A critique of textbook quantum mechanics

----------------------------------------

Textbook quantum mechanics almost invariably gives an overly
misleading, simplified view of the measurement problem.
For example, the well-written and often recommended book
J.J. Sakurai,
Modern Quantum Mechanics (2nd Edition)
represents things as if there were no possible doubts at all about the
interpretation; a student learning exclusively from this book
(and without previous exposure to the still heated foundational debate)
would be very surprised if he afterwards encounters the bewildering
variety of interpretations and the lack of agreement on the foundations
of quantum mechanics.

In the following, I look at Chapter 1 of sakurai's book and expose some
of the hidden (and questionable) assumptions that go into the
discussion.

In Section 1.1., Sakurai introduces the Stern-Gerlach experiment,
where a single (!) beam of silver atoms (with spin $1/2)$ generated by a
thermal source, passes a strong magnet and leaves two (!) spots on
a screen. This well-known nonclassical behavior requires explanation;
a classical beam would either produce a single spot (unspinning
particles) or a strip (randomly spinning particles). The explanation
given is quite common, but nevertheless far from convincing, once the
attention is on foundational issues, namely checking whether the
interpretative assumptions going into the analysis are impeccable.

1. Sakurai reasons after (1.1.2),
''Because the atom as a whole is very heavy,
we expect that the classical concept of trajectory can be
legitimately applied.'' This may be the case, but making this
approximation is already a departure from unitary qunatum physics.
It is well-known that all foundational problems center around the
difficulty to harmonize a linear, unitary, deterministic dynamics
for the wave function with the observed 'collapse' of the wave
function.

However, once a classical variable is allowed, the dynamics
necessarily becomes nonlinear (and most likely stochastic, too),
since there is no linear way to combine quantum and classical dynamics
in such a way that they interact. But once one allows a nonlinear
quantum-classical dynamics, the foundational problems disappear:
L.L. Bonilla and F. Guinea,
Collapse of the wave packet and chaos in a model with classical
and quantum degrees of freedom,
Phys. Rev. A 45 (1992), $7718-7728$
show that Hamiltonian quantum-classical dynamics easily accomodates
collapse with the associated probabilities.

Thus already the beginning of the analysis is tainted by assumptions
that one should avoid when looking at the foundations. Indeed, in view
of the nonlocality intrinsic in quantum mechanics (as Aspect's
experiments showed convincingly), it would be completely consistent
to argue instead that each (!) silver atom in this experiments has
two (!) entangled trajectories.

2. Then it is argued that the location of the spot on the screen is
(up to a calibration factor) a 'measurement' of the z-component of
the spin S. The argument just relies on the behavior of a classical
spinning particle in this situation. This may have been acceptable
at the time the experiment was done (before the intrinsic spin of
the electron was postulated), but in the mean time it is well-known
that naive classical analogy is often misleading in quantum situations
and should not be trusted.

3. Then it is claimed that ''the atoms in the oven are randomly
oriented'', a very questional assumption in view of the fact that
the Copenhagen interpretation expounded in the book explicitly denies
objective statements about microscopic objects when they are not
measured. Moreover, the assumption is not at all verifiable.

Judging from the classical analogy of polarization (expounded by
Sakurai a few pages later), where spin up and down corresponds to
right and left polarized light, the thermal state in the oven should
rather be regarded as being analogous to thermal light which is
unpolarized, and hence be considered as consisting of unoriented
atoms. Note that this analogy is 100 percent isomorphic on the
mathematical level (Bloch vectors - though Sakurai does not use this
useful terminology). Classical partially polarized light shows all
the typical quantum effects related to superposition and mixing.
Even the nonlocal aspects can be reproduced by using beam splitters.
Unfortunately, Sakurai stops discussing
the analogy half way, and does not discuss unpolarized light.

4.Then it is concluded from the experimental finding of the two
spots that ''the SG apparatus splits the original silver beam from
the oven into _two_distinct_ (original italic) components''.
It is well-known that such conclusions are completely unfounded,
and that assuming here two beams contradicts other experiments that
can be done on the system. The Copenhagen interpretation rather
insists on that we can't say anything about the situation between
magent and detector. If one wants to associate a visual intuition
to the situation it can only be that of intrinsically
nonlocal states of silver atoms, localized at two different places.
Calling this two beams requires at least a careful delineation of
what is meant by a beam.

5. From $1-4 it$ is concluded that ''only two possible values of
the z-component of S are observed to be possible.''
This is one of the universally agreed features of the experiment,
but as we can see, it rests on shallow foundations.

6. Considering a sequence of SG experiments, Sakurai says a few lines
before (1.1.4), ''the selection of the $S_z+$ beam by the second
apparatus (SGx) completely destroys any _previous_ (original italic)
information about $S_z''$. Judging from the analogy to classical
polarization, one should rather think that the SG magnet serves as
a filter that transforms the state of the quantum system and reduces
the intensity of the beam.

7. After (1.1.14), Sakurai emphasizes that ''we have deliberately [...]
ignored the quantum aspect of light'' and worked out ''the analogy [...]
with the polarization vectors of the
_classical_electromagnetic_field_ (original italic)''. That the quantum
nature of light never enters the analogy makes polarization a very
valuable analogy to spin since it shows that quantum phenomena
are not qualitatively different from certain classical phenomena
known since Stokes (1849).

8. After introducing the standard Dirac formalsim for quantum mechanics,
Sakurai goes on in section 1.4 to discuss measurements. He starts off
with an argument from authority, ''we first turn to the words of the
great master, P.A.M. Dirac, for guidance'', quoting his statement
''A measurement always causes the system to jump into an eigenstate
of the dynamical variable that is being measured.'' But it is just
one of the controversial questions whether or to which extent this is
the case!

Wigner, in his thorough analysis published in 1983,
E.P.Wigner,
Interpetation of quantum mechanics,
$pp. 260-314$ in:
J.A. Wheeler and W. H. Zurek (eds.),
Quantum theory and measurement.
Princeton Univ. Press, Princeton 1983.
gives a much more cautious, carefully qualified picture of what is
known. Since then, decoherence has become prominent, but does not
make Sakurai's statement less controversial. Moreover, most real
measurements are quite different and require modelling through positive
operator valued measures (POVMs) instead of von Dirac's simple
quantum jump picture.

9. After (1.4.3) comes the definition of measurement: ''When the
measurement causes $|\alpha>$ to change into $|a'>, it$ is said that
A is measured to be a'.'' Compared to measurements in practice,
this is a mock measurement: You kill a mouse (measurement),
then you know that it is dead (measurement result), and say
'I measured that the mouse is dead'. If a measuremnt does not
reveal anything about the state of a system before the measurement
began, it does not deserve to be called a measurement of the system!
In _all_ applications of science, the goal of measurement is
to find out what happened to the intact system, not to the part that
was destroyed by the measurement.

Rather, what Sakurai describes as a measurement would usually be
considered as a preparation, or a filter; cf. the optical analogy
for partially polarized light. Sakurai discusses preparation a little
later, after (1.4.6), under the name of 'selective measurement'.
But what he describes there can in no way be regarded as a measurement
since (if no final screen comes which really performs a measurement)
no information would become available at the filter - one would not
even know that anything passes the filter (except by preparation).

10. So much about Sakurai. Other textbooks differ, of course, in
their detailed approach, but they do not fare much better.
Unfortunately, foundational aspects are poorly represented in
the textbook literature. For those who look for a more positive
perspective, I can recommend the book
A. Peres,
Quantum theory: Concepts and methods,
Kluwer, Dordrecht 1993.
which at least is careful in its use of concepts, though it avoids
the real controversies.

Arnold Neumaier

 PhysOrg.com physics news on PhysOrg.com >> Kenneth Wilson, Nobel winner for physics, dies>> Two collider research teams find evidence of new particle Zc(3900)>> Scientists make first direct images of topological insulator's edge currents


Arnold Neumaier wrote in message news:<40B4A012.5000105@univie.ac.at>... Does it matter though? The Copenhagen interpretation is massively deficient in many ways but works as a "working interpretation". The avarage student will have troubles learning about Hilbert spaces and self adjoint operators first. The lack of anything approaching clean maths in many textbooks was far more worrying to me back then. (I had one Prof who during a QM lecture actually proved something by taylor expanding the $\delta$ function...) Then one can introduce POVMs, von neumanns theory of measurement, Many Worlds, Bohmian trajectories and so on... If there is a deficiency IMO it's primarily in explaining how this totally unsatisfactory situation does not lead to any observable problems, i.e. decoherence. I think the textbooks actually reflect the attitude of a majority of physicists anyways: "Shut up and calculate". I've yet to find a Prof who would mention measurement in the context of QFT at all, and textbooks mention it wrt causality if at all, and when I asked some local string theorists about the situation of the measurement problem in String theory I only got blank looks. --- frank



"Arnold Neumaier" a écrit dans le message de news:40B4A012.5000105@univie.ac.at... > 1. Sakurai reasons after (1.1.2), > ''Because the atom as a whole is very heavy, > we expect that the classical concept of trajectory can be > legitimately applied.'' This may be the case, but making this > approximation is already a departure from unitary qunatum physics. > It is well-known that all foundational problems center around the > difficulty to harmonize a linear, unitary, deterministic dynamics > for the wave function with the observed 'collapse' of the wave > function. That is irrelevant to the result and interpretation of the experiment. > 3. Then it is claimed that ''the atoms in the oven are randomly > oriented'', a very questional assumption in view of the fact that > the Copenhagen interpretation expounded in the book explicitly denies > objective statements about microscopic objects when they are not > measured. Moreover, the assumption is not at all verifiable. It is merely a symmetry condition. The contrary would be incompatible with the rotational symmetry of space. > 4.Then it is concluded from the experimental finding of the two > spots that ''the SG apparatus splits the original silver beam from > the oven into _two_distinct_ (original italic) components''. > It is well-known that such conclusions are completely unfounded, > and that assuming here two beams contradicts other experiments that > can be done on the system. The Copenhagen interpretation rather > insists on that we can't say anything about the situation between > magent and detector. If one wants to associate a visual intuition > to the situation it can only be that of intrinsically > nonlocal states of silver atoms, localized at two different places. > Calling this two beams requires at least a careful delineation of > what is meant by a beam. Yes, That's only an issue of definition. The standard definition of a beam, a location of maximum presence probability and constant momentum, will do. > 8. After introducing the standard Dirac formalsim for quantum > mechanics, Sakurai goes on in section 1.4 to discuss measurements. He > starts off with an argument from authority, ''we first turn to the > words of the great master, P.A.M. Dirac, for guidance'', quoting his > statement ''A measurement always causes the system to jump into an > eigenstate of the dynamical variable that is being measured.'' But it > is just one of the controversial questions whether or to which extent > this is the case! That is postulated in axiomatic QM. There may be other axiom systems, but the book studies that one. > Wigner, in his thorough analysis published in 1983, > E.P.Wigner, > Interpetation of quantum mechanics, > $pp. 260-314$ in: > J.A. Wheeler and W. H. Zurek (eds.), > Quantum theory and measurement. > Princeton Univ. Press, Princeton 1983. > gives a much more cautious, carefully qualified picture of what is > known. Since then, decoherence has become prominent, but does not > make Sakurai's statement less controversial. Moreover, most real > measurements are quite different and require modelling through > positive operator valued measures (POVMs) instead of von Dirac's > simple quantum jump picture. Decoherence doesn't solve anything. That's some other sand in the eyes. > 9. After (1.4.3) comes the definition of measurement: ''When the > measurement causes $|\alpha>$ to change into $|a'>, it$ is said that > A is measured to be a'.'' Compared to measurements in practice, > this is a mock measurement: You kill a mouse (measurement), > then you know that it is dead (measurement result), and say > 'I measured that the mouse is dead'. If a measuremnt does not > reveal anything about the state of a system before the measurement > began, it does not deserve to be called a measurement of the system! > In _all_ applications of science, the goal of measurement is > to find out what happened to the intact system, not to the part that > was destroyed by the measurement. A quantum measurement perturbs the measured system, there is no other way. > Rather, what Sakurai describes as a measurement would usually be > considered as a preparation, or a filter; cf. the optical analogy > for partially polarized light. Sakurai discusses preparation a little > later, after (1.4.6), under the name of 'selective measurement'. > But what he describes there can in no way be regarded as a measurement > since (if no final screen comes which really performs a measurement) > no information would become available at the filter - one would not > even know that anything passes the filter (except by preparation). Preparation is nothing else than a special case of measurement. > 10. So much about Sakurai. Other textbooks differ, of course, in > their detailed approach, but they do not fare much better. > Unfortunately, foundational aspects are poorly represented in > the textbook literature. I don't see any critic to do about that. This textbook seems to expound orthodox QM as it should be. -- ~~~~ clmasse at free dot fr Liberty, Equality, Profitability.

A critique of textbook quantum mechanics

<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>\nOn Mon, 31 May 2004 21:20:27 +0000 (UTC), C.i.m@gmx.net (Frank Hellmann)\nwrote:\n\n&gt;I think the textbooks actually reflect the attitude of a majority of\n&gt;physicists anyways: "Shut up and calculate".\n\nI would add: "And do not ask difficult questions."\n\nAn example of a difficult question: what is the mechanism that causes\nthe detector to click at a given time rather than sooner or later.....\n\nSee e.g. Mielnik, B.: The Screen Problem, Found. Phys.\n24, (1994) 1113--1129\n\nark\n--\n\nArkadiusz Jadczyk\nhttp://www.cassiopaea.org/quantum_future/homepage.htm\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 31 May 2004 21:20:27 $+0000$ (UTC), C.i.m@gmx.net (Frank Hellmann)
wrote:

>I think the textbooks actually reflect the attitude of a majority of
>physicists anyways: "Shut up and calculate".

I would add: "And do not ask difficult questions."

An example of a difficult question: what is the mechanism that causes
the detector to click at a given time rather than sooner or later.....

See e.g. Mielnik, B.: The Screen Problem, Found. Phys.
24, (1994) 1113--1129

ark
--

http://www.cassiopaea.org/quantum_future/homepage.htm

--


"Cl.Massé" wrote in message news:<40ba1d63$0$18308\$626a14ce@news.free.fr>... > Decoherence doesn't solve anything. That's some other sand in the eyes. > Indeed, as a solution to the measurement problem decoherence theory is a joke, but it's currently very fashionable. I spotted some implicit shrugs about its validity (see [1] for an explicit critique), but your bluntness is rare. Regards, IV [1] A. Bassi, G. Ghirardi "A General Argument Against the Universal Validity of the Superposition Principle" at http://www.arxiv.org/abs/http://www....ant-ph/0009020 ---------------------------- "The King was naked and disappointingly so."



Cl.$Mass=E9$ wrote: > "Arnold Neumaier" $a =E9crit$ dans $le mess=$ age > de news:40B4A012.5000105@univie.ac.at... [On Sakurai's treatment of the Stern-Gerlach experiment] >>1. Sakurai reasons after (1.1.2), >>''Because the atom as a whole is very heavy, >>we expect that the classical concept of trajectory can be >>legitimately applied.'' This may be the case, but making this >>approximation is already a departure from unitary qunatum physics. >>It is well-known that all foundational problems center around the >>difficulty to harmonize a linear, unitary, deterministic dynamics >>for the wave function with the observed 'collapse' of the wave >>function. $>=20$ > That is irrelevant to the result and interpretation of the experiment. No. In a classical treatment of trajectories you can never get the entanglement between spin and position that is the basis of the paradoxical features of the Stern-Gerlach experiment. >>3. Then it is claimed that ''the atoms in the oven are randomly >>oriented'', a very questional assumption in view of the fact that >>the Copenhagen interpretation expounded in the book explicitly denies >>objective statements about microscopic objects when they are not >>measured. Moreover, the assumption is not at all verifiable. $>=20$ > It is merely a symmetry condition. The contrary would be incompatible > with the rotational symmetry of space. A typical thermal source already breaks the rotational symmetry. Moreover, unoriented spin 1/2 atoms would also respect the symmetry; just like unpolarized light is the rotationally symmetric version of spin 1 light. >>4.Then it is concluded from the experimental finding of the two >>spots that ''the SG apparatus splits the original silver beam from >>the oven into _two_distinct_ (original italic) components''. >>It is well-known that such conclusions are completely unfounded, >>and that assuming here two beams contradicts other experiments that >>can be done on the system. The Copenhagen interpretation rather >>insists on that we can't say anything about the situation between >>magent and detector. If one wants to associate a visual intuition >>to the situation it can only be that of intrinsically >>nonlocal states of silver atoms, localized at two different places. >>Calling this two beams requires at least a careful delineation of >>what is meant by a beam. $>=20$ > Yes, That's only an issue of definition. The standard definition of a > beam, a location of maximum presence probability and constant momentum,= > will do. Is this standard? I'd like to see a reference. People usually use the term quite loosely. If a single atom passes the source, it is apparently in both beams!? >>9. After (1.4.3) comes the definition of measurement: ''When the >>measurement causes $|\alpha>$ to change into $|a'>, it$ is said that >>A is measured to be a'.'' Compared to measurements in practice, >>this is a mock measurement: You kill a mouse (measurement), >>then you know that it is dead (measurement result), and say >>'I measured that the mouse is dead'. If a measuremnt does not >>reveal anything about the state of a system before the measurement >>began, it does not deserve to be called a measurement of the system! >>In _all_ applications of science, the goal of measurement is >>to find out what happened to the intact system, not to the part that >>was destroyed by the measurement. $>=20$ > A quantum measurement perturbs the measured system, there is no other > way. Many classical measurements do, too; e.g., if we want to find out the chemical composition of a substance, we must destroy some of it. But the analysis of the destroyed part yields a measuremnt of what it was before destruction. This is the hallmark of any real measurement, whether classical or quantum. > Preparation is nothing else than a special case of measurement. No; preparation and measurement are two completely disjoint aspects of an experimental setting. Preparations assume information based on properties of the equipment and the experimental arrangement. They cannot yield anything new, or provide any checks on the assumptions made. Measurements are supposed to yield information about unknown states or check information about putative known states. On the other hand, they may destroy the system (as happens, e.g., in the Stern-Gerlach setting), hecne it is ridiculous to say that a measurement causes the state to change into an eigenstate. In many cases (measurement of collision events) the measurement becomes available only long after the system stopped existing... Preparations assume information based on properties of equipment, and cannot yioeld anything new, or provide any checks on the assumptions made. >>10. So much about Sakurai. Other textbooks differ, of course, in >>their detailed approach, but they do not fare much better. >>Unfortunately, foundational aspects are poorly represented in >>the textbook literature. $>=20$ > I don't see any critic to do about that. This textbook seems to > expound orthodox QM as it should be. Orthodoxy is not always a virtue. Two problem with orthodox QM are that 1. it does not apply to measurements of single quantum systems. For how these are modelled, see, e.g., the survey article MB Plenio and PL Knight, The quantum-jump approach to dissipative dynamics in quantum optics,= Rev. Mod. Phys 70 (1998), $101-144$. This was not a real problem 50 years ago, but it is one now. 2. it requires classical detectors. But we all know that detectors are just large quantum objects. Thus the collapse of the wave function (required for accounting for the behaviour of quantum systems when they pass screens, slits, and other filters) clashes with the superposition principle. This was always a problem, since it shows the inconsistency of orthodox quantum mechanics in the large. Even an introductory textbook should be able to spend a few paragraphs on such issues. Arnold Neumaier



Arnold Neumaier wrote in message news:<40B4A012.5000105@univie.ac.at>... > A critique of textbook quantum mechanics > ---------------------------------------- > > Textbook quantum mechanics almost invariably gives an overly > misleading, simplified view of the measurement problem. > For example, the well-written and often recommended book > J.J. Sakurai, > Modern Quantum Mechanics (2nd Edition) > Addison-Wesley, 1993. > represents things as if there were no possible doubts at all about the > interpretation; a student learning exclusively from this book > (and without previous exposure to the still heated foundational debate) > would be very surprised if he afterwards encounters the bewildering > variety of interpretations and the lack of agreement on the foundations > of quantum mechanics. [snip] In defense of Sakurai, I would say that, although all you write is correct, one cannot justify that on a pedagogical level ! Maybe a footnote should be added in the book, saying that there are a few subtle issues here, but I think you'll agree with me that a student for which it is instructive to read the first chapter of Sakurai shouldn't be exposed to all these for $him/her$ incomprehensible subtleties. The student is even not very well aware of the superposition idea, which this very chapter tries to introduce. The problem, in physics teaching, to try to be too rigorous is just as dangerous as the opposite thing (also very common!) to be too sloppy. For instance, I had a professor in theoretical physics who didn't want to teach quantum field theory because of the mathematical difficulties in its foundations. But in that case, you don't get anywhere either. The aim of books like Sakurai's (and I think they do well at it) is to teach the student problem solving skills in QM. You cannot tackle foundational problems without mastering that. The opposite approach would be, for the average student, much more dramatic: he would be well aware of all subtleties of (mostly unobservable) aspects of the quantum measurement problem, but wouldn't be able to solve a simple problem. So $his/her$ knowledge of QM is absolutely useless for the "working physicist". cheers, Patrick.



Patrick Van Esch wrote: > Arnold Neumaier wrote in message news:<40B4A012.5000105@univie.ac.at>... >> >>Textbook quantum mechanics almost invariably gives an overly >>misleading, simplified view of the measurement problem. >>For example, the well-written and often recommended book >> J.J. Sakurai, >> Modern Quantum Mechanics (2nd Edition) >> Addison-Wesley, 1993. >>represents things as if there were no possible doubts at all about the >>interpretation; a student learning exclusively from this book >>(and without previous exposure to the still heated foundational debate) >>would be very surprised if he afterwards encounters the bewildering >>variety of interpretations and the lack of agreement on the foundations >>of quantum mechanics. > > In defense of Sakurai, I would say that, although all you write is > correct, one cannot justify that on a pedagogical level ! Maybe a > footnote should be added in the book, saying that there are a few > subtle issues here, but I think you'll agree with me that a student > for which it is instructive to read the first chapter of Sakurai > shouldn't be exposed to all these for $him/her$ incomprehensible > subtleties. The student is even not very well aware of the > superposition idea, which this very chapter tries to introduce. Superposition in itself is not difficult to grasp; it is valid for all linear differential equations. And probably students know this already before learning QM. What is new, however, in QM is entanglement, which, in Stern-Gerlach experiments, results in nonlocal states. But here, Sakurai does a poor job. Without much more effort, namley just an informal introduction to coherent states (which are very useful anyway) the student could gain a much deeper and more realistic perspective for QM. Because what really happens in the Stern-Gerlach experiment is that the silver atom is approximately in a superposition of the states |up> tensor $|x_+(t),p_+(t)>$ and |down> tensor $|x_-(t),p_-(t)>,$ where $|x,p>$ denotes a coherent state with position x and momentum p, and $x_+(t),p_+(t)$ (resp$. x_-(t),p_-(t))$ are the phase space trajectories of a classical particle with the magnetic interaction corresponding to spin up (resp. spin down). This is the proper version of the 'classical' handling of the trajectories. (The way Sakurai proceeds, this remains completely obscure - in his account, it looks as if a single silver atom gets two classical trajectories but ends up at only one place.) Thus the Stern-Gerlach experiment would be an ideal opportunity of introducing entanglement between spin states and position states, which is the main thing responsible for nonclassical behavior. One could also give here an excellent illustration for the necessity of the collapse. It ensures that instead of a superposition of |up> tensor |up-spot> and |down> tensor |down-spot> (or the resulting mixture of |up-spot> and |down-spot> when projecting away the invisible spin), we observe (in a single event) exactly one of |up-spot> or |down-spot>, no matter how these look in detail. With such a discussion, much of the confusion about the meaning of QM could be avoided. Arnold Neumaier



In Patrick Van Esch wrote: > Arnold Neumaier wrote in message news: > <40B4A012.5000105@univie.ac.at>... >> A critique of textbook quantum mechanics >> ---------------------------------------- >> >> Textbook quantum mechanics almost invariably gives an overly >> misleading, simplified view of the measurement problem. >> For example, the well-written and often recommended book >> J.J. Sakurai, > > In defense of Sakurai, I would say that, although all you write is > correct, one cannot justify that on a pedagogical level ! Maybe a > footnote should be added in the book, saying that there are a few > subtle issues here, but I think you'll agree with me that a student > for which it is instructive to read the first chapter of Sakurai > shouldn't be exposed to all these for $him/her$ incomprehensible > subtleties. The student is even not very well aware of the With all due respect, this is an example of the "shut up and calculate" approach to QM. Agreed, that's acceptable step along the road to a fuller understanding, but since QM is an incomplete theory, foundational issues MUST be highlighted at some point (IMO) in order to give aspiring theorists directons to proceed. Classical mechanics was only axiomatized in the last half of the 20th century, mostly by Truesdell and Noll. Although I would be hard-pressed to enumerate specific benefits that have accrued as a result, I can state that the mechanics of deformable media is a complete and consistent theory. -- Andrew Resnick, Ph. D. National Center for Microgravity Research NASA Glenn Research Center



Arnold Neumaier wrote in message news:<40C5714F.6060900@univie.ac.at>... > Patrick Van Esch wrote: > > The student is even not very well aware of the > > superposition idea, which this very chapter tries to introduce. > > Superposition in itself is not difficult to grasp; it is valid for all > linear differential equations. And probably students know this already > before learning QM. The mathematical notion of superposition is not difficult. But the physical notion of "superposition of states" is ! It is this very idea which Sakurai tries to convey, in the mathematically simplest situation, namely a 2 state system. Classically, there would only be 2 discrete possibilities, but quantum mechanically we end up with $C^2 (/ R+)$. > > What is new, however, in QM is entanglement, which, in Stern-Gerlach > experiments, results in nonlocal states. > > But here, Sakurai does a poor job. Without much more effort, namley > just an informal introduction to coherent states (which are very > useful anyway) the student could gain a much deeper and more realistic > perspective for QM. Coherent states are introduced only in chapter 3 ! > > Because what really happens in the Stern-Gerlach experiment is that > the silver atom is approximately in a superposition of the states > |up> tensor $|x_+(t),p_+(t)>$ > and > |down> tensor $|x_-(t),p_-(t)>,$ > where $|x,p>$ denotes a coherent state with position x and momentum p, > and $x_+(t),p_+(t)$ (resp$. x_-(t),p_-(t))$ are the phase space trajectories > of a classical particle with the magnetic interaction corresponding > to spin up (resp. spin down). This is the proper version of the > 'classical' handling of the trajectories. (The way Sakurai proceeds, > this remains completely obscure - in his account, it looks as if a > single silver atom gets two classical trajectories but ends up at > only one place.) Honestly, all you write is interesting, but you should master QM on the level of Sakurai before understanding what you say. He's now just trying to introduce $C^2$ as the state space for a 2-state system. After that, at the end of chapter 1, the idea that position is described quantum mechanically is introduced. I do not say that it wouldn't be interesting, at the END of the book, to have a chapter on interpretational issues, and come back to what you are writing above. But in the beginning of chapter 1, you simply should consider a SG machine as a spin measurement along a certain direction. You can say so, in the language of decoherence, that the very interaction with the non-uniform B field is the "act of measurement" where the effective projection on the up or down state takes place, and from there on, you can calculate a trajectory classically. cheers, patrick.



Arnold Neumaier wrote in message news:<40BF417D.7010102@univie.ac.at>... > > Measurements are supposed to yield information about unknown states > or check information about putative known states. On the other hand, > they may destroy the system (as happens, e.g., in the Stern-Gerlach > setting), hecne it is ridiculous to say that a measurement causes > the state to change into an eigenstate. In Copenhagen the wave function does not represent the state of the system. It encodes the observer's knowledge about past and future measurement outcomes. What is cast in one of the measurement operator's eigenvalues by the act of measurement is not the state of the system, but the state of the observer's knowledge. A friend sends me a letter, then he's killed ,say , in a motorcycle accident. The day after his death I receive and read his letter. What I read changes my knowledge of him and of his story, although he no longer is. Now, that's a measurement. >2. it requires classical detectors. >But we all know that detectors are just large quantum objects. >Thus the collapse of the wave function (required for accounting for >the behaviour of quantum systems when they pass screens, slits, >and other filters) clashes with the superposition principle. >This was always a problem, since it shows the inconsistency of >orthodox quantum mechanics in the large. The suprposition principle holds as long as the system's evolution is unitary. Collapse corresponds to the intrinsecally non-unitary act of perception/measurement. IV -------------------- !... nicht allein diese Tropfen sind blosse Erscheinungen, sondern selbst ihre runde Gestalt, ja sogar der Raum, in welchen sie fallen, sind nichts an sich selbst, sondern blosse Modifikationen, oder Grundlagen unserer sinnlichen Anschauung, das transzendentale Objekt aber bleibt uns unbekannt. " ...not only are the drops of rain mere appearances, but even their round shape, and even the space in which they fall, are nothing in themselves, but merely modifications of fundamental forms of our sensible intuition, and the transcendental object remains unknown to us" Kant, I. Critique of Pure Reason.



Italo Vecchi wrote: > Arnold Neumaier wrote in message news:<40BF417D.7010102@univie.ac.at>... > >>Measurements are supposed to yield information about unknown states >>or check information about putative known states. On the other hand, >>they may destroy the system (as happens, e.g., in the Stern-Gerlach >>setting), hence it is ridiculous to say that a measurement causes >>the state to change into an eigenstate. > > In Copenhagen the wave function does not represent the state of the > system. It encodes the observer's knowledge about past and future > measurement outcomes. No. Nature operates independent of what observers know about it. Quantum mechanics was a valid description of Nature already before the first observer existed. Otherwise time-honored dating methods such as Carbon 14 method would be meaningless. [Moderator's note: Italo Vecchi might have meant that the _maximally possible_ observer's knowledge about measurement outcomes is encoded in the wave function. $-usc]$ The study of knowledge is a matter of psychology and not of physics. If the observer gets a heart attack and loses some knowledge because of that, the process in the lab does not change. Thus knowledge does not need to follow either the Schroedinger equation or the collapse postulates. Probabilities depend on the preparation of the system only, and not on what the observer knows about this preparation; indeed, often the measurements serve to find out about the details of how a system was prepared. >>2. it requires classical detectors. >>But we all know that detectors are just large quantum objects. >>Thus the collapse of the wave function (required for accounting for >>the behaviour of quantum systems when they pass screens, slits, >>and other filters) clashes with the superposition principle. >>This was always a problem, since it shows the inconsistency of >>orthodox quantum mechanics in the large. > > The superposition principle holds as long as the system's evolution is > unitary. Collapse corresponds to the intrinsically non-unitary act of > perception/measurement. Perception/measurement is itself a quantum process and hence should be described by QM if it is a consistent description of nature. All the great writers on the subject had been aware of this inconsistency which you try to hide under the carpet. The enigma was and is to specify in a rational way where and how unitarity breaks down. Arnold Neumaier



vecchi@weirdtech.com (Italo Vecchi) wrote: > Indeed, as a solution to the measurement problem decoherence theory is > a joke, What's humorous about it? Its essential statement is that relative to 3 systems (as opposed to only 2) one *does* indeed have basis uniqueness. That's true as a mathematical theorem. Since the problem of basis uniqueness is much of the essence of the measurement problem, then much of the essence of a burden has been relieved by a joke.



vecchi@weirdtech.com (Italo Vecchi) wrote > > Decoherence doesn't solve anything. That's some other sand in the eyes. > > But it exists and has been measured (in experiments with Be ions: http://www.nature.com/nsu/000120/000120-10.html, http://www.nature.com/cgi-taf/DynaPa...69a0_fs.html). So it solves one aspect of the problem of how QM corresponds with reality, since without it such experiments would not make sense. > Indeed, as a solution to the measurement problem decoherence theory is > a joke Why? > but it's currently very fashionable. Which proves nothing either way. > I spotted some implicit shrugs about its validity (...) > but your bluntness is rare. So what? "Sand in the eyes", shrugs, "jokes", bluntness and fashions prove nothing. > (see [1] for an explicit critique) > [1] A. Bassi, G. Ghirardi "A General Argument Against the Universal > Validity of the Superposition Principle" at > http://www.arxiv.org/abs/http://www....ant-ph/0009020 See also C. Anastopoulos, http://www.arxiv.org/abs/http://www....ant-ph/0011123 "Frequently Asked Questions about Decoherence" - esp. pp$. 15-16$ for intrinsic decoherence.



whopkins@csd.uwm.edu (Alfred Einstead) wrote in message news:... > vecchi@weirdtech.com (Italo Vecchi) wrote: > > Indeed, as a solution to the measurement problem decoherence theory is > > a joke, > > What's humorous about it? > > Its essential statement is that relative to 3 systems (as opposed > to only 2) one *does* indeed have basis uniqueness. That's > true as a mathematical theorem. Since the problem of basis > uniqueness is much of the essence of the measurement problem, > then much of the essence of a burden has been relieved by a joke. Who picks those 3 systems? IV



I wrote : > > That is irrelevant to the result and interpretation of the > > experiment. "Arnold Neumaier" a écrit dans le message de news:40BF417D.7010102@univie.ac.at... > No. In a classical treatment of trajectories you can never get the > entanglement between spin and position that is the basis of the > paradoxical features of the Stern-Gerlach experiment. I mean, the description of the trajectory is irrelevant as long as the correlation between spin and trajectory is included in the whole description. In practice, that is realized through a tensor product of two distinct spaces, independently of the real nature of each space. The trajectory can be described in QM terms, but the details added wrt classical terms are irrelevant. > A typical thermal source already breaks the rotational symmetry. It wouldn't be thermal in the first place! "Thermal" means randomization of all the degrees of freedom, including spin. That is literally contrary to any fundamental symmetry breaking > > Yes, That's only an issue of definition. The standard definition of > > a beam, a location of maximum presence probability and constant > > momentum, will do. > Is this standard? I'd like to see a reference. People usually use the > term quite loosely. It need not be used precisely. Nothing depends on its meaning, the intuitive one that fits the explanation is sufficient. > If a single atom passes the source, it is apparently in both beams!? Yes, that's how the Copenhagen interpretation sees it, until the atom is detected. Then, as trajectory and spin are correlated, the spin state collapses onto the corresponding eigenstate, along with the position state. > > A quantum measurement perturbs the measured system, there is no > > other way. > Many classical measurements do, too; e.g., if we want to find out the > chemical composition of a substance, we must destroy some of it. > But the analysis of the destroyed part yields a measuremnt of what > it was before destruction. This is the hallmark of any real > measurement, whether classical or quantum. Not quantum, precisely. Two particles in the same state may be detected with different spins, for example, therefore there is no mean to get know the initial state only through measurement outcomes. The explanation of the uncertainty by a classical perturbation is obsolete, or at worst intuitive. > > Preparation is nothing else than a special case of measurement. > No; preparation and measurement are two completely disjoint aspects > of an experimental setting. > > Preparations assume information based on properties of the equipment > and the experimental arrangement. They cannot yield anything new, > or provide any checks on the assumptions made. > > Measurements are supposed to yield information about unknown states > or check information about putative known states. On the other hand, > they may destroy the system (as happens, e.g., in the Stern-Gerlach > setting), hecne it is ridiculous to say that a measurement causes > the state to change into an eigenstate. An eigenstate of what? That is the question. Actually, an eigenstate of the system particle-apparatus, thus whether the particle is destroyed or not. It is easy to see that a measuring apparatus measuring discrete states can prepare a particle in any of those state just by a measurement and a coincidence setup, or a mechanism able to destroy the outgoing particle if not in the desired state. Any preparing apparatus without exception works like this. An simple example is a beam generator that measures the impulse and eliminate the particles with impulse direction out of the allowed range through a screen. > In many cases (measurement > of collision events) the measurement becomes available only long after > the system stopped existing... > Preparations assume information based on properties of equipment, > and cannot yioeld anything new, or provide any checks on the > assumptions made. The properties of the equipment determines which particle will be eliminated, like in the example of the screen. Preparation and production aren't necessary identical. A preparation put the particle in a pure state, which is impossible without a measurement. > Two problem with orthodox QM are that > > 1. it does not apply to measurements of single quantum systems. > For how these are modelled, see, e.g., the survey article > MB Plenio and PL Knight, > The quantum-jump approach to dissipative dynamics in quantum > optics, > > Rev. Mod. Phys 70 (1998), $101-144$. > This was not a real problem 50 years ago, but it is one now. > > 2. it requires classical detectors. > But we all know that detectors are just large quantum objects. > Thus the collapse of the wave function (required for accounting for > the behaviour of quantum systems when they pass screens, slits, > and other filters) clashes with the superposition principle. > This was always a problem, since it shows the inconsistency of > orthodox quantum mechanics in the large. Those problems aren't solved yet. However, an imperfect, still useful, theory exists : "orthodox" QM. Just like "classical" mechanics was imperfect, but allowed to calculate the planet orbits with an incredible precision. Both are worth being taught on their own right. There isn't and will never be a perfect theory. > Even an introductory textbook should be able to spend a few paragraphs > on such issues. On that, I agree, but it all depends on the purpose of the book. There is a fashion of saying quantum mysteries are but early wonderings caused by an unusual formalism. They are not. -- ~~~~ clmasse at free dot fr Liberty, Equality, Profitability.



Thomas Dent wrote: > vecchi@weirdtech.com (Italo Vecchi) wrote > >>>Decoherence doesn't solve anything. That's some other sand in the eyes. > >>Indeed, as a solution to the measurement problem decoherence theory is >>a joke > > Why? The paper you quoted: > See also C. Anastopoulos, http://www.arxiv.org/abs/http://www....ant-ph/0011123 > "Frequently Asked Questions about Decoherence" - esp. pp$. 15-16$ for > intrinsic decoherence. says on p.$13/14:$ ''it is often claimed that environment induced decoherence provides by itself a solution of the macroobjectification problem [...] One concludes therefore that environment induced decoherence cannot by itself explain the appearance of macroscopic definite properties and a realist interpretation of quantum theory still needs an additional postulate to account for macroobjectification,'' ''a sufficiently classical behaviour for the environment seems to be necessary if it is to act as a decohering agent and we can ask what has brought the environment into such a state ad-infinitum.'' and as concluding sentence on p.16: ''At this stage, however, it is fair to say that there is not conclusive evidence about how the classical world appears and it is likely that a special initial condition is needed in order to guarantee it.'' Thus decoherence assumes on some scale what it purports to derive at other scales. This implies that while it describes something real it does not help in the foundations. Also, decoherence does not say anything about an individual system. If the wave function is assumed to be an objective property of a single quantum system, it must collapse upon measurement to a single eigenstate, and not to a mixture as decoherence predicts. The measurement problem is the problem of explaining why we observe facts and not superpositions or mixtures of all possible facts, and decoherence is completely silent about this. Arnold Neumaier

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