relativity.
So you appear to be saying that you think the processes in
the brain provide a sufficient explanation of subjective
experience. If you do, then you cannot claim that von Neumann
agrees with you:
"It is inherenly entirely correct that the measurement or the related
process of the subjective perception is a new entity relative to
the physical environment and is not reducible to the latter. Indeed,
subjective perception leads us into the intellectual inner life of
the individual, which is extra-observational by its very nature."
von Neumann, Mathematical Foundations of Quantum Mechanics, p. 418
>>>At the time of Bohr, von Neumann and Wigner, the collapse meant
>>>something objective, though it might have been related to the mind
>>>in some unspecified way.
>>
>> I have to disagree with that, although I do not mean it in an
>> adversarial way. The relation to the mind was perfectly clear and
>> very specific for these people, at least by the '50s. Also, since
>> they understood that the wavefunction represented knowledge, the
>> collapse wasn't an objective thing for them.
>Please support your claims by solid evidence!
I do support my claims with solid evidence, but you consistently
pretend that I haven't, which is a dishonest thing for you to
do. The quotations from Heisenberg above where he explicitly
says that collapse corresponds to the reception of knowledge
by the observer, and von Neumann's statements about psycho-physical
parallelism, are solid evidence.
>>>>>Von Neumann takes the collapse as an axiom, hence also testifies to its
>>>>>reality.
>>>>
>>>>He uses it as an axiom, but that doesn't mean that he claimed that
>>>>the wavefunction didn't represent knowledge.
>>
>>>But he certainly didn't claim that the wavefunction does represent
>>>knowledge.
>>
>> As I quoted before,
>>
>> "Let us assume that we do not know the state of a system, S, but
>> that we have made certain measurements about the state of S and
>> know their results. In reality, it always happens this way, because
>> we can learn something about the state of S only from the results
>> of measurements. More precisely, the states are only a theoretical
>> construction, only the results of measurements are actually available,
>> and the problem of physics is to furnish relationships between the
>> results of past and future measurements." p. 337
>>
>> This is exactly a claim that the wavefunction represents
>> knowledge.
>I cannot understand how you can possibly arrive at this statement.
>If your claim were true, what von Neumann actually said (first sentence)
>would mean: ''Let us assume that we do not know what we know (the state
>of S)'', and then he deduces correctly from this (obviously false)
>premise everything he likes.
No; if my claim were true, what von Neumann said would not mean that.
You are using an argument of the form: "If what you said were true,
then X", where X is a contradiction. However, you didn't even attempt
to show how X would follow from the antecedent. You merely stated
that X would follow, as though the fact that you stated it were
a sufficient proof.
>>>No. A proposition is a statement that is true or false,
>>>or undecidable. It has nothing to do with whether or not
>>>anyone knows (or claims to know) its truth or falsehood.
>>
>> Logic, which includes the propositional calculus, is the formal
>> science of inference, and inference can only be done by the mind.
>No. It is routinely (and more reliably) done by computers.
...
>> The desire to assert that logic has nothing to do with the mind is,
>> I believe, rooted in the primitive notion of nobility,
>No. For example, it can be rooted in the fact that logic can
>be performed by microchips, which have little to do with mind as
>commonly understood.
I previously said:
>>I have to anticipate how somebody could reject something as
>>simple as this. The only thing I can think of is that somebody
>>might claim that, since computers can be programmed to do
>>symbolic manipulation, logic has nothing to do with thinking.
>>
>>The problem with this argument is that the fact that computers
>>can do the symbolic manipulation associated with formal logic
>>indicates only that logic can be represented by symbolic
>>manipulations, but establishes nothing about what those
>>symbolic manipulations describe. Logic was established
>>in its present form because those symbolic manipulations
>>describe certain rules of correct thinking.
Now, you did exactly what I predicted - said that logic can be done
by computers and therefore has nothing to do with thinking. You
ignored the fact that I had anticipated this argument and explained
why it is wrong. I will explain again, in more detail, why it is
wrong, and I would ask that the next time you reply, you either
address the argument that I give, or admit that logic does have a
connection to the mind.
The more detailed version of the explanation is:
Yes, computers can do symbolic manipulation, and the
rules of inference and deduction, by which we produce
new knowledge from existing knowledge, have been
characterized accurately enough to be expressed
symbolically. However, the fact that computers can
manipulate symbols does not mean that logic is not
a characterization of inference as done by thinking
people.
I said: The formal system X describes Y.
You said: The formal system X does not describe Y because X
can be implemented in a computer.
In the present case, X refers to symbolic logic and Y refers
to inference, which is what happens when a person goes from
the knowledge that "All men are mortal" and the additional
knowledge that "Socrates is a man" to the knowledge that
"Socrates is mortal".
We could, however, replace X with "The Euler equations", and
Y with "Fluid dynamics", and your argument would just be
as invalid:
Me: The Euler equations describe fluid dynamics
You: The Euler equations don't describe fluid dynamics because the
Euler equations can be implemented in a computer.
In fact, when we use computers to do symbolic logic, we program
them with rules which are specifically chosen because they
match "natural inference", meaning inference done by humans
in the course of their thinking. The rules of symbolic logic
were constructed to describe correct deductive thought, and
computers can be used to manipulate the symbols to produce
conclusions that we trust because we know that, if we carefully
examine each symbolic manipulation that the computer does,
it will agree with a deduction that a human could have
made without the help of the computer.
Please let me know if you understand this, or if I have to
explain it in further detail.
>> I was
>> asserting that von Neumann was aware that we only know the results
>> of measurements,
>I agree with this assertion. It is in flat contradiction with your claim
>that the wave function represents our knowledge. For a wave function
>needs infinitely many bits to specify, while the results of measurements
>(according to what you just stated, the _only_ thing we know about the
>system) can be coded in the finite number of bits making up a protocol.
Any wavefunction that can be written down by a human has a finite
Kolmogorov complexity, otherwise the human wouldn't be able to
write it down. Finite Kolmogorov complexity means finite information.
>> "More precisely, the states are only a theoretical construction,
>> only the results of measurements are actually available, and the
>> problem of physics is to furnish relationships between the results
>> of past and future measurements. To be sure, this is always
>> accomplished through the introduction of the auxilliary concept
>> "state", but the physical theory must then tell us on the one hand
>> how to make from past measurements inferences about the present
>> state, and on the other hand, how to go from the present state to
>> the results of future measurements." p. 337
>>
>> What he is saying is that, in quantum mechanics, what we call
>> a "state" is actually a theoretical construction
>but with the same objective status as mass, temperature, momentum,
>charge distribution, etc. of an object. These are also theoretical
>constructs used to organize our observations.
Almost, but not quite. Different observers will assign different
states to the same system, so it is not quite as objective
as mass or temperature.
>> Basically, you are saying that knowledge is a dirty thing,
>No. You read this into my statements. Knowledge has nothing to
>do with cleanliness. Dirty things can be washed; I wouldn't know
>how to wash knowledge.
Bravo, Arnold. You truly are the master of the metaphor.
>Knowledge is what we (think we) know. This may be a number of
>experimental results to within some accuracy, an approximate
>description of a quantum mechanical state, the rough
>temperature distribution in a room, the behavior of a piece of
>equipment according to the manufacturer's manual (perhaps
>corrected by our own calibration experiments), the weight,
>length and age of the persons working in a room, etc.
>It is (in some idealization) something describable in a finite
>string of symbols.
>On the other hand, fundamental physics is about the mathematical
>model of Nature resulting from such information. This model
>(von Neumann's ''theoretical construction'') is inferred from
>observations and contains more accurate parts, less accurate parts,
>probably a few mistaken parts, and completely unknown parts -
>it is like a 17th century world map, but instead for the
>physical phenomenon under study. The objective state of the
>system is one of the polethora of states compatible with the
>asvailable information - which one, we don't know. But if we know
>sufficiently much, all compatible states are approximately the same,
>so working with any particular of them will give good predicitions.
>Nothing here prevents one of taking the system to be the whole universe.
>The state of the universe must simply be compatible with all details
>we observed in the parts of the universe accessible to our experiments.
It would be helpful if you took care to distinguish between your
own personal interpretation of quantum mechanics and the interpretation
which you claim von Neumann had. Here, I will point out that while
you claim that "fundamental physics is about the mathematical model
of Nature", von Neumann claims that "the problem of physics is
to furnish relations between the results of past and future
measurements." p.337
You will, mostly likely claim that these two positions are compatible,
but they indicate a completely different way of looking at the
task of physics. You want a mathematical model of nature itself,
and think that measurements and their results should be a part
of the model, and shouldn't have any privileged status within
the theory. You are demanding more from fundamental physics than
von Neumann did, who simply wanted relations between the
results of measurements.
>> Also, when you say "I don't buy this," are you saying that
>> you don't believe that von Neumann held this opinion,
>> namely that the principle of psycho-physical parallelism
>> tells us that we can consider what we are observing
>> to be within our own bodies? Because he did:
>>
>> "We wish to measure a temperature. ... [we can] say: this
>> temperature is measured by the thermometer. ... we can
>> calculate the resultant length of the mercury column,
>> and then say: this length is seen by the observer. Going
>> still further, and taking the light source into consideration ...
>> we would say: this image is registered by the retina of the
>> observer. And were our physiological knowledge more precise
>> than it is today, we could go still further, tracing the
>> chemical reactions which produce the impression of this image on
>> the retina, in the optic nerve tract and in the brain, and then in
>> the end say: these chemical changes of his brain cells are
>> perceived by the observer." p.419
>>
>> "That this boundary can be pushed arbitrarily into the interior
>> of the body of the observer is the content of the principle
>> of the psycho-physical parallelism." p.420
>Von Neumann says that collapse happens in each particular physical
>system (defined by its boundary), but that consistency requires that
>if we regard a particular system as part of a bigger system then
>the collapse of the larger system must give, for the smaller system,
>results compatible with the collapse of the smaller system considered
>by itself. This is nothing more than an obvious compatibility
>condition. It has nothing to do with the nature of the two systems,
This is not correct. The boundary separates the observed system
from the observer, and von Neumann is very clear about this:
"We must always divide the world into two parts, the one being
the observed system, the other the observer." p.420
Please note that he says "must".
Please acknowledge that, according to von Neumann,
the boundary separates the observed system from the observer,
and does not merely separate one physical system from another.
Please acknowledge that von Neumann's view, that the task of
physics is to provide relations between the results of
experiments, is crucial to understanding why the boundary,
between the observer and the observed system, must be
placed somewhere. It is quite clearly the observer who
has access to the results of measurements, and who
seeks the relations between them, and that is why there
has to be a boundary between the observer, who examines
the results, and the observed system, which furnishes
the observer with the results.
It is only if you reject von Neumann's view, that the task of physics
is to provide relations between the results of experiments, and
suppose instead that the task of physics is to describe "what's really
going on", that you can think that measurements and their results
don't have a privileged role within physics. It is only if you
think that measurements don't have a privileged role, that you
can drop the demand that the boundary be placed somewhere.
Now you have done this - rejected von Neumann's view of
physics, and you demand an ontology, that is, a description
of the world as it really is in itself and considered
in isolation from the manner in which we know about it,
namely through the results of experiments. As I said
earlier, I will tell you in the other thread where you
can find the proof that your dream is hopeless.
For the moment, please acknowledge that this is indeed what you are
trying to do, and that von Neumann didn't consider your task - a
description of nature in which measurements and the observer have
no privileged role - to be a part of physics.
>You might care to notice that von Neumann carefully avoids to invoke
>either the 'mind' or the observer's 'knowledge'.
He refers to the "process of the subjective perception" on page
418, and, on page 421, divides the world into three parts:
'I [is] everything up to the retina of the observer, II his
retina, nerve tracts and brain, III his abstract "ego."'
By the 'abstract "ego"' he refers to the mind of the observer.
I recommend that you read the relevant parts of the book
before making statements about what he doesn't refer to.
>Von Neumann simply argues that the collapse is consistent with the
>psycho-physical parallelism (to the extent that one can define the
>latter by the assertion that the ''boundary can be pushed arbitrarily
>into the interior of the body of the observer'').
That is not how he defines the principle of psycho-physical
parallelism. He defines it, on page 419, as the principle
"that it must be possible to describe the extra-physical
process of the subjective perception as if it were in
reality in the physical world - i.e., to assign to its
parts equivalent physical processes in the objective
environment, in ordinary space."
>... argument does not require a body or a brain; it is true wherever
>the boundary is placed, for example when the boundary is placed
>between the exposed photographic plate and the process developing
>the plate to see the picture.
>Thus the psycho-physical parallelism is completely inessential for
>the interpretation of the collapse.
He says, on page 418, that the principle of psycho-physical parallelism
"is a fundamental requirement of the scientific viewpoint". On
page 421, he says "The danger lies in the fact that the principle
of the psycho-physical parallelism is violated, so long as it
is not shown that the boundary between the observed system and
the observer can be displaced arbitrarily in the sense given
above."
Clearly, he doesn't want the principle to be violated, and regards
it as rather important, unlike you. Your claim that he considered
it "completely inessential for the interpretation of the collapse"
is incorrect. In fact, he devotes the rest of the chapter, indeed
the rest of the book, to showing that the collapse postulate does
not in fact violate the principle of psycho-physical parallelism.
In doing so, he clearly separates the world into three parts -
one being everything outside the observer's brain, another
being the observer's brain, and the third being the observer
himself, namely the observer's mind, or as he calls, it
the 'abstract "ego"'. I highly recommend that physicists
read this book. It's a very good book.
>> He also didn't have the "subjective means bad" attitude of modern
>> physicists, and was aware that what we deal with in physics is
>> not "the real world", but rather with subjective observations:
>> "Indeed experience only makes statements of this type: an observer
>> has made a certain (subjective) observation; and never any like
>> this: a physical quantity has a certain value." p.420
>Von Neumann is more careful in his use of language than you in your
>interpretation of his words.
>There is a difference between 'experience' and 'experiment'.
>The former is a psychological concept; the latter is a concept
>of physics.
>An experience produces subjective sensory perceptions;
>an experiment produces recorded values of physical quantities.
And the first is bad, and banned from discussion of physics,
while the second is good, and may be talked about.
>> For him, the distinction between the observer and the observed
>> was of fundamental importance in quantum mechanics; this is
>> the so-called quantum/classical boundary:
>> "That is, we must always divide the world into two parts,
>> the one being the observed system, the other the observer. ...
>> The boundary between the two is arbitrary to a large extent. ...
>.. to such an extent that his observer can be an inanimate object
>like a camera or a thermometer.
No; he spends considerable time in chapter six explaining that the
subjective experience of the observer is very important and has to
be considered carefully, to avoid violating the principle of
psycho-physical parallelism. You keep pretending that this is not
the case, claiming that he never mentions the mind, when in fact
he does, and claiming that he considered subjective experience
unimportant, when he thinks it's important enough to devote an
entire chapter to.
You want to give the impression that von Neumann agreed with your
interpretation, because you can thereby claim some credibility for
your personal views. However, von Neumann's interpretation of
quantum mechanics was that it is there to furnish us with relations
between the results of experiments, while your interpretation is
that measurements have no privileged role in physics, and that
quantum mechanics is there to give us a description of the world
as it really is. These viewpoints are in complete opposition.
>> but this does not change the fact that in each method of description
>> the boundary must be placed somewhere, if the method is not to
>> proceed vacuously, i.e., if a comparison with experiment is to be
>> possible." p.420
>>
>> So, from von Neumann's point of view, to use a "wavefunction of the
>> universe" would be to proceed vacuously.
>Only in this last statement I agree with your interpretation of
>his position.
At last. I was beginning to think that you would continue to stick
to the "von Neumann agrees with me" story until you found yourself
saying that true is false.
>At this point my view of quantum mechanics differs from his.
>And with good grounds.
The grounds are the following:
You want a description of the world in which the observer is just
another subsystem of the whole world, and in which measurement
has no privileged role.
Von Neumann believed that the task of physics is to furnish
relations between the results of experiments, and so measurements
and their results must have a privileged role in the formalism.
Von Neumann's view is only consistent if there is a boundary
between the observer and the observed system.
You do not recognise this boundary as important because you
fundamentally disagree with von Neumann about what the
task of physics is. You believe that the task of physics
is to describe the world as it really is, and so it should
be possible to describe the entire world as it really is,
and hence have a "wavefunction of the universe."
Is this accurate?
R.
Arnold Neumaier
Jun10-05, 11:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>> Seratend wrote:\n>\n>> Arnold Neumaier wrote:\n>>\n>>It would be good if you could give a concise formal definition of\n>>what you consider to be _the_ QM formalism. One can state everything\n>>in a few axioms, but it seems that your set of axioms is different from\n>>what I hold to be the common view.\n>>\n> The 6 usual postulates + the mapping of the observables outcomes\n> (defined by the collapse postulate) to the outcomes of real systems.\n> That\'s all.\n\nPlease give an explicit and complete formal statement of what you\nconsider to be the 6 usual postulates + the mapping, so that we have\ncommon ground for discussion.\n\nMuch of what you say depends on separating the formalism from the\ninterpretation, so I\'d like to know precisely what you consider\npart of the formalism.\n\nSo please formulate your postulates such that the formalism\nconsists precisely of everything that can be logically\ndeduced from these postulates. Then I\'ll probe it with some\nquestions to ensure that it indeed may serve this purpose.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>> Seratend wrote:
>
>> Arnold Neumaier wrote:
>>
>>It would be good if you could give a concise formal definition of
>>what you consider to be _the_ QM formalism. One can state everything
>>in a few axioms, but it seems that your set of axioms is different from
>>what I hold to be the common view.
>>
> The 6 usual postulates + the mapping of the observables outcomes
> (defined by the collapse postulate) to the outcomes of real systems.
> That's all.
Please give an explicit and complete formal statement of what you
consider to be the 6 usual postulates + the mapping, so that we have
common ground for discussion.
Much of what you say depends on separating the formalism from the
interpretation, so I'd like to know precisely what you consider
part of the formalism.
So please formulate your postulates such that the formalism
consists precisely of everything that can be logically
deduced from these postulates. Then I'll probe it with some
questions to ensure that it indeed may serve this purpose.
Arnold Neumaier
Arnold Neumaier
Jun10-05, 11:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n>>>Note that in order to recover the probability law in the frequency of\n>>>outcomes we must have the independence of identical systems (hence, we\n>>>need a "preparation" to select the systems).\n>>\n>>But this is not satisfied in many experiments analyzed by quantum\n>>mechanics. For example, in an ion trap, one has the continuous\n>>measurement of a single system, in which the observation at different\n>>times can by no means considered to be observations of independent\n>>systems.\n>>\n> Where is the problem (logically)? (I may miss something).\n\nThe problem is that ensembles require _identically_ prepared\n_independent_ systems. An ion trap has (over a macroscopic\ntime interval) a _single_ system whose measurements are _not_\nindependent.\n\n\n> Do you mean\n> the collapse postulate is not satisfied in continuous measurements?\n\nOf course it isn\'t; but this wasn\'t my point.\n\n(Continuous measurement requires a description as a quantum stochastic\nprocess.)\n\n\n> Please note that when you say a continuous measurement over time of a\n> single system, you mean a single measurement that spans over time of\n> one instance of this system (the measurement has to be specified over\n> time and space or the equivalent observables to have a meaning).\n\nNo I mean a measurement of the single instance of this system at\nmany closely spaced instances of time.\n\n\n> For an example of what I mean, please see "When the unitary evolution\n> is derived from the collapse postulate in QM" in\n> http://www.physicsforums.com/showthread.php?t=72181\n\nWhat you say is that the Schr"odinger equation can be written as\n(H-E) psi = 0 in the extended Hilbert space. Your interpretation\nof this as a measurement is arbitrary, and contrary to the\nmeasurement concept in QM.\n\nFormally one can do many things, but meaningful is much less.\n\n\n>\n>\n>>Thus your conceptual framework for interpreting quantum mechanical\n>>experiments is too restrictive.\n>>\n> I do not understand on how it is too restrictive.\n> I am using the "shut up and calculate" view.\n\nWhich predicts a lot but explains nothing.\n\n\n> When we just have a single experiment trial in all the universe, we\n> just have the only interesting result: the unique set of results of\n> this experiment. There is no way to make predictions (this is also true\n> for CM).\n\nOne wants to (and can) predict some subset of results (e.g. those for\ntomorrow) from another subset (those of today). Just as one can predict\nthe path of a classical particle tomorrow if you know that of today.\nOr as you can predict the acceleration if you know position and velocity.\n\n\n> In addition, it raises an interesting question when we consider the\n> continuous measurement (we suppose all the interactions may be modelled\n> into interaction Hamiltonians, including the interactions of the\n> measurement apparatus):\n> Is it the state of the system that changes upon measurement due to the\n> collapse ("action" of the collapse) or is it the measured values\n> that change continuously upon time ("acknowledgement" of the\n> collapse)?\n\nThe state changes and the measured values change, due to the dynamics\nof the combined system plus environment.\n\n\n\n>>>A physical theory is mainly a choice of description (formally, we are\n>>>free to choose what we want)\n>>\n>>..but only if we don\'t care about the quality of our predictions.\n>>If we want to have good predictions, we must choose what quantum\n>>mechanics tells us to choose.\n>>\n> Every physical theory is a description choice. Good predictions is\n> somewhat a matter of taste (i.e. a practical choice).\n\nBut physicists have the taste to want good, accurate predictions.\nOtherwise they could have stayed with Aristoteles.\n\n\n> For example, take My god determinist theory: the collection of all the\n> "measurable" properties of the universe we may ever know. I call it\n> determinist because, labelling all the properties (and assuming the\n> collection of labels and properties is a ZF set: the only restiction),\n> it defines an implicit function. Does it make good predictions?\n\nIf there is a compact description of it, yes.\n\nThis is precisely what theory does - give a compact description of the\ncollection of all properties of a system (small or large or the whole\nuniverse).\n\nFor example, for a classical point particle over some time, one can take\nas observables all functional of the trajectory x(t). Theory tells that\ngiven six independent such observables (sufficiently well chosen),\nwe can predict all others. _Therefore_ the theory has high predictive value.\n\n\n\n\n>>What is a true outcome in a world described by quantum mechanics/\n>>\n> I have outcomes, hence they are true otherwise I cannot say (logical\n> meaning)\n\nSo your theory says very little.\n\nMy demands on good foundations are much higher:\n_Everything_ physicists talk about in real life must be\nfaithfully represented in the mathematical model.\n\n\n> Note we have an analogue problem in classical mechanics. How can we say\n> the proposition "a particle at position q at time t" is true? The\n> theory does not explain that, it uses it as QM does.\n\nThe theory specifies what is true in the model, and the\nexperimentalist can therefore check the model\'s adequacy.\n\n\n\n> In other words, I may choose to view the "reality" by different\n> mathematical concepts, this does not change the reality, just the\n> description of the reality. The only required property is the\n> conservation of the logic (as I do not know what to take to replace the\n> usual logic).\n\nThere must be an informal but quantitative correspondence between\nwhat is real in the model and what is real in Nature.\nThis correspondence is comminly called the interpretation.\n\n\n\n> Question, why does the computed frequency of head/tails of a coin\n> flipping is 50/50?\n> Is it due to a mysterious ontic property, or is it due to the coin\n> flipping experiment and its description choice (by saying p= n(a)/N)?\n\nIt is due to the formal definition of a fair coin-flip in the\nmathematical model. The probability is 1/2 because we _define_\nit that way. It has a priori _no_ relation to reality.\n\n\n>>You can read about my view of probability theory in my theoretical\n>>physics FAQ at\n>> http://www.mat.univie.ac.at/~neum/physics-faq.txt\n>>\n> I am surprised because, we seem to say almost the same (math results)\n> (except may be for your comments on Bayesian probability).\n> (Note: I have implicitly selected my preferred interpretation of your\n> words : )).\n>\n> However, I have a suggestion: you should explicitly say that the sample\n> space of the sequence of trials of a random variable of more than one\n> value (i.e. P=/=100%) is uncountable.\n\nOnly for an infinite sequence.\n\n> This property explains most of\n> the problems with probabilities and the "uniqueness"\n> (reproducibility) of each infinite sequence.\n\nThe problems are already there for large finite sequences.\nNo one ever observed an infinite sequence of trials.\n\n\n>>What I want as a basis of physics is a mathematically defined\n>>model of the world in which one can give unambiguous descriptions\n>>of all that matters in physics - physical systems, detectors, observers,\n>>individual observations, statistics about these observations,\n>>error analysis, etc. in such a way that it mirrors reality.\n>\n> I understand, however, there is more than one model.\n\nSo far, there is _no_ model coming close to what I want.\n\n\n>>Just as in matheamtical logic, one models the whole logical process\n>>in a concise mathematical framework.\n>>\n> This is a sort of compression process of the "god determinist\n> theory". Therefore, I hope you should accept loss of information\n> (description) in this process.\n\nNo. Mathematical logic loses no information in this modeling process,\nand Physical logic shouldn\'t either.\n\nLoss of information amounts to dissipation\nand should be explained rather than bbuilt in.\n\n\n> I think the QM theory is a concise one (may be too). The main problem\n> seems to be the preferred basis prediction. However, If we look at\n> general relativity we encounter an almost analogue problem: the\n> preferred frame to describe the events.\n\nThe preferred frame in GR is determined by the matter distribution\nin the universe. Only empty space has no preferred frame.\nThis is why we can speak unambiguously about the age of the universe.\n\n\n>>>>Although not very clearly separated in many discussions,\n>>>>these two processes happen never simultaneously but context\n>>>>dependent, and are of course only approximations to more\n>>>>realistic measurement situations.\n>>>>\n>>>>For example, in a Stern-Gerlach experiment, the system (silver atom)\n>>>>moves from the source along the magnet towards the screen with very\n>>>>good accuracy in a unitary (and indeed reversible) way. But a few\n>>>>split moments before it hits the screen it feels its interactions,\n>>>>and describing it as a closed system becomes hopelessly inaccurate.\n>>>>Instead, since the interaction time is very short, it can be\n>>>>described very accurately by an instantaneous collapse.\n>>>\n>>>Why do you say it becomes hopelessly inaccurate?\n>>\n>>Because the closed system in this setting contains >10^20 degrees of\n>>freedom, and we cannot model such systems accurately. We need the\n>>thermodynamic approximation, and with it an unavoidable inaccuracy\n>>in the response to the microscopic particle state.\n>>\n> You can describe the stern-gerlach experiment with an excellent\n> approximation as a closed quantum system.\n\nNo. In a closed quantum system, no collapse ever happens.\n\n\n>>>And How can you really\n>>>apply a collapse to a non closed system? In this case, don\'t you\n>>>think the collapse result (the outcome) should be independent of the\n>>>partial system description versus the whole system (including the\n>>>universe if necessary)?\n>>\n>>Look at the corresponding classical situation. A classical particle\n>>encounters a classical screen (say, a thin foil through which\n>>the particle will most likely escape) involving a huge number\n>>of classical particles bound by (and interacting with the\n>>incident particle) by empirical forces. It ends up in some state\n>>that is determined only probablilistically, once you ignore the\n>>detailed structure of the screen. But it ends up in a _definite_\n>>state.\n>\n> If you say it ends up in a _definite_ state you are implicitly\n> _defining_ a true property for this system instance\n\nOf course: This is a _classical_ system!\n\nI just wanted to say that the classical situation is already precisely\nanalogous to the quantum situation, and needs also a description\nin terms of collapse. So collapse has nothing to do with\nacknowledgment by anyone, but only with lack of control over the\nunmodelled environment.\n\nThere is no need to indroduce an additional level of observers,\nand neither is there a need in the quantum case.\n\n\n>>To describe it, however, without reference to the state of\n>>the screen, necessitates a probabilistic description and a collapse.\n>>\n> But you have a property for the screen, otherwise you cannot apply the\n> collapse ("the don\'t care property or if you prefer, the Identity\n> projector).\n\nIn this analogy, everything computable from the classical deterministic\nstate is a definite property of system, screen, or environment,\ndepending on which part of the state variables are used to compute it.\n\n\n>>The quantum system is - in the consistent experiment interpretation -\n>>completely analogous, except that the dynamics differs in detail\n>>significantly from the classical dynamics.\n>>\n> I am still working on this (I need to understand the logic).\n\nTake your time. It took me several years to gradually adapt to this\nnew point of view. Of course, I had to find out the hard way what\ncould be asserted and how far it reached, while you get everything\nspelled out. So you can take some short cuts...\n\n\nArnold Neumaier\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
>>>Note that in order to recover the probability law in the frequency of
>>>outcomes we must have the independence of identical systems (hence, we
>>>need a "preparation" to select the systems).
>>
>>But this is not satisfied in many experiments analyzed by quantum
>>mechanics. For example, in an ion trap, one has the continuous
>>measurement of a single system, in which the observation at different
>>times can by no means considered to be observations of independent
>>systems.
>>
> Where is the problem (logically)? (I may miss something).
The problem is that ensembles require _identically_ prepared
_independent_ systems. An ion trap has (over a macroscopic
time interval) a _single_ system whose measurements are _not_
independent.
> Do you mean
> the collapse postulate is not satisfied in continuous measurements?
Of course it isn't; but this wasn't my point.
(Continuous measurement requires a description as a quantum stochastic
process.)
> Please note that when you say a continuous measurement over time of a
> single system, you mean a single measurement that spans over time of
> one instance of this system (the measurement has to be specified over
> time and space or the equivalent observables to have a meaning).
No I mean a measurement of the single instance of this system at
many closely spaced instances of time.
> For an example of what I mean, please see "When the unitary evolution
> is derived from the collapse postulate in QM" in
> http://www.physicsforums.com/showthread.php?t=72181
What you say is that the Schr"odinger equation can be written as
(H-E) \psi = in the extended Hilbert space. Your interpretation
of this as a measurement is arbitrary, and contrary to the
measurement concept in QM.
Formally one can do many things, but meaningful is much less.
>
>
>>Thus your conceptual framework for interpreting quantum mechanical
>>experiments is too restrictive.
>>
> I do not understand on how it is too restrictive.
> I am using the "shut up and calculate" view.
Which predicts a lot but explains nothing.
> When we just have a single experiment trial in all the universe, we
> just have the only interesting result: the unique set of results of
> this experiment. There is no way to make predictions (this is also true
> for CM).
One wants to (and can) predict some subset of results (e.g. those for
tomorrow) from another subset (those of today). Just as one can predict
the path of a classical particle tomorrow if you know that of today.
Or as you can predict the acceleration if you know position and velocity.
> In addition, it raises an interesting question when we consider the
> continuous measurement (we suppose all the interactions may be modelled
> into interaction Hamiltonians, including the interactions of the
> measurement apparatus):
> Is it the state of the system that changes upon measurement due to the
> collapse ("action" of the collapse) or is it the measured values
> that change continuously upon time ("acknowledgement" of the
> collapse)?
The state changes and the measured values change, due to the dynamics
of the combined system plus environment.
>>>A physical theory is mainly a choice of description (formally, we are
>>>free to choose what we want)
>>
>>..but only if we don't care about the quality of our predictions.
>>If we want to have good predictions, we must choose what quantum
>>mechanics tells us to choose.
>>
> Every physical theory is a description choice. Good predictions is
> somewhat a matter of taste (i.e. a practical choice).
But physicists have the taste to want good, accurate predictions.
Otherwise they could have stayed with Aristoteles.
> For example, take My god determinist theory: the collection of all the
> "measurable" properties of the universe we may ever know. I call it
> determinist because, labelling all the properties (and assuming the
> collection of labels and properties is a ZF set: the only restiction),
> it defines an implicit function. Does it make good predictions?
If there is a compact description of it, yes.
This is precisely what theory does - give a compact description of the
collection of all properties of a system (small or large or the whole
universe).
For example, for a classical point particle over some time, one can take
as observables all functional of the trajectory x(t). Theory tells that
given six independent such observables (sufficiently well chosen),
we can predict all others. _Therefore_ the theory has high predictive value.
>>What is a true outcome in a world described by quantum mechanics/
>>
> I have outcomes, hence they are true otherwise I cannot say (logical
> meaning)
So your theory says very little.
My demands on good foundations are much higher:
_Everything_ physicists talk about in real life must be
faithfully represented in the mathematical model.
> Note we have an analogue problem in classical mechanics. How can we say
> the proposition "a particle at position q at time t" is true? The
> theory does not explain that, it uses it as QM does.
The theory specifies what is true in the model, and the
experimentalist can therefore check the model's adequacy.
> In other words, I may choose to view the "reality" by different
> mathematical concepts, this does not change the reality, just the
> description of the reality. The only required property is the
> conservation of the logic (as I do not know what to take to replace the
> usual logic).
There must be an informal but quantitative correspondence between
what is real in the model and what is real in Nature.
This correspondence is comminly called the interpretation.
> Question, why does the computed frequency of head/tails of a coin
> flipping is 50/50?
> Is it due to a mysterious ontic property, or is it due to the coin
> flipping experiment and its description choice (by saying p= n(a)/N)?
It is due to the formal definition of a fair coin-flip in the
mathematical model. The probability is 1/2 because we _define_
it that way. It has a priori _no_ relation to reality.
>>You can read about my view of probability theory in my theoretical
>>physics FAQ at
>> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>>
> I am surprised because, we seem to say almost the same (math results)
> (except may be for your comments on Bayesian probability).
> (Note: I have implicitly selected my preferred interpretation of your
> words : )).
>
> However, I have a suggestion: you should explicitly say that the sample
> space of the sequence of trials of a random variable of more than one
> value (i.e. P=/=100%) is uncountable.
Only for an infinite sequence.
> This property explains most of
> the problems with probabilities and the "uniqueness"
> (reproducibility) of each infinite sequence.
The problems are already there for large finite sequences.
No one ever observed an infinite sequence of trials.
>>What I want as a basis of physics is a mathematically defined
>>model of the world in which one can give unambiguous descriptions
>>of all that matters in physics - physical systems, detectors, observers,
>>individual observations, statistics about these observations,
>>error analysis, etc. in such a way that it mirrors reality.
>
> I understand, however, there is more than one model.
So far, there is _no_ model coming close to what I want.
>>Just as in matheamtical logic, one models the whole logical process
>>in a concise mathematical framework.
>>
> This is a sort of compression process of the "god determinist
> theory". Therefore, I hope you should accept loss of information
> (description) in this process.
No. Mathematical logic loses no information in this modeling process,
and Physical logic shouldn't either.
Loss of information amounts to dissipation
and should be explained rather than bbuilt in.
> I think the QM theory is a concise one (may be too). The main problem
> seems to be the preferred basis prediction. However, If we look at
> general relativity we encounter an almost analogue problem: the
> preferred frame to describe the events.
The preferred frame in GR is determined by the matter distribution
in the universe. Only empty space has no preferred frame.
This is why we can speak unambiguously about the age of the universe.
>>>>Although not very clearly separated in many discussions,
>>>>these two processes happen never simultaneously but context
>>>>dependent, and are of course only approximations to more
>>>>realistic measurement situations.
>>>>
>>>>For example, in a Stern-Gerlach experiment, the system (silver atom)
>>>>moves from the source along the magnet towards the screen with very
>>>>good accuracy in a unitary (and indeed reversible) way. But a few
>>>>split moments before it hits the screen it feels its interactions,
>>>>and describing it as a closed system becomes hopelessly inaccurate.
>>>>Instead, since the interaction time is very short, it can be
>>>>described very accurately by an instantaneous collapse.
>>>
>>>Why do you say it becomes hopelessly inaccurate?
>>
>>Because the closed system in this setting contains >10^20 degrees of
>>freedom, and we cannot model such systems accurately. We need the
>>thermodynamic approximation, and with it an unavoidable inaccuracy
>>in the response to the microscopic particle state.
>>
> You can describe the stern-gerlach experiment with an excellent
> approximation as a closed quantum system.
No. In a closed quantum system, no collapse ever happens.
>>>And How can you really
>>>apply a collapse to a non closed system? In this case, don't you
>>>think the collapse result (the outcome) should be independent of the
>>>partial system description versus the whole system (including the
>>>universe if necessary)?
>>
>>Look at the corresponding classical situation. A classical particle
>>encounters a classical screen (say, a thin foil through which
>>the particle will most likely escape) involving a huge number
>>of classical particles bound by (and interacting with the
>>incident particle) by empirical forces. It ends up in some state
>>that is determined only probablilistically, once you ignore the
>>detailed structure of the screen. But it ends up in a _definite_
>>state.
>
> If you say it ends up in a _definite_ state you are implicitly
> _defining_ a true property for this system instance
Of course: This is a _classical_ system!
I just wanted to say that the classical situation is already precisely
analogous to the quantum situation, and needs also a description
in terms of collapse. So collapse has nothing to do with
acknowledgment by anyone, but only with lack of control over the
unmodelled environment.
There is no need to indroduce an additional level of observers,
and neither is there a need in the quantum case.
>>To describe it, however, without reference to the state of
>>the screen, necessitates a probabilistic description and a collapse.
>>
> But you have a property for the screen, otherwise you cannot apply the
> collapse ("the don't care property or if you prefer, the Identity
> projector).
In this analogy, everything computable from the classical deterministic
state is a definite property of system, screen, or environment,
depending on which part of the state variables are used to compute it.
>>The quantum system is - in the consistent experiment interpretation -
>>completely analogous, except that the dynamics differs in detail
>>significantly from the classical dynamics.
>>
> I am still working on this (I need to understand the logic).
Take your time. It took me several years to gradually adapt to this
new point of view. Of course, I had to find out the hard way what
could be asserted and how far it reached, while you get everything
spelled out. So you can take some short cuts...
Arnold Neumaier
Aaron Bergman
Jun11-05, 01:20 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1118332974.477877.171900@g44g2000cwa.googlegroups .com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n\n> > I didn\'t think I was making any controversial statements here. This same\n> > idea appears in III.E (.3 in particular) of the paper that was referred\n> > to earlier on this thread, quant-ph/0312059.\n> >\n> Good, this was a paper I have studied a long time ago.\n>\n> Let me quote the section F:\n>\nYou mean III.E.4.\n\n[...quote...]\n\n> (this sectionf is against your schmidt basis claim)\n\nNo, it\'s not. Read the very next paragraph after the one you quoted. The\nonly problem, as it said, is when you have near degeneracy.\n\n> Now , take the formula (3.8) page 14 of the same document,\n\n(3.8) is on page 10. Are we reading the same paper?\n\n> change the\n> basis of the system, apparatus and environment and, apply the weak\n> argument of the mean time orthogonality of the environment basis (what\n> is done between 3.13 and 3.14 of section III.E => you end with the same\n> approximated decomposition but with completely different basis, for the\n> system and apparatus (eq. 3.14).\n\n(3.13) and (3.14) are in III.D, not III.E.\n\nAnyways, decompositions into three Hilbert spaces are unique.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1118332974.477877.171900@g44g2000cwa.googlegroups. com>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> > I didn't think I was making any controversial statements here. This same
> > idea appears in III.E (.3 in particular) of the paper that was referred
> > to earlier on this thread, http://www.arxiv.org/abs/quant-ph/0312059.
> >
> Good, this was a paper I have studied a long time ago.
>
> Let me quote the section F:
>
You mean III.E.4.
[...quote...]
> (this sectionf is against your schmidt basis claim)
No, it's not. Read the very next paragraph after the one you quoted. The
only problem, as it said, is when you have near degeneracy.
> Now , take the formula (3.8) page 14 of the same document,
(3.8) is on page 10. Are we reading the same paper?
> change the
> basis of the system, apparatus and environment and, apply the weak
> argument of the mean time orthogonality of the environment basis (what
> is done between 3.13 and 3.14 of section III.E => you end with the same
> approximated decomposition but with completely different basis, for the
> system and apparatus (eq. 3.14).
(3.13) and (3.14) are in III.D, not III.E.
Anyways, decompositions into three Hilbert spaces are unique.
Aaron
Arnold Neumaier
Jun11-05, 02:44 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>So you assume the collapse rather than deriving it.\n>>You postulate the existence of objective hidden variables\n>>(the observable clicks) that follow an uncontrolled, unmodelled\n>>dynamics correlated to the wave function according to the postulated\n>>Born rule. This is a cheap way out.\n>>\n> I just say that the QM model does not describe the outcomes, but the\n> occurrence of outcomes. I hope you understand what I mean (this is a\n> choice of description).\n\nNo, I don\'t. It sounds as if you are saying, the QM model does not\ndescribe the real world but the occurence of it. This does not make\nsense to me.\n\n\n>>I want _better_ foundations. The clicks are not things unrelated to\n>>quantum mechanics, but they are macroscopic pressure distributions\n>>in the air surrounding the ear that hears the click. No pressure\n>>distribution characteristic of a click implies no click to be heard.\n>>\n> This is our problem of misunderstanding. By no way the QM formalism\n> explains the outcomes. So what you are looking for is:\n>\n> a) a na=EFve prediction of the outcomes that may context dependent: it\n> depends on the experiment you choose. You already have bohmian\n> mechanics, that has adds new equation: the bohmian path of a particle.\n\nI don\'t consider Bohmian mechanics to be a sensible solution.\nSee quant-ph/0001011.\n\n\n> b) the time evolution of some configurations with the conservation the\n> P~100% statistics of the outcomes. (may be better words could be use to\n> describe what I mean)\n\nIn a good foundation, the observable statistics should be derived,\nnot postulated. Just like in classical mechanics.\n\n\n> I think this is the last case you are looking for (using mainly the law\n> of large numbers and ergodicity properties, etc ...). This is the\n> interesting one (the one you are interested).\n\nNote that I stated the _goal_ of what I consider a good foundation.\nNothing that exists so far meets my demands, not even my own\nconsistent experiment interpretation (though it comes close).\n\n\n>>The collapse challenge is to demonstrate the emergence of this\n>>particular pressure distribution at the time it is observed,\n>>by considering the air as the quantum system which statistical\n>>mechanics claims it to be.\n>>\n> So what you call "collapse challenge" is the description of some\n> systems with 100% statistics. As explained above, this has nothing to\n> do with the collapse (we need to apply).\n\nWe talk across each other; we mean something different by collapse.\nThat\'s why I think it is so important to have clearly spelled out the\nformal basis of our discussion. This should result in less ambiguity.\n\n\n> I you prefer, let\'s change, your system by a classical system\n> described by the Hilbert space formalism and the unitary evolution of\n> the liouvillian operator.\n>\n> See for example: quant-ph/0301172: Topics in Koopman-von Neumann Theory\n>\n> Do you see we still have a collapse postulate?\n\nNot if the initial distribution is a Dirac distribution, as commonly\nassumed in classical mechanics.\n\nThe situation is different in statistical mechanics, but there I\nchallenge the traditional interpretation. My consistent experiment\ninterpretation provides a radically different view of the matter\nnot suffering from the traditional foundational problems of\nstatistical mechanics as described, e.g. in\nL. Sklar,\nPhysics and Chance,\nCambridge Univ. Press, Cambridge 1993.\n\n\n>>>In any case, we have for a given instance of this system a property\n>>>false that becomes true. This has no meaning in this formalism.\n>>\n>>Then your formalism is severely deficient, not consistent with\n>>what textbooks assert.\n>>\n> All the textbooks, I known (may be not the best ones : ), that deal\n> with the formalism does not say more than what I say. We always have\n> the danger when reading a text to give more signification to the words\n> than they really mean. For example, the words interpretation of the\n> "before" and the "after" in the collapse postulate. Adding an\n> extra meaning to these words most of the time leads to incoherent\n> propositions.\n\nThat\'s why I want to see what you exactly refer to with \'the formalism\'.\nApparently you strip it of almost all words. But then how can one give\nmeaning to the formalism? It _requires_ an interpretation.\n\n\n>>The objective change of pressure distribution has a well-defined\n>>meaning in the statistical mechanics description of the system\n>>(particle + air).\n>>\n> In QM also.\n\nOK, please tell me its well-defined meaning in \'the formalism\',\nas you understand it.\n\n\n>>The formalism of quantum statistical mechanics says more.\n>>It says that a macroscopic quantum system has definite macroscopic\n>>observables such as the pressure distribution of the air,\n>>given by the usual thermodynamical formalism.\n>>\n> QM formalism allows system to have macroscopic observables with ~100%\n> statistical distributions. However to say that a macroscopic observable\n> has a value, you need the collapse postulate.\n\nNo. Statistical mechanics defines the macroscopic observables to be\ncertain canonical functions of certain expectations, not \'values\'\nin the sense of the collapse postulate.\n\nThe grand canonical ensemble does _not_ collapse to a pure state upon\na measurement of the pressure.\n\n\n\n>>>I just say, that in the statistical description choice of the\n>>>QM theory formalism, the collapse is just the notification of the\n>>>results of experimental trials (a property is true). Saying more than\n>>>that is interpreting the theory with the risk of modifying the theory.\n>>\n>>In the statistical interpretation, the collapse is just the change\n>>of description caused by taking conditional expectations under a\n>>change of the condition. Nothing needs to be explained on that level.\n>>\n>>What needs explanation is how the individual system is related to\n>>the statistical description.\n>>\n> ?\n> I mean, It is related to the statistical description by its outcome.\n\nThe statistical description is a description of what happens to\nan ensemble of identically and independently prepared systems.\nIt says _nothing_ at all about what happens to a single system.\n\nNow _all_ observations physicists ever made are (with exceptions of a\nfew observations made by astronauts) observations about certaim\nobservables within _one_ particular large quantum system called the\nEarth. (Even observations of the stars are in reality observations\nabout the electromagnetic field measured by the photographic plates.)\n\nNo matter what you say, these are observations about\na _single_ system, believed universally to be described by the\nstandard model plus gravity. At least all statistical mechanics,\nand with it all we know about physics, derived from it.\n\nThus there is a need to explain how this single system behaves in\nagreement with quantum mechanics. We cannot prepare independent\nand idenitcally distributed earths!\n\n\n>>If we increase the size of the quantum system it becomes more and more\n>>unique. If the system is large enough (e.g. the Moon), the system\n>>is an individual, and it is no longer possible to prepare identically\n>>distributed copies of the Moon. But we still can observe it, and we\n>>still believe it is governed by quantum mechanics, since no one can\n>>point at any size where quantum mechanics starts to be inapplicable.\n>>\n>>Here is the need for explanation!\n>>\n> I do not understand you (I am trying).\n>\n> QM formalism says, e.g. decoherence, that there may exist macroscopic\n> systems with 100% statistical distribution (of a given set of outcomes\n> at different times=3D> implicitly defines a path): for a given system\n> with an outcome at time to (a(to)), we are able to deduce values of the\n> outcomes at other times (e.g. a(t)): for 100% of the systems with\n> outcome a(to).\n\n100% means eigenstates. This is not what decoherence says.\n\nDecoherence produces mixtures as projections of bigger rank one\ndensity matrices. It is _not_ permitted (as explained in my\ncomment in quant-ph/0505172 on how decoherence handles the\ncollapse challenge) to regard this mixture as a statistical mixture\nof pure states since the bigger density matrices cannot be\ndecomposed that way.\n\n\n> Now what I do not understand, is the connection of this statistical\n> prediction with the formal problem of finding several identical\n> instances of the same object and the collapse (i.e. with the outcome\n> a(to)).\n\nWell, this is the traditional definition of an ensemble.\n\n\n>>The statistical interpretation has a similar conflict; it assumes\n>>the reality of the objective event, the measurement result,\n>>and forgets to say which macroscopic observations are entitled to\n>>be taken as objective events. This is questionable.\n>>\n> Yes, this is what I call the problem of the preferred basis prediction.\n\nEven if you have a preferred basis, this still does not address my\nconcern.\n\n\n> Currently, with the QM formalism we have to choose the Hamiltonian for\n> the unitary evolution and basis where we have the measurement results.\n> It seems there is too many degrees of freedom to mach theoretical\n> results with reality (just by rotating the basis of a given observable,\n> we change the statistical behaviour in huge proportions).\n\nYou might like the consistent experiment interprtation. Within it,\nreality is determined by the state of the universe together\nwith the selection of the system to be considered.\n\n\n>>I reject the statistical interpretation as being the fundamental\n>>description of nature. It cannot be consistently applied to the\n>>many situations where quantum mechnaics is applied routinely\n>>although no two identically distributed realizations can be produced.\n>>\n> I think I have not understand what you mean by "statistical\n> interpretation".\n\nThe idea that the state of a quantum system is nothing objective\nbut only a recipe to calculate probabilities.\n\n\n\n>>>Here, I want to understand what you really mean by physical collapse.\n>>\n>>The physical collapse is the response of a small quantum system\n>>to interactions of very short duration with a detector not modelled\n>>in detail.\n>>\n> Do you accept the formal mapping:\n>\n> "physical collapse " <=3D> {set of interactions modelling + formal\n> collapse including basis selection of the collapse}\n\nNo.\n\nThe formal collapse is the replacement of a general pure state\nby its projection to an eigenspace of some family of commuting\nHermitiam operators with discrete spectrum. The physical collapse\nis what I stated above.\n\nWhat you call a formal mapping is already an interpretation\n(and one that I don\'t subscribe to).\n\nMy interpretation of the relation is that the formal collapse is\nan idealization of what happens during the physical collapse\nthat enables the latter to be described in terms of the state\nof the system only (while an exact description would need\ncomplete information about the whole environment).\n\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>So you assume the collapse rather than deriving it.
>>You postulate the existence of objective hidden variables
>>(the observable clicks) that follow an uncontrolled, unmodelled
>>dynamics correlated to the wave function according to the postulated
>>Born rule. This is a cheap way out.
>>
> I just say that the QM model does not describe the outcomes, but the
> occurrence of outcomes. I hope you understand what I mean (this is a
> choice of description).
No, I don't. It sounds as if you are saying, the QM model does not
describe the real world but the occurence of it. This does not make
sense to me.
>>I want _better_ foundations. The clicks are not things unrelated to
>>quantum mechanics, but they are macroscopic pressure distributions
>>in the air surrounding the ear that hears the click. No pressure
>>distribution characteristic of a click implies no click to be heard.
>>
> This is our problem of misunderstanding. By no way the QM formalism
> explains the outcomes. So what you are looking for is:
>
> a) a na=EFve prediction of the outcomes that may context dependent: it
> depends on the experiment you choose. You already have bohmian
> mechanics, that has adds new equation: the bohmian path of a particle.
I don't consider Bohmian mechanics to be a sensible solution.
See http://www.arxiv.org/abs/quant-ph/0001011.
> b) the time evolution of some configurations with the conservation the
> P~100% statistics of the outcomes. (may be better words could be use to
> describe what I mean)
In a good foundation, the observable statistics should be derived,
not postulated. Just like in classical mechanics.
> I think this is the last case you are looking for (using mainly the law
> of large numbers and ergodicity properties, etc ...). This is the
> interesting one (the one you are interested).
Note that I stated the _goal_ of what I consider a good foundation.
Nothing that exists so far meets my demands, not even my own
consistent experiment interpretation (though it comes close).
>>The collapse challenge is to demonstrate the emergence of this
>>particular pressure distribution at the time it is observed,
>>by considering the air as the quantum system which statistical
>>mechanics claims it to be.
>>
> So what you call "collapse challenge" is the description of some
> systems with 100% statistics. As explained above, this has nothing to
> do with the collapse (we need to apply).
We talk across each other; we mean something different by collapse.
That's why I think it is so important to have clearly spelled out the
formal basis of our discussion. This should result in less ambiguity.
> I you prefer, let's change, your system by a classical system
> described by the Hilbert space formalism and the unitary evolution of
> the liouvillian operator.
>
> See for example: http://www.arxiv.org/abs/quant-ph/0301172: Topics in Koopman-von Neumann Theory
>
> Do you see we still have a collapse postulate?
Not if the initial distribution is a Dirac distribution, as commonly
assumed in classical mechanics.
The situation is different in statistical mechanics, but there I
challenge the traditional interpretation. My consistent experiment
interpretation provides a radically different view of the matter
not suffering from the traditional foundational problems of
statistical mechanics as described, e.g. in
L. Sklar,
Physics and Chance,
Cambridge Univ. Press, Cambridge 1993.
>>>In any case, we have for a given instance of this system a property
>>>false that becomes true. This has no meaning in this formalism.
>>
>>Then your formalism is severely deficient, not consistent with
>>what textbooks assert.
>>
> All the textbooks, I known (may be not the best ones : ), that deal
> with the formalism does not say more than what I say. We always have
> the danger when reading a text to give more signification to the words
> than they really mean. For example, the words interpretation of the
> "before" and the "after" in the collapse postulate. Adding an
> extra meaning to these words most of the time leads to incoherent
> propositions.
That's why I want to see what you exactly refer to with 'the formalism'.
Apparently you strip it of almost all words. But then how can one give
meaning to the formalism? It _requires_ an interpretation.
>>The objective change of pressure distribution has a well-defined
>>meaning in the statistical mechanics description of the system
>>(particle + air).
>>
> In QM also.
OK, please tell me its well-defined meaning in 'the formalism',
as you understand it.
>>The formalism of quantum statistical mechanics says more.
>>It says that a macroscopic quantum system has definite macroscopic
>>observables such as the pressure distribution of the air,
>>given by the usual thermodynamical formalism.
>>
> QM formalism allows system to have macroscopic observables with ~100%
> statistical distributions. However to say that a macroscopic observable
> has a value, you need the collapse postulate.
No. Statistical mechanics defines the macroscopic observables to be
certain canonical functions of certain expectations, not 'values'
in the sense of the collapse postulate.
The grand canonical ensemble does _not_ collapse to a pure state upon
a measurement of the pressure.
>>>I just say, that in the statistical description choice of the
>>>QM theory formalism, the collapse is just the notification of the
>>>results of experimental trials (a property is true). Saying more than
>>>that is interpreting the theory with the risk of modifying the theory.
>>
>>In the statistical interpretation, the collapse is just the change
>>of description caused by taking conditional expectations under a
>>change of the condition. Nothing needs to be explained on that level.
>>
>>What needs explanation is how the individual system is related to
>>the statistical description.
>>
> ?
> I mean, It is related to the statistical description by its outcome.
The statistical description is a description of what happens to
an ensemble of identically and independently prepared systems.
It says _nothing_ at all about what happens to a single system.
Now _all_ observations physicists ever made are (with exceptions of a
few observations made by astronauts) observations about certaim
observables within _one_ particular large quantum system called the
Earth. (Even observations of the stars are in reality observations
about the electromagnetic field measured by the photographic plates.)
No matter what you say, these are observations about
a _single_ system, believed universally to be described by the
standard model plus gravity. At least all statistical mechanics,
and with it all we know about physics, derived from it.
Thus there is a need to explain how this single system behaves in
agreement with quantum mechanics. We cannot prepare independent
and idenitcally distributed earths!
>>If we increase the size of the quantum system it becomes more and more
>>unique. If the system is large enough (e.g. the Moon), the system
>>is an individual, and it is no longer possible to prepare identically
>>distributed copies of the Moon. But we still can observe it, and we
>>still believe it is governed by quantum mechanics, since no one can
>>point at any size where quantum mechanics starts to be inapplicable.
>>
>>Here is the need for explanation!
>>
> I do not understand you (I am trying).
>
> QM formalism says, e.g. decoherence, that there may exist macroscopic
> systems with 100% statistical distribution (of a given set of outcomes
> at different times=3D> implicitly defines a path): for a given system
> with an outcome at time to (a(to)), we are able to deduce values of the
> outcomes at other times (e.g. a(t)): for 100% of the systems with
> outcome a(to).
100% means eigenstates. This is not what decoherence says.
Decoherence produces mixtures as projections of bigger rank one
density matrices. It is _not_ permitted (as explained in my
comment in http://www.arxiv.org/abs/quant-ph/0505172 on how decoherence handles the
collapse challenge) to regard this mixture as a statistical mixture
of pure states since the bigger density matrices cannot be
decomposed that way.
> Now what I do not understand, is the connection of this statistical
> prediction with the formal problem of finding several identical
> instances of the same object and the collapse (i.e. with the outcome
> a(to)).
Well, this is the traditional definition of an ensemble.
>>The statistical interpretation has a similar conflict; it assumes
>>the reality of the objective event, the measurement result,
>>and forgets to say which macroscopic observations are entitled to
>>be taken as objective events. This is questionable.
>>
> Yes, this is what I call the problem of the preferred basis prediction.
Even if you have a preferred basis, this still does not address my
concern.
> Currently, with the QM formalism we have to choose the Hamiltonian for
> the unitary evolution and basis where we have the measurement results.
> It seems there is too many degrees of freedom to mach theoretical
> results with reality (just by rotating the basis of a given observable,
> we change the statistical behaviour in huge proportions).
You might like the consistent experiment interprtation. Within it,
reality is determined by the state of the universe together
with the selection of the system to be considered.
>>I reject the statistical interpretation as being the fundamental
>>description of nature. It cannot be consistently applied to the
>>many situations where quantum mechnaics is applied routinely
>>although no two identically distributed realizations can be produced.
>>
> I think I have not understand what you mean by "statistical
> interpretation".
The idea that the state of a quantum system is nothing objective
but only a recipe to calculate probabilities.
>>>Here, I want to understand what you really mean by physical collapse.
>>
>>The physical collapse is the response of a small quantum system
>>to interactions of very short duration with a detector not modelled
>>in detail.
>>
> Do you accept the formal mapping:
>
> "physical collapse " <=3D> {set of interactions modelling + formal
> collapse including basis selection of the collapse}
No.
The formal collapse is the replacement of a general pure state
by its projection to an eigenspace of some family of commuting
Hermitiam operators with discrete spectrum. The physical collapse
is what I stated above.
What you call a formal mapping is already an interpretation
(and one that I don't subscribe to).
My interpretation of the relation is that the formal collapse is
an idealization of what happens during the physical collapse
that enables the latter to be described in terms of the state
of the system only (while an exact description would need
complete information about the whole environment).
Arnold Neumaier
Arnold Neumaier
Jun11-05, 02:44 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Seratend wrote:\n\n> Arnold Neumaier wrote:\n>\n>>Seratend wrote:\n>>\n>>>We are at the heart of the problem between the formalism of the theory\n>>>and the interpretation.\n>>>Please note that the measurement part of the theory does not require\n>>>any interaction.\n>>\n>>The formalism itself has nothing to do with the real world, unless\n>>it is given _some_ interpretation.\n>>\n>>Real measurement requires real interactions.\n>>\n> QM formalism does not say what is a real measurement. QM formalism\n> speaks about the collapse postulate and the born rules and the unitary\n> evolution. That\'s all.\n\nI hope you\'ll give somewhere a precise definition of what the QM\nformalism speaks about. What you assert sounds (in its delineation)\nvery different from what I commonly read.\n\n\n> I need quantum interactions to describe the whole unitary evolution of\n> the system and the measurement apparatus object.\n\nThis is not unitary unless you also include the environment interacting\nwith the apparatus. Decoherence is all about this important observation.\n\n\n> Unitary evolutions\n> introduce statistical correlations between the system and the\n> measurement apparatus object (including the environment if necessary to\n> describe the evolution).\n> We use these statistical correlations on the statistics of formal\n> measurement results of this whole system (including the "measurement\n> apparatus" that has not to be confused with the formal measurement\n> result). That\'s what the formalism allows one to say (hence the\n> requirement of interactions to correlate the measurement apparatus to\n> the system).\n\nThus the formalism says nothing without interpretation, since it is not\napplicable to the real world without it...\n\n\n> Saying the measurement\n> apparatus does a formal measurement is interpretation (completely out\n> of the scope of the QM formalism). I do not refute the interpretation,\n> nor I can\'t as long as it is consistent with the formalism.\n\nA measurement apparatus deserves its name only if it indeed performs\nmeasurements.\n\n\n>>The theory models these by assuming collapse under measurement,\n>>no matter whether in the eyes of the observer or whether objective.\n>>At least this is the traditional way of viewing the formalism.\n>>\n> This is the traditional *interpretation* of the formalism.\n> I am just using the logic in the context of the formalism: I do not\n> explain why I observe a result, just that when this result is true, I\n> have a collapse. No interaction is involved in this logical\n> affirmation.\n\nBut interaction is involved in being able to observe the result.\nYou cannot read a pointer unless you interact with it.\n\nI don\'t think the problesms of qunatum mechanics go away simply\nby nit-picking on words.\n\n\n>>>The observer outside or inside the system has no\n>>>meaning in the QM formalism (only in the interpretations).\n>>\n>>The QM formalism is about closed systems in which no measurements\n>>happen by definition of what it means to be closed. There are no\n>>measurements in the formalism.\n>>\n> So, Do you claim the measurement postulates of QM formalism are wrong\n> in some obscure cases?\n\nNo. I claim the measurement postulates of QM describe a very early\n(1932) stage of quantum mechanical measurement theory that is long\nbeing superseded in practice. A more modern view related to modern\nexperimental practice is in\nV.B. Braginsky and F. Ya. Khalili\nQuantum measurement,\nCambridge Univ. Press, Cambridge 1992.\nOn p.28 they write:\n\'\'It is important to note that in many _real_ [original kursiv]\nmeasurements the final state is substantially different\nfrom |q_n>.\'\' [the eigenstate after measurwement of q]\nand continue on p.30:\n\'\'We turn attention, now, from idealized, exact measurements,\nto the development of a formalism that will help us to handle\nmore nearly realistic, approximate measurements.\'\'\nThen follow 1050 further pages with the modern view.\n\n\n> The main difference is on the collapse of the word meanings: what you\n> call measurement is not the measurement described in QM formalism.\n\nWhat I call measurement is what experimentalists call measurement.\nOnly that counts. Physics is there to explain experiments, and\nif some theorists use the term \'measurement\' in a different sense,\nI am not interested, and claim that this usage has no practical\nrelevance (except to cloud the issues).\n\n\n\n>>And I don\'t understand what a \'property\' is; the traditional QM\n>>formalism has no place for it. If you want to stay on the formal\n>>side you are only allowed to talk about operators, states, Hilbert\n>>spaces and other on the formal level well-defined concepts.\n>>\n> With the outcomes mapping with the "reality", the property\n> "outcome of A is a" has both a signification in a real object as\n> well as in a symbolic one.\n> (here property: the mathematical signification. You can use proposition\n> if you it is more adequate).\n\nDo you mean by "outcome of A is a" - "a is an eigenvalue of A"?\nThen I can see how it is represented in the formalism.\nBut then I can\'t see how it is related to reality.\n\n\n> In the traditional formalism of QM, when the collapse postulate is\n> true, the property "outcome of A is a" is true. This is a property\n> of the considered system (logic).If this property is false the\n> corresponding collapse postulate is also false => the collapse of a\n> system is a property of the system (QM formalism).\n>\n> I am not inventing new words, I am just using mathematical results of\n> the QM formalism.\n\nThis conservation makes little sense unless you clearly state a\ncomplete set of rules that defines your QM formalism. We misunderstand\neach other constantly.\n\n\n\n\n> What you say is true: the local state of an opened system does not\n> evolve unitary. This is a result of QM formalism. No need to interpret\n> this result. The coupling of these open systems define a global\n> unitary evolution and hence a local non unitary evolution that may have\n> some interesting properties (localisation of the state on a subset of\n> possible outcomes in a give basis, etc ...). This again is given by the\n> QM formalism.\n>\n> Therefore, strictly speaking, you can only say that the evolution of a\n> local state of a given system is non unitary. However, in a more\n> common language you can say the system does not evolve unitary,\n> assuming implicitly you are speaking of the local state.\n>\n> However, strictly speaking, a local outcome of a system is a global\n> outcome of the whole system (including the universe) in the QM\n> formalism: we always apply a projector\n> P=|local><local|(x)Id_restoftheworld when we say we have a peculiar\n> outcome. The property applies to the whole universe, strictly speaking.\n\nI agree to that part. This is why one needs a QM of the universe\nto talk about closed systems, and has to infer from this QM of the\nuniverse the properties of the open parts that we actually can observe.\n\nBut this is _not_ done commonly, resulting in the known foundational\nmess.\n\n>>Von Neumann\'s 1932 postulates are no longer believed to be valid\n>>for small systems since it is well recognized that these are\n>>necessarily open.\n>>\n> This is a matter of words. What you say is that you always have\n> interactions with other parts of the world, even for a small system.\n> This in no case refutes the fundamental postulates.\n\nThe postulates cannot be refuted, but their domain of valididy\nis open to experiment. In particular, they apply only to closed\nsystems, and this means only to the universe as a whole.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Seratend wrote:
> Arnold Neumaier wrote:
>
>>Seratend wrote:
>>
>>>We are at the heart of the problem between the formalism of the theory
>>>and the interpretation.
>>>Please note that the measurement part of the theory does not require
>>>any interaction.
>>
>>The formalism itself has nothing to do with the real world, unless
>>it is given _some_ interpretation.
>>
>>Real measurement requires real interactions.
>>
> QM formalism does not say what is a real measurement. QM formalism
> speaks about the collapse postulate and the born rules and the unitary
> evolution. That's all.
I hope you'll give somewhere a precise definition of what the QM
formalism speaks about. What you assert sounds (in its delineation)
very different from what I commonly read.
> I need quantum interactions to describe the whole unitary evolution of
> the system and the measurement apparatus object.
This is not unitary unless you also include the environment interacting
with the apparatus. Decoherence is all about this important observation.
> Unitary evolutions
> introduce statistical correlations between the system and the
> measurement apparatus object (including the environment if necessary to
> describe the evolution).
> We use these statistical correlations on the statistics of formal
> measurement results of this whole system (including the "measurement
> apparatus" that has not to be confused with the formal measurement
> result). That's what the formalism allows one to say (hence the
> requirement of interactions to correlate the measurement apparatus to
> the system).
Thus the formalism says nothing without interpretation, since it is not
applicable to the real world without it...
> Saying the measurement
> apparatus does a formal measurement is interpretation (completely out
> of the scope of the QM formalism). I do not refute the interpretation,
> nor I can't as long as it is consistent with the formalism.
A measurement apparatus deserves its name only if it indeed performs
measurements.
>>The theory models these by assuming collapse under measurement,
>>no matter whether in the eyes of the observer or whether objective.
>>At least this is the traditional way of viewing the formalism.
>>
> This is the traditional *interpretation* of the formalism.
> I am just using the logic in the context of the formalism: I do not
> explain why I observe a result, just that when this result is true, I
> have a collapse. No interaction is involved in this logical
> affirmation.
But interaction is involved in being able to observe the result.
You cannot read a pointer unless you interact with it.
I don't think the problesms of qunatum mechanics go away simply
by nit-picking on words.
>>>The observer outside or inside the system has no
>>>meaning in the QM formalism (only in the interpretations).
>>
>>The QM formalism is about closed systems in which no measurements
>>happen by definition of what it means to be closed. There are no
>>measurements in the formalism.
>>
> So, Do you claim the measurement postulates of QM formalism are wrong
> in some obscure cases?
No. I claim the measurement postulates of QM describe a very early
(1932) stage of quantum mechanical measurement theory that is long
being superseded in practice. A more modern view related to modern
experimental practice is in
V.B. Braginsky and F. Ya. Khalili
Quantum measurement,
Cambridge Univ. Press, Cambridge 1992.
On p.28 they write:
''It is important to note that in many _real_ [original kursiv]
measurements the final state is substantially different
from |q_n>.'' [the eigenstate after measurwement of q]
and continue on p.30:
''We turn attention, now, from idealized, exact measurements,
to the development of a formalism that will help us to handle
more nearly realistic, approximate measurements.''
Then follow 1050 further pages with the modern view.
> The main difference is on the collapse of the word meanings: what you
> call measurement is not the measurement described in QM formalism.
What I call measurement is what experimentalists call measurement.
Only that counts. Physics is there to explain experiments, and
if some theorists use the term 'measurement' in a different sense,
I am not interested, and claim that this usage has no practical
relevance (except to cloud the issues).
>>And I don't understand what a 'property' is; the traditional QM
>>formalism has no place for it. If you want to stay on the formal
>>side you are only allowed to talk about operators, states, Hilbert
>>spaces and other on the formal level well-defined concepts.
>>
> With the outcomes mapping with the "reality", the property
> "outcome of A is a" has both a signification in a real object as
> well as in a symbolic one.
> (here property: the mathematical signification. You can use proposition
> if you it is more adequate).
Do you mean by "outcome of A is a" - "a is an eigenvalue of A"?
Then I can see how it is represented in the formalism.
But then I can't see how it is related to reality.
> In the traditional formalism of QM, when the collapse postulate is
> true, the property "outcome of A is a" is true. This is a property
> of the considered system (logic).If this property is false the
> corresponding collapse postulate is also false => the collapse of a
> system is a property of the system (QM formalism).
>
> I am not inventing new words, I am just using mathematical results of
> the QM formalism.
This conservation makes little sense unless you clearly state a
complete set of rules that defines your QM formalism. We misunderstand
each other constantly.
> What you say is true: the local state of an opened system does not
> evolve unitary. This is a result of QM formalism. No need to interpret
> this result. The coupling of these open systems define a global
> unitary evolution and hence a local non unitary evolution that may have
> some interesting properties (localisation of the state on a subset of
> possible outcomes in a give basis, etc ...). This again is given by the
> QM formalism.
>
> Therefore, strictly speaking, you can only say that the evolution of a
> local state of a given system is non unitary. However, in a more
> common language you can say the system does not evolve unitary,
> assuming implicitly you are speaking of the local state.
>
> However, strictly speaking, a local outcome of a system is a global
> outcome of the whole system (including the universe) in the QM
> formalism: we always apply a projector
> P=|local><local|(x)Id_restoftheworld when we say we have a peculiar
> outcome. The property applies to the whole universe, strictly speaking.
I agree to that part. This is why one needs a QM of the universe
to talk about closed systems, and has to infer from this QM of the
universe the properties of the open parts that we actually can observe.
But this is _not_ done commonly, resulting in the known foundational
mess.
>>Von Neumann's 1932 postulates are no longer believed to be valid
>>for small systems since it is well recognized that these are
>>necessarily open.
>>
> This is a matter of words. What you say is that you always have
> interactions with other parts of the world, even for a small system.
> This in no case refutes the fundamental postulates.
The postulates cannot be refuted, but their domain of valididy
is open to experiment. In particular, they apply only to closed
systems, and this means only to the universe as a whole.
Arnold Neumaier
Eugene Stefanovich
Jun11-05, 02:46 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n\n> My demands on good foundations are much higher:\n> _Everything_ physicists talk about in real life must be\n> faithfully represented in the mathematical model.\n\n\nI believe that\'s can not be done in quantum mechanics.\nTake for example the double-slit experiment in which photons are\nreleased one-by-one. Quantum mechanics\nhas no power to predict where each individual photon will hit the\nscreen. QM can only predict the distribution of the probability.\nQuantum mechanics has no power to predict when exactly each\nindividual radioactive nucleus will decay. QM can only\npredict the dependence of the decay probability on time (the decay\nlaw).\n\nEugene.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> My demands on good foundations are much higher:
> _Everything_ physicists talk about in real life must be
> faithfully represented in the mathematical model.
I believe that's can not be done in quantum mechanics.
Take for example the double-slit experiment in which photons are
released one-by-one. Quantum mechanics
has no power to predict where each individual photon will hit the
screen. QM can only predict the distribution of the probability.
Quantum mechanics has no power to predict when exactly each
individual radioactive nucleus will decay. QM can only
predict the dependence of the decay probability on time (the decay
law).
Eugene.
Seratend
Jun11-05, 05:39 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1118332974.477877.171900@g44g2000cwa.googlegroups .com>,\n> "Seratend" <ser_monmail@yahoo.fr> wrote:\n>\n> > Aaron Bergman wrote:\n>\n> > > I didn\'t think I was making any controversial statements here. This same\n> > > idea appears in III.E (.3 in particular) of the paper that was referred\n> > > to earlier on this thread, quant-ph/0312059.\n> > >\n> > Good, this was a paper I have studied a long time ago.\n> >\n> > Let me quote the section F:\n> >\n> You mean III.E.4.\n>\n: )\n\nI\'ve said I\'ve read this paper a long time ago (the initial version\nv1!).\nI\'ll try to read the new version (v3!) later.\n\n> [...quote...]\n>\n> > (this sectionf is against your schmidt basis claim)\n>\n> No, it\'s not.\n\n: ))\n\nWell. I quote the end of this section:\n\n"In summary, it is important to emphasize that stability\n(or a similar criterion) is the relevant requirement for\nthe emergence of a preferred quasiclassical basis, which\ncan in general not be achieved by simply diagonalizing\nthe instantaneous reduced density matrix."\n\nthat means, for me, the Schmidt basis is not the criterion to find the\nbasis of measurement.\n\nAnd the end of this section:\n\n" However, the eigenstates of the decohered reduced density matrix will\nin many situations approximate the quasiclassical stable\npointer states well, especially when these pointer states\nare sufficiently nondegenerate."\n\nI like the "in many situations" and the "approximate" words to try to\nescape form the problems. We are again in the approximation domain\nwhere we can say what we want depending on the assumptions. In other\nwords, these adequate *external* assumptions define the basis.\n\nI like also "when these pointer states [of the apparatus] are\nsufficiently non-degenerate". One of the main properties of\nmacroscopic systems seems to be their high degree of degeneracy for\nevery value of their presupposed associated observables leading to huge\npossibilities of entanglement with the environment.\nAssuming this entanglement always leads (without giving a formal\nexplanation) to the quasi orthogonality of <en|em>, in the good basis,\nis somewhat cheap.\n\n> Anyways, decompositions into three Hilbert spaces are unique.\n>\nI do not understand you. You know, provided sufficient properties, the\ndecomposition of *each state* are unique. For each state, you have a\ndifferent decomposition and hence a different basis. What I said above\napplies also to this case. How can you find a unique measurement basis\nform this unique assertion that should not be in principle state\ndependant.\n\nTherefore, in order to be coherent, we need the approximation of the\ndecompositions (in order to find a sufficient "stable" basis of\nmeasurement). Once we use these approximations, we are no more sure\nthat there are not many approximations with totally different bases,\nhence again the problem.\n\nThe first result of this study is that the strict Schmidt basis\ndecomposition does not work to predict the basis of the measurement\n(hopefully, it is consistent with the postulates of QM). The rest is\nanalogue to the learning of the basis by effective experiments and\nafter saying that the basis for this type of experiment is a peculiar\none (we just use other words: selection of adequate approximations, etc\n...).\n\nUp to know, you have not proved the ability of decoherence to predict a\nbasis of a measurement without an external assumption which is, in\naddition, context dependant (it depends on the type of experiment!).\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1118332974.477877.171900@g44g2000cwa.googlegroups. com>,
> "Seratend" <ser_monmail@yahoo.fr> wrote:
>
> > Aaron Bergman wrote:
>
> > > I didn't think I was making any controversial statements here. This same
> > > idea appears in III.E (.3 in particular) of the paper that was referred
> > > to earlier on this thread, http://www.arxiv.org/abs/quant-ph/0312059.
> > >
> > Good, this was a paper I have studied a long time ago.
> >
> > Let me quote the section F:
> >
> You mean III.E.4.
>
: )
I've said I've read this paper a long time ago (the initial version
v1!).
I'll try to read the new version (v3!) later.
> [...quote...]
>
> > (this sectionf is against your schmidt basis claim)
>
> No, it's not.
: ))
Well. I quote the end of this section:
"In summary, it is important to emphasize that stability
(or a similar criterion) is the relevant requirement for
the emergence of a preferred quasiclassical basis, which
can in general not be achieved by simply diagonalizing
the instantaneous reduced density matrix."
that means, for me, the Schmidt basis is not the criterion to find the
basis of measurement.
And the end of this section:
" However, the eigenstates of the decohered reduced density matrix will
in many situations approximate the quasiclassical stable
pointer states well, especially when these pointer states
are sufficiently nondegenerate."
I like the "in many situations" and the "approximate" words to try to
escape form the problems. We are again in the approximation domain
where we can say what we want depending on the assumptions. In other
words, these adequate *external* assumptions define the basis.
I like also "when these pointer states [of the apparatus] are
sufficiently non-degenerate". One of the main properties of
macroscopic systems seems to be their high degree of degeneracy for
every value of their presupposed associated observables leading to huge
possibilities of entanglement with the environment.
Assuming this entanglement always leads (without giving a formal
explanation) to the quasi orthogonality of <en|em>, in the good basis,
is somewhat cheap.
> Anyways, decompositions into three Hilbert spaces are unique.
>
I do not understand you. You know, provided sufficient properties, the
decomposition of *each state* are unique. For each state, you have a
different decomposition and hence a different basis. What I said above
applies also to this case. How can you find a unique measurement basis
form this unique assertion that should not be in principle state
dependant.
Therefore, in order to be coherent, we need the approximation of the
decompositions (in order to find a sufficient "stable" basis of
measurement). Once we use these approximations, we are no more sure
that there are not many approximations with totally different bases,
hence again the problem.
The first result of this study is that the strict Schmidt basis
decomposition does not work to predict the basis of the measurement
(hopefully, it is consistent with the postulates of QM). The rest is
analogue to the learning of the basis by effective experiments and
after saying that the basis for this type of experiment is a peculiar
one (we just use other words: selection of adequate approximations, etc
...).
Up to know, you have not proved the ability of decoherence to predict a
basis of a measurement without an external assumption which is, in
addition, context dependant (it depends on the type of experiment!).
Seratend.
Seratend
Jun11-05, 05:39 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>[Collapsing the 2 previous posts:]\n\nArnold Neumaier wrote:\n\n> Please give an explicit and complete formal statement of what you\n> consider to be the 6 usual postulates + the mapping, so that we have\n> common ground for discussion.\n>\nArnold Neumaier wrote:\n\n> > QM formalism does not say what is a real measurement. QM formalism\n> > speaks about the collapse postulate and the born rules and the unitary\n> > evolution. That\'s all.\n>\n> I hope you\'ll give somewhere a precise definition of what the QM\n> formalism speaks about. What you assert sounds (in its delineation)\n> very different from what I commonly read.\n>\n>\nGood remark. I was assuming we have a common ground concerning QM\ntheory formalism and this may not be completely true.\n\nI hope you understand my point of view: I want logical deductions\nhypotheses that may be falsified by the experiments based on the QM\nformalism (the 6 postulates below).\n\nThe six postulates of QM theory I use are (what I call the formalism\n[of the theory]):\n\n(One can find them in an almost identical form in "mécanique\nquantique I", Cohen-Tannoudji, Diu, Laloe, 1977).\n\nPostulate 1:\n=========\nThe state of a "system" at time t is a unit vector |psi(t)> of a\nseparable complex Hilbert space H.\n\n(note: unit vector is sometimes replaced by ray, or simply by a vector)\n(note: sometimes the state is called "the complete knowledge of a\nsystem")\n\nPostulate 2:\n=======\nEvery "physical variable" A_phys of a system is represented by an\noperator A defined on H. This operator is an observable.\n\nThe observable operator property is usually interpreted as an hermitian\noperator where its eigenvectors form a basis, or a generalized basis,\nof the space H.\n\nThis is the mapping A_phys --> A. We usually add (implicitly) the\nfollowing property to this postulate: the mapping between A_phys and A\nis bijective\n\nPostulate 3:\n========\nThe "measurement result" of a physical variable A_phys represented\nby the observable A is *one* of the eigenvalues of A:\n\nMes_result(A_phys)= a, a in spec(A)\n\nThis is the formal mapping: result of a physical experiment -->\neigenvalue of an observable.\n\nWe usually suppose, in addition a bijective mapping between the set of\neigenvalues of the observable A and the set of possible values of the\nphysical variable A_phys.\n\nThe bijective property is sufficient to explain the constraints on the\nmeasurement (the possible set of properties) of non commuting\nobservables (and hence on the physical variables) and the contextuality\nof the "measurement result" (by the non commutativity of observables).\n\nPostulate 4:\n=======\nThe measurement result "a" of a physical observable represented by\nthe observable A of a system with a *unit* state |psi> has the\n*probability*:\n\na) a is in the discrete spectrum part of A:\n\nP(a||psi>)= <psi|P_a|psi>\n\nWhere P_a is the projector in the eingenspace of the observable A for\nthe eigenvalue A.\n\nb) a is the continuous spectrum part of A:\n\nP(a||psi>)da= <psi|P_a|psi>da\n\nWhere P_a is the projector in the eingenspace of the observable A for\nthe eigenvalue A.\n( b is just a derivation of a, as we can only "certainly" measure\nresults with probability occurrences different from 0: we can only\nmeasures a set of continuous eigenvalues with a measure different from\n0 => automatically defines a locally discrete observable, function of\nthe continuous observable)\n\nPostutale 4 is consistent whenever we have a bijective bi-measurable\nmapping between the physical variable set of values and the observable\nset of eigenvalues.\nthe probability law on the set of values of the physical observable\ninfers a probability law on the set of eigenvalues and in the same for\nother way through this bi-measurable mapping.\n\nTherefore, taking a set of N independent identical systems (state\n|psi>: postulate 1), we have:\nn(a)/N --> P(a||psi>) when N goes to the infinity, formally from the\nlaws of large number.\n\nPostulate 4 and the previous ones allow the formal mapping of the\nstatistics of experimental results into the statistics given by an\nobservable and a state.\nWe can therefore call "a" an outcome of a given experiment (probability\nlanguage).\n\nPostulate 5:\n=======\nIf a system is in a state |psi_before> "before" the "measurement\nresult is a" of a given physical variable A_phys, the state of the\nsystem "just after" the measurement is the normalized projected\nstate |psi_after>:\n\n|psi_after>= P_a.|psi_before>/sqrt[<psi_before|P_a|psi_before>]\n\nWhere P_a is the projector in the eigenspace of the observable A for\nthe eigenvalue a.\n\nNote: the results are given in a statistical view, in other words,\n"gives the result a", usually assumes that P(a||psi>)=/=0\n\n\nPostulate 6:\n========\nThe evolution in time of the state vector |psi(t)> of a system is given\nby the Schrödinger equation:\n\nIhbard/dt|psi(t)>= H(t)|psi(t)>.\n\nWhere H is the observable associated to the *total* energy of the\n"system" (the total energy physical variable). H is called the\nHamiltonian of the system.\n\n==========================\n\nThe postulates 2 - 3 in fact already defines the formal mapping\nbetween the experiment results ("the reality") and the mathematical\nobjects ("the theory") (the one to one logical correspondence between\nthe experiment values and the eigenvalues).\n\nPostulate 4 is the born rules and postulate 5 is what I call the formal\nmeasurement in previous posts.\n\nPostulates 1-5 are the description choice of the theory (in principle\nnot falsifiable) . Postulate 6 is the real content of the theory\n(falsifiable).\n\nIf you need some additional clarifications, do not hesitate to ask.\n>\n> > I need quantum interactions to describe the whole unitary evolution of\n> > the system and the measurement apparatus object.\n>\n> This is not unitary unless you also include the environment interacting\n> with the apparatus.\n\nAgreed in the "reality".\nIt was implicitly assumed in the measurement apparatus object whenever\nit is required for the model (to give correst results).\nSee postulate 6.\n\n> > We use these statistical correlations on the statistics of formal\n> > measurement results of this whole system (including the "measurement\n> > apparatus" that has not to be confused with the formal measurement\n> > result). That\'s what the formalism allows one to say (hence the\n> > requirement of interactions to correlate the measurement apparatus to\n> > the system).\n>\n> Thus the formalism says nothing without interpretation, since it is not\n> applicable to the real world without it...\n>\nSee Postulates 2 - 3. We have a direct connection between the\neigenvalues of observables with measurement results of "real word".\nNote that the postulates 2-3 are descriptive postulates and not\npredictive postulates.\nIn addition, postulate 4 allows one to calculate the probability law\nbased on a set of identical independent systems.\nTherefore, the formalism is sufficient to build logical assertions an\nverifications concerning the "real world": the formal description\nand verification.\n>\n> > Saying the measurement\n> > apparatus does a formal measurement is interpretation (completely out\n> > of the scope of the QM formalism). I do not refute the interpretation,\n> > nor I can\'t as long as it is consistent with the formalism.\n>\n> A measurement apparatus deserves its name only if it indeed performs\n> measurements.\n>\nYes. It is what I call an external definition (somewhat recursive : ):\nWe can define formally a measurement apparatus with the indentification\nof a subsystem attached to a local observable where we have the\nmeasurement results. It defines an external property that does not\nchange the QM formalism.\n\nIn this case the measurement apparatus is formally defined by the local\nhilbert space of the local observable. However, giving such a\nmeasurement apparatus (the local hilbert space) does not define the\nlocal observable giving the measurement results. In other words, such a\nmeasurement apparatus definition does define the measurement\nobservable.\n\n>\n> But interaction is involved in being able to observe the result.\n> You cannot read a pointer unless you interact with it.\n>\nIt depends on what you mean by the words "observe" and "read".\n\n>From postulate 3, I have only measurement results: "Outcome of A is a",\na property of the considered "system". This is sufficient to\ndescribe the "system" outcomes. Only the properties (the outcome\nvalues) of a complete set of commuting observable are possible to\ndescribe completely one "system" (postulate 1+property of the set\nof complete set of commuting observables).\n\nThe interactions, if they exist, are part of the unitary evolution\ndescription of the "system" (they define the Hamiltonian\nobservable).\n\n(Here I use the "system" used by the 6 postulates. It includes, the\n"real" system, the "measurement apparatus" and the environment\nif necessary in order to have a unitary evolution).\n\n>\n> I don\'t think the problems of quantum mechanics go away simply\n> by nit-picking on words.\n>\nNo they do not. The formalism of QM allows one to better find the\nproblems, especially the prediction problems not solved by the 6\npostulates. We may concentrate on the logical deductions provided by\nthe formalism in order to answer to some questions such as the one of\nthe preferred basis.\n\nQM formalism allows one to separate, in a very formal way, the\npredictions from the observations. In CM, I do not question why a\nparticle is at a given position (the description used by CM: it is a\nchoice). Postulates 1-5 are of the same form, with a minor change: the\ndescription is contextual (the choice depends on the experiment).\nTherefore we have a new problem in QM: the prediction of the context of\na given experiment (i.e. the observable of the experiment - the\npreferred basis of the measurement results) as it is not fixed by the\npostulates. (In CM it is fixed once forever: the position).\n\nCurrently I do not know if it is important or not to have such a\nprediction, as this prediction may be (not?) solved in the limit of\nlarge systems, by some properties (may be decoherence, a thermodynamic\nresult, ...). I think this is the central question of the measurement.\n\n> > So, Do you claim the measurement postulates of QM formalism are wrong\n> > in some obscure cases?\n>\n> No. I claim the measurement postulates of QM describe a very early\n> (1932) stage of quantum mechanical measurement theory that is long\n> being superseded in practice. A more modern view related to modern\n> experimental practice is in\n> V.B. Braginsky and F. Ya. Khalili\n> Quantum measurement,\n> Cambridge Univ. Press, Cambridge 1992.\n> On p.28 they write:\n> \'\'It is important to note that in many _real_ [original kursiv]\n> measurements the final state is substantially different\n> from |q_n>.\'\' [the eigenstate after measurwement of q]\n> and continue on p.30:\n> \'\'We turn attention, now, from idealized, exact measurements,\n> to the development of a formalism that will help us to handle\n> more nearly realistic, approximate measurements.\'\'\n> Then follow 1050 further pages with the modern view.\n>\nI do not question the development of a model of "realistic\napproximate measurements" as long as we are not confusing the goals\nof such models: these models keep the theory (the 6 postulates, hence\nthe "formal measurement"). These models just allow one to get some\ngeneral results, such as\na) Some formal results on some large systems (such as non unitary local\nevolution, determinist local evolution, decoherence results, ...)\nb) The prediction of the basis of a measurement.\nc) etc ...\nDecoherence provides results on point a). However, I have not found any\nconcluding result concerning point b: the prediction of the context of\na peculiar experiment.\n>\n> > The main difference is on the collapse of the word meanings: what you\n> > call measurement is not the measurement described in QM formalism.\n>\n> What I call measurement is what experimentalists call measurement.\n> Only that counts.\n\nThink on the meaning of this sentence. Only logic counts.\nExperimentalists need the formalism to make logical affirmations. Once\nagain: call "measurement" what you want as long as it does not\nchange the measurement result meaning/mapping given by the QM\npostulates. If you/experimentalist change that, you change the theory\n(description modification).\n\nTherefore, If you prefer to reserve the measurement word to a specific\ndefinition. Ok. However, we have to take care in not mixing " a\nmeasurement result" from this definition with the "measurement\nresults" of postulate 3-4-5 (the description of "real experiments").\n\nI will try to restrict myself to "measurement results" (meaning\ngiven by postulates) in order to avoid a confusion with\n"measurements".\n\n>Physics is there to explain experiments, and\n> if some theorists use the term \'measurement\' in a different sense,\n> I am not interested, and claim that this usage has no practical\n> relevance (except to cloud the issues).\n>\nI do not follow you. The formalism avoids such confusions. We know\nexactly what are the descriptions (collected from the experiments) and\nwhat are the predictions (prediction of some experimental results -\nhere statistics). How to be more clear and practical?\n>From this formalism, I know, clearly, it does not predict the context\nof the experiments (the basis of the measurement results).\nThis is very clear, at least for me, and it helps me in asking some\npractical questions, that the formalism does not seem to solve.\n>\n> >>\n> > With the outcomes mapping with the "reality", the property\n> > "outcome of A is a" has both a signification in a real object as\n> > well as in a symbolic one.\n> > (here property: the mathematical signification. You can use proposition\n> > if you it is more adequate).\n>\n> Do you mean by "outcome of A is a" - "a is an eigenvalue of A"?\n\nyes\n\n\n> Then I can see how it is represented in the formalism.\n> But then I can\'t see how it is related to reality.\n>\nCf postulate 3: "outcome of A_phys is a". The physical variable\nA_phys of this system has the value a (in the "reality"). Therefore\nfrom postulate 2, a is the eigenvalue of A (the operator observable\nassociated to the physical variable A_phys).\n\n(postulate 3 is mainly the desciption of reality by the quantum\nobjects).\n\n(I am using the probabilistic language as from postulate 4, I know it\napplies formally to each set of identical experiments: statistical\nview).\n\n>\n> > In the traditional formalism of QM, when the collapse postulate is\n> > true, the property "outcome of A is a" is true. This is a property\n> > of the considered system (logic).If this property is false the\n> > corresponding collapse postulate is also false => the collapse of a\n> > system is a property of the system (QM formalism).\n> >\n> > I am not inventing new words, I am just using mathematical results of\n> > the QM formalism.\n>\n> This conservation makes little sense unless you clearly state a\n> complete set of rules that defines your QM formalism. We misunderstand\n> each other constantly.\n>\nI hope my view is clearer now.\n>\n> >>Von Neumann\'s 1932 postulates are no longer believed to be valid\n> >>for small systems since it is well recognized that these are\n> >>necessarily open.\n> >>\n> > This is a matter of words. What you say is that you always have\n> > interactions with other parts of the world, even for a small system.\n> > This in no case refutes the fundamental postulates.\n>\n> The postulates cannot be refuted, but their domain of valididy\n> is open to experiment.\n\nPerfectly agree. The theory (its postulates) hopefully may be falsified\nby experiments. We mainly have 2 choices in case of falsification:\neither the Hamiltonian is not correct or either the unitary evolution\ndoes not strictly apply. Other ones may exist but they are less evident\n: ). The definition of another theory may require the choice of a new\ndescription (for simple and practical results reason).\n\n> In particular, they apply only to closed\n> systems, and this means only to the universe as a whole.\n>\nStritcly speaking yes.\n(we need to have some additionnal decoherence properties in order to\nknow what criterion/ria to use in order to consider a block separated\nfrom the rest of the universe)\n\nSeratend.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>[Collapsing the 2 previous posts:]
Arnold Neumaier wrote:
> Please give an explicit and complete formal statement of what you
> consider to be the 6 usual postulates + the mapping, so that we have
> common ground for discussion.
>
Arnold Neumaier wrote:
> > QM formalism does not say what is a real measurement. QM formalism
> > speaks about the collapse postulate and the born rules and the unitary
> > evolution. That's all.
>
> I hope you'll give somewhere a precise definition of what the QM
> formalism speaks about. What you assert sounds (in its delineation)
> very different from what I commonly read.
>
>
Good remark. I was assuming we have a common ground concerning QM
theory formalism and this may not be completely true.
I hope you understand my point of view: I want logical deductions
hypotheses that may be falsified by the experiments based on the QM
formalism (the 6 postulates below).
The six postulates of QM theory I use are (what I call the formalism
[of the theory]):
(One can find them in an almost identical form in "mécanique
quantique I", Cohen-Tannoudji, Diu, Laloe, 1977).
Postulate 1:
=========
The state of a "system" at time t is a unit vector |\psi(t)> of a
separable complex Hilbert space H.
(note: unit vector is sometimes replaced by ray, or simply by a vector)
(note: sometimes the state is called "the complete knowledge of a
system")
Postulate 2:
=======
Every "physical variable" A_{phys} of a system is represented by an
operator A defined on H. This operator is an observable.
The observable operator property is usually interpreted as an hermitian
operator where its eigenvectors form a basis, or a generalized basis,
of the space H.
This is the mapping A_{phys} --> A. We usually add (implicitly) the
following property to this postulate: the mapping between A_{phys} and A
is bijective
Postulate 3:
========
The "measurement result" of a physical variable A_{phys} represented
by the observable A is *one* of the eigenvalues of A:
Mes_result(A_{phys})= a, a[/itex] in spec(A)
This is the formal mapping: result of a physical experiment -->
eigenvalue of an observable.
We usually suppose, in addition a bijective mapping between the set of
eigenvalues of the observable A and the set of possible values of the
physical variable A_{phys}.
The bijective property is sufficient to explain the constraints on the
measurement (the possible set of properties) of non commuting
observables (and hence on the physical variables) and the contextuality
of the "measurement result" (by the non commutativity of observables).
Postulate 4:
=======
The measurement result "a" of a physical observable represented by
the observable A of a system with a *unit* state |\psi> has the
*probability*:
a) a is in the discrete spectrum part of A:
[itex]P(a||\psi>)= <\psi|P_a|\psi>
Where P_a is the projector in the eingenspace of the observable A for
the eigenvalue A.
b) a is the continuous spectrum part of A:
P(a||\psi>)da= <\psi|P_a|\psi>da
Where P_a is the projector in the eingenspace of the observable A for
the eigenvalue A.
( b is just a derivation of a, as we can only "certainly" measure
results with probability occurrences different from 0: we can only
measures a set of continuous eigenvalues with a measure different from
=> automatically defines a locally discrete observable, function of
the continuous observable)
Postutale 4 is consistent whenever we have a bijective bi-measurable
mapping between the physical variable set of values and the observable
set of eigenvalues.
the probability law on the set of values of the physical observable
infers a probability law on the set of eigenvalues and in the same for
other way through this bi-measurable mapping.
Therefore, taking a set of N independent identical systems (state
|\psi>: postulate 1), we have:
n(a)/N --> P(a||\psi>) when N goes to the infinity, formally from the
laws of large number.
Postulate 4 and the previous ones allow the formal mapping of the
statistics of experimental results into the statistics given by an
observable and a state.
We can therefore call "a" an outcome of a given experiment (probability
language).
Postulate 5:
=======
If a system is in a state |\psi_before> "before" the "measurement
result is a" of a given physical variable A_{phys}, the state of the
system "just after" the measurement is the normalized projected
state |\psi_after>:|\psi_after>= P_a.|\psi_before>/\sqrt[<\psi_before|P_a|\psi_before>]
Where P_a is the projector in the eigenspace of the observable A for
the eigenvalue a.
Note: the results are given in a statistical view, in other words,
"gives the result a", usually assumes that P(a||\psi>)=/=0
Postulate 6:
========
The evolution in time of the state vector |\psi(t)> of a system is given
by the Schrödinger equation:
Ihbard/dt|\psi(t)>= H(t)|\psi(t)>.
Where H is the observable associated to the *total* energy of the
"system" (the total energy physical variable). H is called the
Hamiltonian of the system.
==========================
The postulates 2 - 3 in fact already defines the formal mapping
between the experiment results ("the reality") and the mathematical
objects ("the theory") (the one to one logical correspondence between
the experiment values and the eigenvalues).
Postulate 4 is the born rules and postulate 5 is what I call the formal
measurement in previous posts.
Postulates 1-5 are the description choice of the theory (in principle
not falsifiable) . Postulate 6 is the real content of the theory
(falsifiable).
If you need some additional clarifications, do not hesitate to ask.
>
> > I need quantum interactions to describe the whole unitary evolution of
> > the system and the measurement apparatus object.
>
> This is not unitary unless you also include the environment interacting
> with the apparatus.
Agreed in the "reality".
It was implicitly assumed in the measurement apparatus object whenever
it is required for the model (to give correst results).
See postulate 6.
> > We use these statistical correlations on the statistics of formal
> > measurement results of this whole system (including the "measurement
> > apparatus" that has not to be confused with the formal measurement
> > result). That's what the formalism allows one to say (hence the
> > requirement of interactions to correlate the measurement apparatus to
> > the system).
>
> Thus the formalism says nothing without interpretation, since it is not
> applicable to the real world without it...
>
See Postulates 2 - 3. We have a direct connection between the
eigenvalues of observables with measurement results of "real word".
Note that the postulates 2-3 are descriptive postulates and not
predictive postulates.
In addition, postulate 4 allows one to calculate the probability law
based on a set of identical independent systems.
Therefore, the formalism is sufficient to build logical assertions an
verifications concerning the "real world": the formal description
and verification.
>
> > Saying the measurement
> > apparatus does a formal measurement is interpretation (completely out
> > of the scope of the QM formalism). I do not refute the interpretation,
> > nor I can't as long as it is consistent with the formalism.
>
> A measurement apparatus deserves its name only if it indeed performs
> measurements.
>
Yes. It is what I call an external definition (somewhat recursive : ):
We can define formally a measurement apparatus with the indentification
of a subsystem attached to a local observable where we have the
measurement results. It defines an external property that does not
change the QM formalism.
In this case the measurement apparatus is formally defined by the local
hilbert space of the local observable. However, giving such a
measurement apparatus (the local hilbert space) does not define the
local observable giving the measurement results. In other words, such a
measurement apparatus definition does define the measurement
observable.
>
> But interaction is involved in being able to observe the result.
> You cannot read a pointer unless you interact with it.
>
It depends on what you mean by the words "observe" and "read".
>From postulate 3, I have only measurement results: "Outcome of A is a",
a property of the considered "system". This is sufficient to
describe the "system" outcomes. Only the properties (the outcome
values) of a complete set of commuting observable are possible to
describe completely one "system" (postulate 1+property of the set
of complete set of commuting observables).
The interactions, if they exist, are part of the unitary evolution
description of the "system" (they define the Hamiltonian
observable).
(Here I use the "system" used by the 6 postulates. It includes, the
"real" system, the "measurement apparatus" and the environment
if necessary in order to have a unitary evolution).
>
> I don't think the problems of quantum mechanics go away simply
> by nit-picking on words.
>
No they do not. The formalism of QM allows one to better find the
problems, especially the prediction problems not solved by the 6
postulates. We may concentrate on the logical deductions provided by
the formalism in order to answer to some questions such as the one of
the preferred basis.
QM formalism allows one to separate, in a very formal way, the
predictions from the observations. In CM, I do not question why a
particle is at a given position (the description used by CM: it is a
choice). Postulates 1-5 are of the same form, with a minor change: the
description is contextual (the choice depends on the experiment).
Therefore we have a new problem in QM: the prediction of the context of
a given experiment (i.e. the observable of the experiment - the
preferred basis of the measurement results) as it is not fixed by the
postulates. (In CM it is fixed once forever: the position).
Currently I do not know if it is important or not to have such a
prediction, as this prediction may be (not?) solved in the limit of
large systems, by some properties (may be decoherence, a thermodynamic
result, ...). I think this is the central question of the measurement.
> > So, Do you claim the measurement postulates of QM formalism are wrong
> > in some obscure cases?
>
> No. I claim the measurement postulates of QM describe a very early
> (1932) stage of quantum mechanical measurement theory that is long
> being superseded in practice. A more modern view related to modern
> experimental practice is in
> V.B. Braginsky and F. Ya. Khalili
> Quantum measurement,
> Cambridge Univ. Press, Cambridge 1992.
> On p.28 they write:
> ''It is important to note that in many _real_ [original kursiv]
> measurements the final state is substantially different
> from |q_n>.'' [the eigenstate after measurwement of q]
> and continue on p.30:
> ''We turn attention, now, from idealized, exact measurements,
> to the development of a formalism that will help us to handle
> more nearly realistic, approximate measurements.''
> Then follow 1050 further pages with the modern view.
>
I do not question the development of a model of "realistic
approximate measurements" as long as we are not confusing the goals
of such models: these models keep the theory (the 6 postulates, hence
the "formal measurement"). These models just allow one to get some
general results, such as
a) Some formal results on some large systems (such as non unitary local
evolution, determinist local evolution, decoherence results, ...)
b) The prediction of the basis of a measurement.
c) etc ...
Decoherence provides results on point a). However, I have not found any
concluding result concerning point b: the prediction of the context of
a peculiar experiment.
>
> > The main difference is on the collapse of the word meanings: what you
> > call measurement is not the measurement described in QM formalism.
>
> What I call measurement is what experimentalists call measurement.
> Only that counts.
Think on the meaning of this sentence. Only logic counts.
Experimentalists need the formalism to make logical affirmations. Once
again: call "measurement" what you want as long as it does not
change the measurement result meaning/mapping given by the QM
postulates. If you/experimentalist change that, you change the theory
(description modification).
Therefore, If you prefer to reserve the measurement word to a specific
definition. Ok. However, we have to take care in not mixing " a
measurement result" from this definition with the "measurement
results" of postulate 3-4-5 (the description of "real experiments").
I will try to restrict myself to "measurement results" (meaning
given by postulates) in order to avoid a confusion with
"measurements".
>Physics is there to explain experiments, and
> if some theorists use the term 'measurement' in a different sense,
> I am not interested, and claim that this usage has no practical
> relevance (except to cloud the issues).
>
I do not follow you. The formalism avoids such confusions. We know
exactly what are the descriptions (collected from the experiments) and
what are the predictions (prediction of some experimental results -
here statistics). How to be more clear and practical?
>From this formalism, I know, clearly, it does not predict the context
of the experiments (the basis of the measurement results).
This is very clear, at least for me, and it helps me in asking some
practical questions, that the formalism does not seem to solve.
>
> >>
> > With the outcomes mapping with the "reality", the property
> > "outcome of A is a" has both a signification in a real object as
> > well as in a symbolic one.
> > (here property: the mathematical signification. You can use proposition
> > if you it is more adequate).
>
> Do you mean by "outcome of A is a" - "a is an eigenvalue of A"?
yes
> Then I can see how it is represented in the formalism.
> But then I can't see how it is related to reality.
>
Cf postulate 3: "outcome of A_{phys} is a". The physical variable
A_{phys} of this system has the value a (in the "reality"). Therefore
from postulate 2, a is the eigenvalue of A (the operator observable
associated to the physical variable A_{phys}).
(postulate 3 is mainly the desciption of reality by the quantum
objects).
(I am using the probabilistic language as from postulate 4, I know it
applies formally to each set of identical experiments: statistical
view).
>
> > In the traditional formalism of QM, when the collapse postulate is
> > true, the property "outcome of A is a" is true. This is a property
> > of the considered system (logic).If this property is false the
> > corresponding collapse postulate is also false => the collapse of a
> > system is a property of the system (QM formalism).
> >
> > I am not inventing new words, I am just using mathematical results of
> > the QM formalism.
>
> This conservation makes little sense unless you clearly state a
> complete set of rules that defines your QM formalism. We misunderstand
> each other constantly.
>
I hope my view is clearer now.
>
> >>Von Neumann's 1932 postulates are no longer believed to be valid
> >>for small systems since it is well recognized that these are
> >>necessarily open.
> >>
> > This is a matter of words. What you say is that you always have
> > interactions with other parts of the world, even for a small system.
> > This in no case refutes the fundamental postulates.
>
> The postulates cannot be refuted, but their domain of valididy
> is open to experiment.
Perfectly agree. The theory (its postulates) hopefully may be falsified
by experiments. We mainly have 2 choices in case of falsification:
either the Hamiltonian is not correct or either the unitary evolution
does not strictly apply. Other ones may exist but they are less evident
: ). The definition of another theory may require the choice of a new
description (for simple and practical results reason).
> In particular, they apply only to closed
> systems, and this means only to the universe as a whole.
>
Stritcly speaking yes.
(we need to have some additionnal decoherence properties in order to
know what criterion/ria to use in order to consider a block separated
from the rest of the universe)
Seratend.
Aaron Bergman
Jun12-05, 12:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1118483664.352801.309460@o13g2000cwo.googlegroups .com>,\nSeratend <ser_monmail@yahoo.fr> wrote:\n\n> And the end of this section:\n>\n> " However, the eigenstates of the decohered reduced density matrix will\n> in many situations approximate the quasiclassical stable\n> pointer states well, especially when these pointer states\n> are sufficiently nondegenerate."\n>\n> I like the "in many situations" and the "approximate" words to try to\n> escape form the problems. We are again in the approximation domain\n> where we can say what we want depending on the assumptions. In other\n> words, these adequate *external* assumptions define the basis.\n\nI don\'t think so. There are some technical issues, but for any\nexperiment you can describe where a human observer can gain information,\nthere isn\'t going to be a problem.\n\nI believe that in any such experiment there is, a priori, a set of\nmacrostates that encode the measurement. If there were no such thing,\nthen the observer could not gain information. Secondly, decoherence\n(which you believe in as best I can tell) diagonalizes the reduced\ndensity matrix in this basis of states.\n\nNow, if you want to argue that the only way we can determine the\nmeasurement macrostates is experimentally, I\'ll just have to disagree\nwith you. This is not a quantum problem; it\'s just a matter of the\ndescription of the measurement apparatus.\n\n[...]\n>\n> Up to know, you have not proved the ability of decoherence to predict a\n> basis of a measurement without an external assumption which is, in\n> addition, context dependant (it depends on the type of experiment!).\n\nDecoherence doesn\'t predict anything. Decoherence is a process that\ndiagonalizes the reduced the density matrix in a particular basis.\nBecause decoherence is just unitary evolution, given any experimental\nsetup, we can determine *solely from the rules of quantum mechanics* the\nbasis in which the reduced density matrix is diagonalized. All we have\nto do is wait the decoherence time.\n\nThe only needed information here is which trace we take to get the\nreduced density matrix, but that is part of definition of the experiment.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1118483664.352801.309460@o13g2000cwo.googlegroups. com>,
Seratend <ser_monmail@yahoo.fr> wrote:
> And the end of this section:
>
> " However, the eigenstates of the decohered reduced density matrix will
> in many situations approximate the quasiclassical stable
> pointer states well, especially when these pointer states
> are sufficiently nondegenerate."
>
> I like the "in many situations" and the "approximate" words to try to
> escape form the problems. We are again in the approximation domain
> where we can say what we want depending on the assumptions. In other
> words, these adequate *external* assumptions define the basis.
I don't think so. There are some technical issues, but for any
experiment you can describe where a human observer can gain information,
there isn't going to be a problem.
I believe that in any such experiment there is, a priori, a set of
macrostates that encode the measurement. If there were no such thing,
then the observer could not gain information. Secondly, decoherence
(which you believe in as best I can tell) diagonalizes the reduced
density matrix in this basis of states.
Now, if you want to argue that the only way we can determine the
measurement macrostates is experimentally, I'll just have to disagree
with you. This is not a quantum problem; it's just a matter of the
description of the measurement apparatus.
[...]
>
> Up to know, you have not proved the ability of decoherence to predict a
> basis of a measurement without an external assumption which is, in
> addition, context dependant (it depends on the type of experiment!).
Decoherence doesn't predict anything. Decoherence is a process that
diagonalizes the reduced the density matrix in a particular basis.
Because decoherence is just unitary evolution, given any experimental
setup, we can determine *solely from the rules of quantum mechanics* the
basis in which the reduced density matrix is diagonalized. All we have
to do is wait the decoherence time.
The only needed information here is which trace we take to get the
reduced density matrix, but that is part of definition of the experiment.
Aaron
Aaron Bergman
Jun12-05, 02:28 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <abergman-8D870A.21041011062005@localhost>,\nAaron Bergman <abergman@physics.utexas.edu> wrote:\n\n> Decoherence doesn\'t predict anything.\n\nPerhaps I should better say that decoherence doesn\'t predict anything\nthat unitary evolution doesn\'t.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <abergman-8D870A.21041011062005@localhost>,
Aaron Bergman <abergman@physics.utexas.edu> wrote:
> Decoherence doesn't predict anything.
Perhaps I should better say that decoherence doesn't predict anything
that unitary evolution doesn't.
Aaron
Seratend
Jun13-05, 01:17 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> In article <1118483664.352801.309460@o13g2000cwo.googlegroups .com>,\n> Seratend <ser_monmail@yahoo.fr> wrote:\n>\n> > And the end of this section:\n> >\n> > " However, the eigenstates of the decohered reduced density matrix will\n> > in many situations approximate the quasiclassical stable\n> > pointer states well, especially when these pointer states\n> > are sufficiently nondegenerate."\n> >\n> > I like the "in many situations" and the "approximate" words to try to\n> > escape form the problems. We are again in the approximation domain\n> > where we can say what we want depending on the assumptions. In other\n> > words, these adequate *external* assumptions define the basis.\n>\n> I don\'t think so. There are some technical issues, but for any\n> experiment you can describe where a human observer can gain information,\n> there isn\'t going to be a problem.\n>\nHere we are again : ), you are using an external assumption: the human\nobserver has a single preferred local basis.\nOk, now, how can you get, from QM theory, such an affirmation?\n\nSeratend.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> In article <1118483664.352801.309460@o13g2000cwo.googlegroups. com>,
> Seratend <ser_monmail@yahoo.fr> wrote:
>
> > And the end of this section:
> >
> > " However, the eigenstates of the decohered reduced density matrix will
> > in many situations approximate the quasiclassical stable
> > pointer states well, especially when these pointer states
> > are sufficiently nondegenerate."
> >
> > I like the "in many situations" and the "approximate" words to try to
> > escape form the problems. We are again in the approximation domain
> > where we can say what we want depending on the assumptions. In other
> > words, these adequate *external* assumptions define the basis.
>
> I don't think so. There are some technical issues, but for any
> experiment you can describe where a human observer can gain information,
> there isn't going to be a problem.
>
Here we are again : ), you are using an external assumption: the human
observer has a single preferred local basis.
Ok, now, how can you get, from QM theory, such an affirmation?
Seratend.
I.Vecchi
Jun13-05, 10:18 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> for any\n> experiment you can describe where a human observer can gain information,\n> there isn\'t going to be a problem.\n\nMaybe, but then you are saying that the measurement process is "human\nobserver"-dependent, right?\n\n>\n> I believe that in any such experiment there is, a priori, a set of\n> macrostates that encode the measurement.\n\nYou mean for the "human observer" ? Are you saying that\'s the "human\nobserver" that determines the basis?\n\n>If there were no such thing,\n> then the observer could not gain information. Secondly, decoherence\n> (which you believe in as best I can tell) diagonalizes the reduced\n> density matrix in this basis of states.\n\nThe point here is that the experiments DO NOT exhibit DT\'s\ndiagonalisation of the density matrix, which is a formal construct\nbased on unphysical assumptions. What one can observe is that relatives\nphases are being randomly perturbed , so that the observer is unable to\ntrack/detect the corresponding interference patterns. As a simple\nexample consider a Mach-Zehnder interferometer where a random phase\nchanger has been inserted in one of the arms. For an observer that has\naccessonly to the detector , it will look as if the photons have\n"decohered", i.e. their behaviour will be the same as if they were\nbeing fired up one or the other arm of the interferometer. Random phase\nchange destroys the interference patterns for the external observer,\nbut it does not diagonalise the density martix, nor does it pick a\nbasis.\n\n> Decoherence doesn\'t predict anything. Decoherence is a process that\n> diagonalizes the reduced the density matrix in a particular basis.\n> Because decoherence is just unitary evolution, given any experimental\n> setup, we can determine *solely from the rules of quantum mechanics* the\n> basis in which the reduced density matrix is diagonalized. All we have\n> to do is wait the decoherence time.\n\nAnd keep the faith.\n\nIV\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> for any
> experiment you can describe where a human observer can gain information,
> there isn't going to be a problem.
Maybe, but then you are saying that the measurement process is "human
observer"-dependent, right?
>
> I believe that in any such experiment there is, a priori, a set of
> macrostates that encode the measurement.
You mean for the "human observer" ? Are you saying that's the "human
observer" that determines the basis?
>If there were no such thing,
> then the observer could not gain information. Secondly, decoherence
> (which you believe in as best I can tell) diagonalizes the reduced
> density matrix in this basis of states.
The point here is that the experiments DO NOT exhibit DT's
diagonalisation of the density matrix, which is a formal construct
based on unphysical assumptions. What one can observe is that relatives
phases are being randomly perturbed , so that the observer is unable to
track/detect the corresponding interference patterns. As a simple
example consider a Mach-Zehnder interferometer where a random phase
changer has been inserted in one of the arms. For an observer that has
accessonly to the detector , it will look as if the photons have
"decohered", i.e. their behaviour will be the same as if they were
being fired up one or the other arm of the interferometer. Random phase
change destroys the interference patterns for the external observer,
but it does not diagonalise the density martix, nor does it pick a
basis.
> Decoherence doesn't predict anything. Decoherence is a process that
> diagonalizes the reduced the density matrix in a particular basis.
> Because decoherence is just unitary evolution, given any experimental
> setup, we can determine *solely from the rules of quantum mechanics* the
> basis in which the reduced density matrix is diagonalized. All we have
> to do is wait the decoherence time.
And keep the faith.
IV
Aaron Bergman
Jun13-05, 12:19 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1118659478.518851.280290@g14g2000cwa.googlegroups .com>,\n"I.Vecchi" <vecchi@weirdtech.com> wrote:\n\n> Aaron Bergman wrote:\n> > for any\n> > experiment you can describe where a human observer can gain information,\n> > there isn\'t going to be a problem.\n>\n> Maybe, but then you are saying that the measurement process is "human\n> observer"-dependent, right?\n\nI\'m describing a pragmatic approach. In general, I don\'t think that\ndecoherence solves the problem of measurement. But, if we postulate that\nmeasurements occur as I describe, then decoherence describes how the\nmacroscopic and microscopic observables entangle and select the basis\nfor the microscopic observables.\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1118659478.518851.280290@g14g2000cwa.googlegroups. com>,
"I.Vecchi" <vecchi@weirdtech.com> wrote:
> Aaron Bergman wrote:
> > for any
> > experiment you can describe where a human observer can gain information,
> > there isn't going to be a problem.
>
> Maybe, but then you are saying that the measurement process is "human
> observer"-dependent, right?
I'm describing a pragmatic approach. In general, I don't think that
decoherence solves the problem of measurement. But, if we postulate that
measurements occur as I describe, then decoherence describes how the
macroscopic and microscopic observables entangle and select the basis
for the microscopic observables.
Aaron
Aaron Bergman
Jun13-05, 12:19 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <1118600151.915458.310130@g43g2000cwa.googlegroups .com>,\n"Seratend" <ser_monmail@yahoo.fr> wrote:\n\n> Aaron Bergman wrote:\n> > In article <1118483664.352801.309460@o13g2000cwo.googlegroups .com>,\n> > Seratend <ser_monmail@yahoo.fr> wrote:\n> >\n> > > And the end of this section:\n> > >\n> > > " However, the eigenstates of the decohered reduced density matrix will\n> > > in many situations approximate the quasiclassical stable\n> > > pointer states well, especially when these pointer states\n> > > are sufficiently nondegenerate."\n> > >\n> > > I like the "in many situations" and the "approximate" words to try to\n> > > escape form the problems. We are again in the approximation domain\n> > > where we can say what we want depending on the assumptions. In other\n> > > words, these adequate *external* assumptions define the basis.\n> >\n> > I don\'t think so. There are some technical issues, but for any\n> > experiment you can describe where a human observer can gain information,\n> > there isn\'t going to be a problem.\n> >\n> Here we are again : ), you are using an external assumption: the human\n> observer has a single preferred local basis.\n> Ok, now, how can you get, from QM theory, such an affirmation?\n\nNo, the apparatus does if the human is going to gain information from\nit. (Although I suppose, perhaps, that one might have to appeal to rods\nand cones in some situation.)\n\nAaron\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <1118600151.915458.310130@g43g2000cwa.googlegroups. com>,
"Seratend" <ser_monmail@yahoo.fr> wrote:
> Aaron Bergman wrote:
> > In article <1118483664.352801.309460@o13g2000cwo.googlegroups. com>,
> > Seratend <ser_monmail@yahoo.fr> wrote:
> >
> > > And the end of this section:
> > >
> > > " However, the eigenstates of the decohered reduced density matrix will
> > > in many situations approximate the quasiclassical stable
> > > pointer states well, especially when these pointer states
> > > are sufficiently nondegenerate."
> > >
> > > I like the "in many situations" and the "approximate" words to try to
> > > escape form the problems. We are again in the approximation domain
> > > where we can say what we want depending on the assumptions. In other
> > > words, these adequate *external* assumptions define the basis.
> >
> > I don't think so. There are some technical issues, but for any
> > experiment you can describe where a human observer can gain information,
> > there isn't going to be a problem.
> >
> Here we are again : ), you are using an external assumption: the human
> observer has a single preferred local basis.
> Ok, now, how can you get, from QM theory, such an affirmation?
No, the apparatus does if the human is going to gain information from
it. (Although I suppose, perhaps, that one might have to appeal to rods
and cones in some situation.)
Aaron
I.Vecchi
Jun14-05, 12:22 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Bergman wrote:\n> for any\n> experiment you can describe where a human observer can gain information,\n> there isn\'t going to be a problem.\n\nMaybe, but then you are saying that the measurement process is "human\nobserver"-dependent, right?\n\n>\n> I believe that in any such experiment there is, a priori, a set of\n> macrostates that encode the measurement.\n\nYou mean for the "human observer" ? Are you saying that\'s the "human\nobserver" that determines the basis?\n\n>If there were no such thing,\n> then the observer could not gain information. Secondly, decoherence\n> (which you believe in as best I can tell) diagonalizes the reduced\n> density matrix in this basis of states.\n\nThe point here is that the experiments DO NOT exhibit DT\'s\ndiagonalisation of the density matrix, which is a formal construct\nbased on unphysical assumptions. What one can observe is that relatives\nphases are being randomly perturbed , so that the observer is unable to\ntrack/detect the corresponding interference patterns. As a simple\nexample consider a Mach-Zehnder interferometer where a random phase\nchanger has been inserted in one of the arms. For an observer that has\naccessonly to the detector , it will look as if the photons have\n"decohered", i.e. their behaviour will be the same as if they were\nbeing fired up one or the other arm of the interferometer. Random phase\nchange destroys the interference patterns for the external observer,\nbut it does not diagonalise the density martix, nor does it pick a\nbasis.\n\n> Decoherence doesn\'t predict anything. Decoherence is a process that\n> diagonalizes the reduced the density matrix in a particular basis.\n> Because decoherence is just unitary evolution, given any experimental\n> setup, we can determine *solely from the rules of quantum mechanics* the\n> basis in which the reduced density matrix is diagonalized. All we have\n> to do is wait the decoherence time.\n\nAnd keep the faith.\n\nIV\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Bergman wrote:
> for any
> experiment you can describe where a human observer can gain information,
> there isn't going to be a problem.
Maybe, but then you are saying that the measurement process is "human
observer"-dependent, right?
>
> I believe that in any such experiment there is, a priori, a set of
> macrostates that encode the measurement.
You mean for the "human observer" ? Are you saying that's the "human
observer" that determines the basis?
>If there were no such thing,
> then the observer could not gain information. Secondly, decoherence
> (which you believe in as best I can tell) diagonalizes the reduced
> density matrix in this basis of states.
The point here is that the experiments DO NOT exhibit DT's
diagonalisation of the density matrix, which is a formal construct
based on unphysical assumptions. What one can observe is that relatives
phases are being randomly perturbed , so that the observer is unable to
track/detect the corresponding interference patterns. As a simple
example consider a Mach-Zehnder interferometer where a random phase
changer has been inserted in one of the arms. For an observer that has
accessonly to the detector , it will look as if the photons have
"decohered", i.e. their behaviour will be the same as if they were
being fired up one or the other arm of the interferometer. Random phase
change destroys the interference patterns for the external observer,
but it does not diagonalise the density martix, nor does it pick a
basis.
> Decoherence doesn't predict anything. Decoherence is a process that
> diagonalizes the reduced the density matrix in a particular basis.
> Because decoherence is just unitary evolution, given any experimental
> setup, we can determine *solely from the rules of quantum mechanics* the
> basis in which the reduced density matrix is diagonalized. All we have
> to do is wait the decoherence time.
And keep the faith.
IV
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Having raised the question, I am awed by the explosive debate that\nensued.\n\nMost of our contributors have stuck to a discussion of what it means to\nreduce a state-vector in the Hamiltonian (canonical) approach to\nquantum mechanics. I would like to point out that in the Feynman\nversion of QM (the spacetime approach), there is no physical operation\ncorresponding to reduction. In the spacetime version you are simply\nasking the question: what are my chances of ending up in that quantum\nstate if I start from this quantum state. Since the spacetime approach\ngives us all the physics, I suspect that \'state-vector reduction\' might\nin fact be an artefact of the Hamiltonian approach to quantum mechanics\nwith all its operators and what not.\n\nI am probably and hopefully wrong, for there is a problem with that. It\nhas to do with the directionality of time:\n\nConsider the collision of 10 or more elementary particles. The\namplitude of them going from an orderly initial (measured) state to a\ndisorderly final (measured) state is exactly the same as that of their\ngoing from the disorderly state to the orderly state. Why? Just\ncalculate the Feynman diagram. Or think \'unitary evolution\'. Or just\nsay <a|b> is the complex conjugate of <b|a>.\n\nHowever, we *know* that the final state should be more disorderly than\nthe initial state. Because there are more such disorderly states than\norderly states. Where is the catch?\n\n-Souvik\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Having raised the question, I am awed by the explosive debate that
ensued.
Most of our contributors have stuck to a discussion of what it means to
reduce a state-vector in the Hamiltonian (canonical) approach to
quantum mechanics. I would like to point out that in the Feynman
version of QM (the spacetime approach), there is no physical operation
corresponding to reduction. In the spacetime version you are simply
asking the question: what are my chances of ending up in that quantum
state if I start from this quantum state. Since the spacetime approach
gives us all the physics, I suspect that 'state-vector reduction' might
in fact be an artefact of the Hamiltonian approach to quantum mechanics
with all its operators and what not.
I am probably and hopefully wrong, for there is a problem with that. It
has to do with the directionality of time:
Consider the collision of 10 or more elementary particles. The
amplitude of them going from an orderly initial (measured) state to a
disorderly final (measured) state is exactly the same as that of their
going from the disorderly state to the orderly state. Why? Just
calculate the Feynman diagram. Or think 'unitary evolution'. Or just
say <a|b> is the complex conjugate of <b|a>.
However, we *know* that the final state should be more disorderly than
the initial state. Because there are more such disorderly states than
orderly states. Where is the catch?
-Souvik
Arnold Neumaier
Jun19-05, 12:32 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>rof@maths.tcd.ie wrote:\n>\n>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>>\n>>>>rof@maths.tcd.ie wrote:\n>>>\n>>>I may have confused the official Copenhagen interpretation with\n>>>what Bohr, Heisenberg, von Neumann and so on believed. As Scerir\n>>>pointed out in this thread, Heisenberg said "The discontinuous change\n>>>in the probability function, however, takes place with the act\n>>>of registration, because it is the discontinuous change\n>>>of our knowledge in the instant of registration that has its\n>>>image in the discontinuous change of the probability function.",\n>>>Hiesenberg, "Physics and Philosophy", 1958\n>\n>>I commented that already. the \'acto of registration\' happens on the\n>>photographic plate or in the eye, not in the mind, and is simply\n>>the irreversible magnification due to dissipation by interaction with\n>>a macroscopic detector. It is objective and has no connection to\n>>any \'knowledge\'.\n>\n>>... only that your interpretation of what he said in terms of\n>>knowledge is a postmodern interpretation, and either the\n>>Copenhagen interpretation nor Heisenberg\'s intention.\n>\n> Heisenberg said "it is the discontinuous change of our knowledge\n> in the instant of registration that has its image in the discontinuous\n> change of the probability function."\n\nThis is in a 1958 essay for the general public, not in a paper on the\nfoundations of quantum mechanics. I don\'t read \'the first three minutes\'\nor \'a short history of time\' to find out about interpretation issues\nin relativity. Similarly, Heisenberg\'s book is not representative of\nthe Copenhagen interpretation.\n\nThe reprint collection\nJ.A. Wheeler and W. H. Zurek,\nQuantum theory and measurement.\nPrinceton Univ. Press, Princeton 1983.\ncontains 49 papers, only one of them by Heisenberg. It is from 1927\nand shows nothing of the subjectivist view of the late Heisenberg.\n\n\n> of what he said. Then you accused me of having a distorted\n> interpretation because I took Heisenberg at his word, and\n> proceeded to insult me by calling my interpretation postmodern.\n\nYou are too easily insulted. First by three question marks, now by\nthe word postmodern. And you don\'t hesitate to insult others by\ndistance diagnosing them of mental illness...\n\n\n>>>with the mental disease that I\n>>>ranted about in an earlier post:\n>>>http://groups-beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source\n>\n>>This is a long post, I cannot recognize myself reflected in it.\n>>Neither do I recognize signs of a mental disease in my behavior.\n>\n> It is extremely rare that one spots a mental disease in oneself,\n> but let me assure you that you are a textbook case.\n\nWhile you may be a competent physicist I doubt your expertise at\nmedical diagnosis.\n\nAnd since my time is limited and I prefer to discuss with polite people\nand about physics rather than psychology, I\'ll discontinue this discussion.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>rof@maths.tcd.ie wrote:
>
>>>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>>
>>>>rof@maths.tcd.ie wrote:
>>>
>>>I may have confused the official Copenhagen interpretation with
>>>what Bohr, Heisenberg, von Neumann and so on believed. As Scerir
>>>pointed out in this thread, Heisenberg said "The discontinuous change
>>>in the probability function, however, takes place with the act
>>>of registration, because it is the discontinuous change
>>>of our knowledge in the instant of registration that has its
>>>image in the discontinuous change of the probability function.",
>>>Hiesenberg, "Physics and Philosophy", 1958
>
>>I commented that already. the 'acto of registration' happens on the
>>photographic plate or in the eye, not in the mind, and is simply
>>the irreversible magnification due to dissipation by interaction with
>>a macroscopic detector. It is objective and has no connection to
>>any 'knowledge'.
>
>>... only that your interpretation of what he said in terms of
>>knowledge is a postmodern interpretation, and either the
>>Copenhagen interpretation nor Heisenberg's intention.
>
> Heisenberg said "it is the discontinuous change of our knowledge
> in the instant of registration that has its image in the discontinuous
> change of the probability function."
This is in a 1958 essay for the general public, not in a paper on the
foundations of quantum mechanics. I don't read 'the first three minutes'
or 'a short history of time' to find out about interpretation issues
in relativity. Similarly, Heisenberg's book is not representative of
the Copenhagen interpretation.
The reprint collection
J.A. Wheeler and W. H. Zurek,
Quantum theory and measurement.
Princeton Univ. Press, Princeton 1983.
contains 49 papers, only one of them by Heisenberg. It is from 1927
and shows nothing of the subjectivist view of the late Heisenberg.
> of what he said. Then you accused me of having a distorted
> interpretation because I took Heisenberg at his word, and
> proceeded to insult me by calling my interpretation postmodern.
You are too easily insulted. First by three question marks, now by
the word postmodern. And you don't hesitate to insult others by
distance diagnosing them of mental illness...
>>>with the mental disease that I
>>>ranted about in an earlier post:
>>>http://groups-\beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source
>
>>This is a long post, I cannot recognize myself reflected in it.
>>Neither do I recognize signs of a mental disease in my behavior.
>
> It is extremely rare that one spots a mental disease in oneself,
> but let me assure you that you are a textbook case.
While you may be a competent physicist I doubt your expertise at
medical diagnosis.
And since my time is limited and I prefer to discuss with polite people
and about physics rather than psychology, I'll discontinue this discussion.
Arnold Neumaier
Arnold Neumaier
Jun21-05, 08:00 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Souvik wrote:\n\n> However, we *know* that the final state should be more disorderly than\n> the initial state. Because there are more such disorderly states than\n> orderly states. Where is the catch?\n\nThe catch is that Feynman\'s approach is purely unitary while\nnature isn\'t, because of the second law. I believe that the second\nlaw is intrinsically related to (and should imply) state reduction.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Souvik wrote:
> However, we *know* that the final state should be more disorderly than
> the initial state. Because there are more such disorderly states than
> orderly states. Where is the catch?
The catch is that Feynman's approach is purely unitary while
nature isn't, because of the second law. I believe that the second
law is intrinsically related to (and should imply) state reduction.
Arnold Neumaier
rof@maths.tcd.ie
Jun21-05, 08:00 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Souvik <souvik1982@gmail.com> writes:\n\n>It has to do with the directionality of time:\n\n>Consider the collision of 10 or more elementary particles. The\n>amplitude of them going from an orderly initial (measured) state to a\n>disorderly final (measured) state is exactly the same as that of their\n>going from the disorderly state to the orderly state. Why? Just\n>calculate the Feynman diagram. Or think \'unitary evolution\'. Or just\n>say <a|b> is the complex conjugate of <b|a>.\n\n>However, we *know* that the final state should be more disorderly than\n>the initial state. Because there are more such disorderly states than\n>orderly states. Where is the catch?\n\nThis might not be exactly what you\'re looking for, but it\'s not quite\nthe case that the probability of going from |a> to |b> is the same\nas the probability of going from |b> to |a>. The amplitude of\ngoing from |a> to |b> is <b|exp(-iHt)|a>, while the amplitude\nof going the other way is <a|exp(-iHt)|b>. These aren\'t\ncomplex conjugates of each other, because the complex conjugate\nof <b|exp(-iHt)|a> is <a|exp(iHt)|b>.\n\nThat is, the probability of going from |a> to |b> with Hamiltonian\nH is the same as the probability of going from |b> to |a> with\nHamiltonian -H.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Souvik <souvik1982@gmail.com> writes:
>It has to do with the directionality of time:
>Consider the collision of 10 or more elementary particles. The
>amplitude of them going from an orderly initial (measured) state to a
>disorderly final (measured) state is exactly the same as that of their
>going from the disorderly state to the orderly state. Why? Just
>calculate the Feynman diagram. Or think 'unitary evolution'. Or just
>say <a|b> is the complex conjugate of <b|a>.
>However, we *know* that the final state should be more disorderly than
>the initial state. Because there are more such disorderly states than
>orderly states. Where is the catch?
This might not be exactly what you're looking for, but it's not quite
the case that the probability of going from |a> to |b> is the same
as the probability of going from |b> to |a>. The amplitude of
going from |a> to |b> is <b|\exp(-iHt)|a>, while the amplitude
of going the other way is <a|\exp(-iHt)|b>. These aren't
complex conjugates of each other, because the complex conjugate
of <b|\exp(-iHt)|a> is <a|\exp(iHt)|b>.
That is, the probability of going from |a> to |b> with Hamiltonian
H is the same as the probability of going from |b> to |a> with
Hamiltonian -H.
R.
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