View Full Version : conundrum regarding propagation of virtual particles
vernonner3voltazim
Oct22-04, 12:31 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>\nFeynman\'s "sum over histories" method of explaining\ncertain quantum-mechanical interactions works nice,\nand a lot of people think it may be an accurate\ninterpretation of Reality. On the other hand,\nFeynman once suggested that anti-particles were\nmerely ordinary particles that happened to be\ntravelling backward in Time, relative to us, and\nthat math, too, works nice. But few think it is\nan accurate interpretation of Reality; it is just\na useful tool.\n\nOne thing about the sum-over-histories model is\nthat it assumes virtual photons travelling between\nelectric charges can do so at every possible speed\nfrom zero up to infinity. Well, if this model is\nso good, shouldn\'t it work for other Forces than\nElectromagnetism?\n\nConsider the Strong Nuclear Force. The virtual\npions that carry quarks and gluons between\nprotons and neutrons in the nucleus have a fair\namount of mass. The Uncertainty Principle allows\nthem to borrow that energy for just enough time\nto cross the nucleus. To be more specific, this\nborrowing is VERY STRICTLY TIME-LIMITED. As a\nresult (as described by Yukawa well before\nFeynman\'s trick came along), the pions can only\npropagate so far, and indeed the Strong Force\nhas a very sharp cut-off with respect to its\nrange of action.\n\nMy point here is that if we applied the sum-over-\nhistories method to virtual pions and the Strong\nForce, then some of those pions should be able\nto go infinitely fast and consequently the\nStrong Force would have a much greater range\nthan is observed. This indicates that probably\nwe cannot apply (in terms of "interpretative\nmeaning") the sum-over-histories method to\nthat aspect of the Strong Force. It MAY also\nindicate that while sum-over-histories is a\ngood tool, it is not a valid interpretation\neven for the Electromagnetic Force, to say that\nall those virtual photons are taking all\npossible paths (space-like and time-like).\n\nWhich brings me to ask whether or not there is\nSOME OTHER technique that works just fine to\nexplain QED without sum-over-histories, and\nonly involves virtual photons that propagate\nonly at light-speed. Is there? Thanks in\nadvance!\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>Feynman's "sum over histories" method of explaining
certain quantum-mechanical interactions works nice,
and a lot of people think it may be an accurate
interpretation of Reality. On the other hand,
Feynman once suggested that anti-particles were
merely ordinary particles that happened to be
travelling backward in Time, relative to us, and
that math, too, works nice. But few think it is
an accurate interpretation of Reality; it is just
a useful tool.
One thing about the sum-over-histories model is
that it assumes virtual photons travelling between
electric charges can do so at every possible speed
from zero up to infinity. Well, if this model is
so good, shouldn't it work for other Forces than
Electromagnetism?
Consider the Strong Nuclear Force. The virtual
pions that carry quarks and gluons between
protons and neutrons in the nucleus have a fair
amount of mass. The Uncertainty Principle allows
them to borrow that energy for just enough time
to cross the nucleus. To be more specific, this
borrowing is VERY STRICTLY TIME-LIMITED. As a
result (as described by Yukawa well before
Feynman's trick came along), the pions can only
propagate so far, and indeed the Strong Force
has a very sharp cut-off with respect to its
range of action.
My point here is that if we applied the sum-over-
histories method to virtual pions and the Strong
Force, then some of those pions should be able
to go infinitely fast and consequently the
Strong Force would have a much greater range
than is observed. This indicates that probably
we cannot apply (in terms of "interpretative
meaning") the sum-over-histories method to
that aspect of the Strong Force. It MAY also
indicate that while sum-over-histories is a
good tool, it is not a valid interpretation
even for the Electromagnetic Force, to say that
all those virtual photons are taking all
possible paths (space-like and time-like).
Which brings me to ask whether or not there is
SOME OTHER technique that works just fine to
explain QED without sum-over-histories, and
only involves virtual photons that propagate
only at light-speed. Is there? Thanks in
advance!
Igor Khavkine
Oct24-04, 09:04 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\nOn Fri, 22 Oct 2004 17:31:39 +0000, vernonner3voltazim wrote:\n\n>\n> Feynman\'s "sum over histories" method of explaining certain\n> quantum-mechanical interactions works nice, and a lot of people think it\n> may be an accurate interpretation of Reality. On the other hand, Feynman\n> once suggested that anti-particles were merely ordinary particles that\n> happened to be travelling backward in Time, relative to us, and that math,\n> too, works nice. But few think it is an accurate interpretation of\n> Reality; it is just a useful tool.\n\nThis should tell you something about Reality or perhaps about people\'s\ninterpretations of it. Or both.\n\n> One thing about the sum-over-histories model is that it assumes virtual\n> photons travelling between electric charges can do so at every possible\n> speed from zero up to infinity. Well, if this model is so good, shouldn\'t\n> it work for other Forces than Electromagnetism?\n\nAs far as physicists are concerned, the usual operator and Feynman\'s\nformulations of quantum mechanics are equivalent. So yes, it does work for\nother things besides electromagnetism.\n\n> Consider the Strong Nuclear Force. The virtual pions that carry quarks\n> and gluons between protons and neutrons in the nucleus have a fair amount\n> of mass. The Uncertainty Principle allows them to borrow that energy for\n> just enough time to cross the nucleus. To be more specific, this\n> borrowing is VERY STRICTLY TIME-LIMITED. As a result (as described by\n> Yukawa well before Feynman\'s trick came along), the pions can only\n> propagate so far, and indeed the Strong Force has a very sharp cut-off\n> with respect to its range of action.\n>\n> My point here is that if we applied the sum-over- histories method to\n> virtual pions and the Strong Force, then some of those pions should be\n> able to go infinitely fast and consequently the Strong Force would have a\n> much greater range than is observed. This indicates that probably we\n> cannot apply (in terms of "interpretative meaning") the sum-over-histories\n> method to that aspect of the Strong Force. It MAY also indicate that\n> while sum-over-histories is a good tool, it is not a valid interpretation\n> even for the Electromagnetic Force, to say that all those virtual photons\n> are taking all possible paths (space-like and time-like).\n\nYou are forgetting cancellation in Feynman\'s "sum over histories". The\namplitudes given to pions that travel very far is such that their sum is\nnegligible once all paths are taken into account.\n\n> Which brings me to ask whether or not there is SOME OTHER technique that\n> works just fine to explain QED without sum-over-histories, and only\n> involves virtual photons that propagate only at light-speed. Is there?\n> Thanks in advance!\n\nWhat you refer to as "techniques" are simply ways of visualizing the\nactual calculations. The visualization is not strictly necessary. In fact\nthe same calculation can be visualized in several different ways, some\ninvolve virtual particles, some involve sums over histories, some involve\nneither. There\'s been a couple of recent threads about virtual particles\nhere. Check out the news group archives for further discussion.\n\nIgor\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>On Fri, 22 Oct 2004 17:31:39 +0000, vernonner3voltazim wrote:
>
> Feynman's "sum over histories" method of explaining certain
> quantum-mechanical interactions works nice, and a lot of people think it
> may be an accurate interpretation of Reality. On the other hand, Feynman
> once suggested that anti-particles were merely ordinary particles that
> happened to be travelling backward in Time, relative to us, and that math,
> too, works nice. But few think it is an accurate interpretation of
> Reality; it is just a useful tool.
This should tell you something about Reality or perhaps about people's
interpretations of it. Or both.
> One thing about the sum-over-histories model is that it assumes virtual
> photons travelling between electric charges can do so at every possible
> speed from zero up to infinity. Well, if this model is so good, shouldn't
> it work for other Forces than Electromagnetism?
As far as physicists are concerned, the usual operator and Feynman's
formulations of quantum mechanics are equivalent. So yes, it does work for
other things besides electromagnetism.
> Consider the Strong Nuclear Force. The virtual pions that carry quarks
> and gluons between protons and neutrons in the nucleus have a fair amount
> of mass. The Uncertainty Principle allows them to borrow that energy for
> just enough time to cross the nucleus. To be more specific, this
> borrowing is VERY STRICTLY TIME-LIMITED. As a result (as described by
> Yukawa well before Feynman's trick came along), the pions can only
> propagate so far, and indeed the Strong Force has a very sharp cut-off
> with respect to its range of action.
>
> My point here is that if we applied the sum-over- histories method to
> virtual pions and the Strong Force, then some of those pions should be
> able to go infinitely fast and consequently the Strong Force would have a
> much greater range than is observed. This indicates that probably we
> cannot apply (in terms of "interpretative meaning") the sum-over-histories
> method to that aspect of the Strong Force. It MAY also indicate that
> while sum-over-histories is a good tool, it is not a valid interpretation
> even for the Electromagnetic Force, to say that all those virtual photons
> are taking all possible paths (space-like and time-like).
You are forgetting cancellation in Feynman's "sum over histories". The
amplitudes given to pions that travel very far is such that their sum is
negligible once all paths are taken into account.
> Which brings me to ask whether or not there is SOME OTHER technique that
> works just fine to explain QED without sum-over-histories, and only
> involves virtual photons that propagate only at light-speed. Is there?
> Thanks in advance!
What you refer to as "techniques" are simply ways of visualizing the
actual calculations. The visualization is not strictly necessary. In fact
the same calculation can be visualized in several different ways, some
involve virtual particles, some involve sums over histories, some involve
neither. There's been a couple of recent threads about virtual particles
here. Check out the news group archives for further discussion.
Igor
Frank Hellmann
Oct24-04, 09:04 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\n\n\nvnemitz@pinn.net (vernonner3voltazim) wrote in message news:<42336979.0410210804.3dca9e1a@posting.google. com>...\n> Which brings me to ask whether or not there is\n> SOME OTHER technique that works just fine to\n> explain QED without sum-over-histories,\n\nUhmm.... Pick up a QFT course/book. You are mistaking the paths in the\nintegral for virtual particles. The paths in the integral are all of\nreal particles which always travel at finite speeds in the end,\nvirtual particles only appear in the perturbative expansion of the\nintegral. You can also always do the original operator based QFT.\n\nFurthermore, Feynman path integrals do work for the strong coupling.\nThe long range behaviour of the strong force comes out right in the\nscaling. This is precisely what Gross, Politzer and Wilczek just got\ntheir Nobel prize for.\nOf course you can also use cannonical, operator based quantization,\nbut apparently it\'s very difficult to make work for the strong\ninteraction due to gauge invariance. For pathintegrals you use the\nFaddeev Popov Ghosts to do this, You need to factor out a vast space\nof possible paths related by gauge symmetry and therefore physically\nequivalent, there is some highly nontrivial dependency of the space to\nmod out on the actual physics in QCD (as opposed to QED which is why\nFeynman could get away without it), so what you do is to write the\nfactors appearing in the path integral as fake physics interacting\nwith the real physics: Ghost fields.\n\nBasically you have to remember that the more unphysical a path the\nless does it contribute to the (quantum) physics. And even though\nvirtual photons can travell at high speeds, real ones never can.\nFurthermore virtual photons only appear in the perturbative expansion\nof QED. The perturbative expansion of QCD, however only applies by\nvirtue of being perturbative, at very high energies (and very short\ndistances) when the quarks are quasi free and the coupling is weak.\n\n\n---\nfrank\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>vnemitz@pinn.net (vernonner3voltazim) wrote in message news:<42336979.0410210804.3dca9e1a@posting.google.com>...
> Which brings me to ask whether or not there is
> SOME OTHER technique that works just fine to
> explain QED without sum-over-histories,
Uhmm.... Pick up a QFT course/book. You are mistaking the paths in the
integral for virtual particles. The paths in the integral are all of
real particles which always travel at finite speeds in the end,
virtual particles only appear in the perturbative expansion of the
integral. You can also always do the original operator based QFT.
Furthermore, Feynman path integrals do work for the strong coupling.
The long range behaviour of the strong force comes out right in the
scaling. This is precisely what Gross, Politzer and Wilczek just got
their Nobel prize for.
Of course you can also use cannonical, operator based quantization,
but apparently it's very difficult to make work for the strong
interaction due to gauge invariance. For pathintegrals you use the
Faddeev Popov Ghosts to do this, You need to factor out a vast space
of possible paths related by gauge symmetry and therefore physically
equivalent, there is some highly nontrivial dependency of the space to
mod out on the actual physics in QCD (as opposed to QED which is why
Feynman could get away without it), so what you do is to write the
factors appearing in the path integral as fake physics interacting
with the real physics: Ghost fields.
Basically you have to remember that the more unphysical a path the
less does it contribute to the (quantum) physics. And even though
virtual photons can travell at high speeds, real ones never can.
Furthermore virtual photons only appear in the perturbative expansion
of QED. The perturbative expansion of QCD, however only applies by
virtue of being perturbative, at very high energies (and very short
distances) when the quarks are quasi free and the coupling is weak.
---
frank
Arnold Neumaier
Oct26-04, 12:54 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>Greysky wrote:\n> "Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote\n\n>>As far as I know a virtual\n>>particle-antiparticle pair, of total energy dE can exist for a time\n>>dt, provided dt and dE satisfy Heisenberg\'s uncertainty principle. For\n>>the time that they exist I don\'t see any reason that the particles are\n>>not just as real as any other.\n\nWhat do you mean by \'really existing for an unobservably small time\'?\n\nIf you use \'real\' in a sufficiently vague sense, then you are right.\nGhosts are also real then, since they cost the sleep of many a\nsuperstitious person. Having an explanation said to cause some\nobservable effect is therefore not enough to qualify for \'realness\'.\n\n\n>> As for observational evidence, the fact\n>>that we cannot observe them is not a problem - after all try observing\n>>a single quark ! We know that they are they because otherwise the\n>>charge on an electron would be quite different.\n\nQuarks are considered real because one cannot dispense with them in\nany coherent explanation of high energy physics.\n\nVirtual particles are not considered real since they arise only in a\nparticular approach to high energy physics - perturbation theory\nbefore renormalization - that does not even survive the modifications\nneeded to remove the infinities. Moreover, the virtual particle content\nof a real state depends so much on the details of the computational\nscheme (canonical or light front quantization, standard or\nrenormalization group enhances perturbation theory, etc.) that\ncalling virtual particles real produces a very weird picture of reality.\n\n\n>> Also there are effects\n>>which are attributed to virtal particles such as the Casimir effect\n>>which are observable. I still am yet to be convinced by any argument\n>>that these particles are not real.\n>>\n> They are \'real\' in the sense that imaginary particles can produce physical\n> effects that can and are directly measurable. Nuclear force shielding: The\n> nuclear forces in an atom are diminished significantly because of the cloud\n> of virtual particles which surround the nucleus:\n\nThis is just figurative speech. One couldn\'t even count the number of\nvirtual particles in the cloud, or give _any_ specific information\nabout it. Due to renormalization effects, all these virtual particles\nwould have infinite mass and interact infinitely strongly. And once the\nparticles are renormalized, the whole virtual spook disappears\ncompletely, but the shielding forces are of course still there - as\nrenormalized effective interactions.\n\n\n> While virtual particles exist, they behave\n> just like their real counterparts: If I were to smash in a pumpkin head\n> (this being close to October) with a baseball bat made of virtual particles,\n> the pieces of pumpkin would indeed go flying everywhere.\n\nUnfortunately, this is an impossible scenario. One cannot have objects\nmade of virtual particles only: Such objects only produce vacuum bubbles,\nwhich are completely renormalized away in the first step where one\nrestricts attention to 1PI Feynman graphs.\n\nOnce a particle is observable, it is real - on-shell, with\np^2=m^2c^2, where m is the particle (bound state) mass.\n\nYou can choose between a spooky world with virtual particles and\ninfinities all over the place, or a rational world from which virtual\nparticles are banned except as crude aids to give a superficial\ninitial illustration of renormalization effects.\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>Greysky wrote:
> "Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote
>>As far as I know a virtual
>>particle-antiparticle pair, of total energy dE can exist for a time
>>dt, provided dt and dE satisfy Heisenberg's uncertainty principle. For
>>the time that they exist I don't see any reason that the particles are
>>not just as real as any other.
What do you mean by 'really existing for an unobservably small time'?
If you use 'real' in a sufficiently vague sense, then you are right.
Ghosts are also real then, since they cost the sleep of many a
superstitious person. Having an explanation said to cause some
observable effect is therefore not enough to qualify for 'realness'.
>> As for observational evidence, the fact
>>that we cannot observe them is not a problem - after all try observing
>>a single quark ! We know that they are they because otherwise the
>>charge on an electron would be quite different.
Quarks are considered real because one cannot dispense with them in
any coherent explanation of high energy physics.
Virtual particles are not considered real since they arise only in a
particular approach to high energy physics - perturbation theory
before renormalization - that does not even survive the modifications
needed to remove the infinities. Moreover, the virtual particle content
of a real state depends so much on the details of the computational
scheme (canonical or light front quantization, standard or
renormalization group enhances perturbation theory, etc.) that
calling virtual particles real produces a very weird picture of reality.
>> Also there are effects
>>which are attributed to virtal particles such as the Casimir effect
>>which are observable. I still am yet to be convinced by any argument
>>that these particles are not real.
>>
> They are 'real' in the sense that imaginary particles can produce physical
> effects that can and are directly measurable. Nuclear force shielding: The
> nuclear forces in an atom are diminished significantly because of the cloud
> of virtual particles which surround the nucleus:
This is just figurative speech. One couldn't even count the number of
virtual particles in the cloud, or give _any_ specific information
about it. Due to renormalization effects, all these virtual particles
would have infinite mass and interact infinitely strongly. And once the
particles are renormalized, the whole virtual spook disappears
completely, but the shielding forces are of course still there - as
renormalized effective interactions.
> While virtual particles exist, they behave
> just like their real counterparts: If I were to smash in a pumpkin head
> (this being close to October) with a baseball bat made of virtual particles,
> the pieces of pumpkin would indeed go flying everywhere.
Unfortunately, this is an impossible scenario. One cannot have objects
made of virtual particles only: Such objects only produce vacuum bubbles,
which are completely renormalized away in the first step where one
restricts attention to 1PI Feynman graphs.
Once a particle is observable, it is real - on-shell, with
p^2=m^{2c}^2, where m is the particle (bound state) mass.
You can choose between a spooky world with virtual particles and
infinities all over the place, or a rational world from which virtual
particles are banned except as crude aids to give a superficial
initial illustration of renormalization effects.
Arnold Neumaier
Igor Khavkine
Oct26-04, 12:54 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>On Tue, 28 Sep 2004 15:20:02 +0000, Ian Taylor wrote:\n\n> As I said in my original e-mail if someone comes up with a convincing\n> argument for why virtual particles are not real, I\'m prepared to change my\n> mind. Making the above statements (such as a virtual electron is as\n> different to a real electron as chalk is to cheese is not to my mind at\n> all convincing). As far as I know a virtual particle-antiparticle pair, of\n> total energy dE can exist for a time dt, provided dt and dE satisfy\n> Heisenberg\'s uncertainty principle. For the time that they exist I don\'t\n> see any reason that the particles are not just as real as any other. As\n> for observational evidence, the fact that we cannot observe them is not a\n> problem - after all try observing a single quark ! We know that they are\n> they because otherwise the charge on an electron would be quite different.\n> Also there are effects which are attributed to virtal particles such as\n> the Casimir effect which are observable. I still am yet to be convinced by\n> any argument that these particles are not real.\n\nFirst, I\'d like to point out that no-one beside yourself is responsible\nfor whatever virtual things (particles or otherwise) are running around in\nyour head. Rather than challenging people to correct your misconceptions,\na better attitude would be to try to learn more about what physicists call\n"virtual particles" and then make a decision for yourself whether they are\n"real" or not.\n\nWith that in mind, let me tell you how virtual particles come up in\ncalculations. I\'m not going to tell you what "real" is, but I\'ll tell you\nhow we decide that a particle is there or not. Take some process and put\ndetectors around it. The detectors make localized measurements that tell\nyou the energy and momentum of something. You say that this something is a\nparticle. Let us not belabor the "reality" of this scenario because I\'ve\nnot even introduced virtual particles yet.\n\nNow, you\'ve got some experimental results and you want to compare them to\npredictions of your theory. If this theory happens to be say QED, you go\noff and do the calculations. How do you do these calculations? Because of\nthe complexity of the theory one must make approximations. What kind of\napproximations? Like for any problem there may be more than one\napproximation you can make. In principle, three come to mind at the\nmoment, but there could be more:\n\n1) Do some perturbative calculations that involve scribbling diagrams on\npaper with solid and wavy lines that look awful lot like photons and\nelectrons, and evaluating integrals associated with them.\n\n2) Concoct some large matrix representation of your states and operators,\nthen go to your futuristic supercomputer and make it solve some matrix\ndifferential equations.\n\n3) Write down the path integral formulation of the same problem and go off\nto another futuristic supercomputer and make it crunch some numbers to\nevaluate this integral.\n\nIf you did your calculations right in the end you get the same answer with\nall of the above. However, virtual particles only come up in method (1),\nthey are an interpretation of the calculation steps that conveniently\ninvolve drawing very suggestive diagrams. But other methods have their own\ninterpretations. In (3) you picture a particle wandering around in all\npossible paths and averaging contributions from each path you arrive at\nsomething close to the classical path with some corrections. In (2) you\nnote that as the state (wave function if you will) evolves with time it\nbecomes a superposition of states representing classically exclusive\nalternatives, but only finitely many of them since you matrix\nrepresentation is necessarily finite-dimensional.\n\nI\'m sure you\'ve at least heard of the above interpretations of\nquantum-mechanical and field-theoretical calculations. So if you start\nasking yourself about the reality of virtual particles, I think you\nshould start asking yourself whether the paths taken by electrons in the\npath integral and the superpositions and finite dimensionality of the\nmatrix approximation are real.\n\nWell, are they?\n\nIgor\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>On Tue, 28 Sep 2004 15:20:02 +0000, Ian Taylor wrote:
> As I said in my original e-mail if someone comes up with a convincing
> argument for why virtual particles are not real, I'm prepared to change my
> mind. Making the above statements (such as a virtual electron is as
> different to a real electron as chalk is to cheese is not to my mind at
> all convincing). As far as I know a virtual particle-antiparticle pair, of
> total energy dE can exist for a time dt, provided dt and dE satisfy
> Heisenberg's uncertainty principle. For the time that they exist I don't
> see any reason that the particles are not just as real as any other. As
> for observational evidence, the fact that we cannot observe them is not a
> problem - after all try observing a single quark ! We know that they are
> they because otherwise the charge on an electron would be quite different.
> Also there are effects which are attributed to virtal particles such as
> the Casimir effect which are observable. I still am yet to be convinced by
> any argument that these particles are not real.
First, I'd like to point out that no-one beside yourself is responsible
for whatever virtual things (particles or otherwise) are running around in
your head. Rather than challenging people to correct your misconceptions,
a better attitude would be to try to learn more about what physicists call
"virtual particles" and then make a decision for yourself whether they are
"real" or not.
With that in mind, let me tell you how virtual particles come up in
calculations. I'm not going to tell you what "real" is, but I'll tell you
how we decide that a particle is there or not. Take some process and put
detectors around it. The detectors make localized measurements that tell
you the energy and momentum of something. You say that this something is a
particle. Let us not belabor the "reality" of this scenario because I've
not even introduced virtual particles yet.
Now, you've got some experimental results and you want to compare them to
predictions of your theory. If this theory happens to be say QED, you go
off and do the calculations. How do you do these calculations? Because of
the complexity of the theory one must make approximations. What kind of
approximations? Like for any problem there may be more than one
approximation you can make. In principle, three come to mind at the
moment, but there could be more:
1) Do some perturbative calculations that involve scribbling diagrams on
paper with solid and wavy lines that look awful lot like photons and
electrons, and evaluating integrals associated with them.
2) Concoct some large matrix representation of your states and operators,
then go to your futuristic supercomputer and make it solve some matrix
differential equations.
3) Write down the path integral formulation of the same problem and go off
to another futuristic supercomputer and make it crunch some numbers to
evaluate this integral.
If you did your calculations right in the end you get the same answer with
all of the above. However, virtual particles only come up in method (1),
they are an interpretation of the calculation steps that conveniently
involve drawing very suggestive diagrams. But other methods have their own
interpretations. In (3) you picture a particle wandering around in all
possible paths and averaging contributions from each path you arrive at
something close to the classical path with some corrections. In (2) you
note that as the state (wave function if you will) evolves with time it
becomes a superposition of states representing classically exclusive
alternatives, but only finitely many of them since you matrix
representation is necessarily finite-dimensional.
I'm sure you've at least heard of the above interpretations of
quantum-mechanical and field-theoretical calculations. So if you start
asking yourself about the reality of virtual particles, I think you
should start asking yourself whether the paths taken by electrons in the
path integral and the superpositions and finite dimensionality of the
matrix approximation are real.
Well, are they?
Igor
greywolf42
Oct26-04, 12:56 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>"Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote in message\nnews:2eefbf19.0409271242.48e55ac1@posting .google.com...\n>\n> "greywolf42" <mingstb@marssim-ss.com> wrote in message\nnews:<EtL5d.11865\\$o06.10345@news.flashn ewsgroups.com>...\n> > "Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote in message\n> > news:2eefbf19.0409250112.2abcaafe@posting.google.c om...\n\n> > > A number of people here have stated that virtual particles are not\n> > > "real", and just a calculational device. This has confused me for two\n> > > reasons\n> > >\n> > > 1. I was always taught that particles such as electrons are\n> > > indistinguishable, so that if you swap two electrons around you would\n> > > never be able to tell.\n> >\n> > Yep. Electrons are electrons.\n> >\n> > > So if a virtual electron-antielectron pair is\n> > > created, if we could somehow swap the virtual electron for a real\n> > > electron how would we know ?\n> >\n> > Simply because a \'virtual electron\' is not real. The mathematical device\n> > of a \'virtual electron\' is fundamentally distinguishable from a \'real\n> > electron.\' The former is not observable at all. The latter is\n> > observable.\n> >\n> > Don\'t be confused by the word \'electron\' in the phrase \'virtual\n> > electron.\' The two are as different as cheese and chalk.\n> >\n> > > However this indistinguishability idea\n> > > seems (to me at least) to be at variance with the view that virtual\n> > > particles are not real.\n> >\n> > It is \'at variance\' because a virtual electron is not the same as a real\n> > electron.\n> >\n> > > 2. In Stephen Hawking\'s calculation of a black hole\'s temperature, the\n> > > physical picture painted is that a virtual pair of particles appears\n> > > near the event horizon, and one falls in to the black hole, and the\n> > > other is emitted (at least this is how I have seen it explained). In\n> > > this case the virtual particles (which according to some don\'t really\n> > > exist) somehow become real !\n> >\n> > A virtual particle that "exited" the black hole would remain a virtual\n> > particle. It would not really exist.\n> >\n> > > Clearly I am of the view that virtual particles are just as real as\n> > > real particles, but I am prepared to change my mind if someone puts\n> > > forward a sufficiently convincing argument to the contrary.\n> >\n> > What is the basis for your opinion that virtual particles are \'just as\n> > real\' as real particles. When the former -- by definition -- can never\n> > be directly observed. While the latter can be directly observed?\n>\n> As I said in my original e-mail if someone comes up with a convincing\n> argument for why virtual particles are not real, I\'m prepared to\n> change my mind. Making the above statements (such as a virtual\n> electron is as different to a real electron as chalk is to cheese is\n> not to my mind at all convincing).\n\nThe cheese and chalk comment was physically superfluous, I admit. However,\nthe rest of the arguments remain.\n\nThe fundamental difference remains observability. \'Virtual electrons\' are\nnot observable. \'Real\' electrons are observable.\n\n> As far as I know a virtual\n> particle-antiparticle pair, of total energy dE can exist for a time\n> dt, provided dt and dE satisfy Heisenberg\'s uncertainty principle.\n\nThat is indeed the theory.\n\n> For\n> the time that they exist I don\'t see any reason that the particles are\n> not just as real as any other.\n\nBecause even though they \'exist\' according to the theory, they cannot ever\nbe observed in the laboratory ... again, according to the theory.\n\n> As for observational evidence, the fact\n> that we cannot observe them is not a problem - after all try observing\n> a single quark!\n\nA telling choice of example. Quarks are also among the theoretically\nunobservable particles. However, quarks were originally presumed to be\nobservable. Until they were not observed. Then a new force (not one of the\nmain 4) was postulated to prevent \'free\' quarks from theoretical existence.\nQuarks can only be theoretically inferred from secondary reactions.\n\nA better particle for you to champion would be the neutrino. But the\nneutrino (though hard to observe) seems to be observable. (\'Something\' sure\narrived just before the SN 1987a light pulse.)\n\n> We know that they are they because otherwise the\n> charge on an electron would be quite different.\n\nWe \'know\' no such thing. Since the electron is what it is, there is no way\nto check your claim in the lab. This is called assuming your conclusion.\n\n> Also there are effects\n> which are attributed to virtal particles such as the Casimir effect\n> which are observable.\n\nThe casimir effect is indeed observable. However, the effect is not the\npresumed theoretical cause. And there are other theories that can (and may\nin future be) explain the casimir effect.\n\n> I still am yet to be convinced by any argument\n> that these particles are not real.\n\nThat is your choice, so long as you actually apply the scientific method ...\nand not simply agree with what an authority taught you.\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\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>"Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote in message
news:2eefbf19.0409271242.48e55ac1@posting.google.c om...
>
> "greywolf42" <mingstb@marssim-ss.com> wrote in message
news:<EtL5d.11865$o06.10345@news.flashnewsgroups.com>...
> > "Ian Taylor" <iantaylor2uk@yahoo.co.uk> wrote in message
> > news:2eefbf19.0409250112.2abcaafe@posting.google.c om...
> > > A number of people here have stated that virtual particles are not
> > > "real", and just a calculational device. This has confused me for two
> > > reasons
> > >
> > > 1. I was always taught that particles such as electrons are
> > > indistinguishable, so that if you swap two electrons around you would
> > > never be able to tell.
> >
> > Yep. Electrons are electrons.
> >
> > > So if a virtual electron-antielectron pair is
> > > created, if we could somehow swap the virtual electron for a real
> > > electron how would we know ?
> >
> > Simply because a 'virtual electron' is not real. The mathematical device
> > of a 'virtual electron' is fundamentally distinguishable from a 'real
> > electron.' The former is not observable at all. The latter is
> > observable.
> >
> > Don't be confused by the word 'electron' in the phrase 'virtual
> > electron.' The two are as different as cheese and chalk.
> >
> > > However this indistinguishability idea
> > > seems (to me at least) to be at variance with the view that virtual
> > > particles are not real.
> >
> > It is 'at variance' because a virtual electron is not the same as a real
> > electron.
> >
> > > 2. In Stephen Hawking's calculation of a black hole's temperature, the
> > > physical picture painted is that a virtual pair of particles appears
> > > near the event horizon, and one falls in to the black hole, and the
> > > other is emitted (at least this is how I have seen it explained). In
> > > this case the virtual particles (which according to some don't really
> > > exist) somehow become real !
> >
> > A virtual particle that "exited" the black hole would remain a virtual
> > particle. It would not really exist.
> >
> > > Clearly I am of the view that virtual particles are just as real as
> > > real particles, but I am prepared to change my mind if someone puts
> > > forward a sufficiently convincing argument to the contrary.
> >
> > What is the basis for your opinion that virtual particles are 'just as
> > real' as real particles. When the former -- by definition -- can never
> > be directly observed. While the latter can be directly observed?
>
> As I said in my original e-mail if someone comes up with a convincing
> argument for why virtual particles are not real, I'm prepared to
> change my mind. Making the above statements (such as a virtual
> electron is as different to a real electron as chalk is to cheese is
> not to my mind at all convincing).
The cheese and chalk comment was physically superfluous, I admit. However,
the rest of the arguments remain.
The fundamental difference remains observability. 'Virtual electrons' are
not observable. 'Real' electrons are observable.
> As far as I know a virtual
> particle-antiparticle pair, of total energy dE can exist for a time
> dt, provided dt and dE satisfy Heisenberg's uncertainty principle.
That is indeed the theory.
> For
> the time that they exist I don't see any reason that the particles are
> not just as real as any other.
Because even though they 'exist' according to the theory, they cannot ever
be observed in the laboratory ... again, according to the theory.
> As for observational evidence, the fact
> that we cannot observe them is not a problem - after all try observing
> a single quark!
A telling choice of example. Quarks are also among the theoretically
unobservable particles. However, quarks were originally presumed to be
observable. Until they were not observed. Then a new force (not one of the
main 4) was postulated to prevent 'free' quarks from theoretical existence.
Quarks can only be theoretically inferred from secondary reactions.
A better particle for you to champion would be the neutrino. But the
neutrino (though hard to observe) seems to be observable. ('Something' sure
arrived just before the SN 1987a light pulse.)
> We know that they are they because otherwise the
> charge on an electron would be quite different.
We 'know' no such thing. Since the electron is what it is, there is no way
to check your claim in the lab. This is called assuming your conclusion.
> Also there are effects
> which are attributed to virtal particles such as the Casimir effect
> which are observable.
The casimir effect is indeed observable. However, the effect is not the
presumed theoretical cause. And there are other theories that can (and may
in future be) explain the casimir effect.
> I still am yet to be convinced by any argument
> that these particles are not real.
That is your choice, so long as you actually apply the scientific method ...
and not simply agree with what an authority taught you.
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}
Jesse Mazer
Oct26-04, 12:56 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>This is explained at length in the secition\n>\'\'How real are \'virtual particles\'?\'\' of my theoretical physics FAQ at\n> http://www.mat.univie.ac.at/~neum/physics-faq.txt\n>\n>If you don\'t find this convincing, please state your reasons, and\n>I\'ll improve the argumentation.\n>\n>\n>\n\nFrom popular descriptions I had been under the impression that Feynman\ndiagrams of virtual particle interactions were the quantum field theory\nequivalent of different possible paths in the path integral approach to\nnonrelativistic quantum mechanics--i.e. you take the conditions found by\nyour initial measurement and then sum all possible paths/Feynman\ndiagrams to find the probability of various possible outcomes when you\nmake your next measurement. But reading your FAQ answer it seems things\nare more complicated--would you say the Feynman diagrams of virtual\nparticle interactions should be seen as even less "real" in some sense\nthan the paths in the path integral? For example, would the many-worlds\ninterpretation say that the paths in the path integral represent the\nactual paths of alternate versions of the same particle, but not\nnecessarily say the same thing about Feynman diagrams?\n\n\n\n\n>\n>\n>>Casmir effect, Lamb shift, Rabi vacuum oscillations, electron\n>>anomalous g-factor... How would you rationalize the Casimir effect,\n>>an etalon excluding virtual modes to measurable effect with force\n>>varying as the inverse fourth power of the separation, as "just a\n>>calculational device?"\n>>\n>>\n>\n>Of course, physicists would not talk of virtual particles if the concept\n>had no relevance at all. However, in terms of real particles, the\n>above effects all show up as a consequence of renormalized, effective\n>interactions. Only these have a real meaning in terms of observable\n>effects.\n>\n>\n>Arnold Neumaier\n>\n>\n>\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>Arnold Neumaier wrote:
>This is explained at length in the secition
>''How real are 'virtual particles'?'' of my theoretical physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>
>If you don't find this convincing, please state your reasons, and
>I'll improve the argumentation.
>
>
>
From popular descriptions I had been under the impression that Feynman
diagrams of virtual particle interactions were the quantum field theory
equivalent of different possible paths in the path integral approach to
nonrelativistic quantum mechanics--i.e. you take the conditions found by
your initial measurement and then sum all possible paths/Feynman
diagrams to find the probability of various possible outcomes when you
make your next measurement. But reading your FAQ answer it seems things
are more complicated--would you say the Feynman diagrams of virtual
particle interactions should be seen as even less "real" in some sense
than the paths in the path integral? For example, would the many-worlds
interpretation say that the paths in the path integral represent the
actual paths of alternate versions of the same particle, but not
necessarily say the same thing about Feynman diagrams?
>
>
>>Casmir effect, Lamb shift, Rabi vacuum oscillations, electron
>>anomalous g-factor... How would you rationalize the Casimir effect,
>>an etalon excluding virtual modes to measurable effect with force
>>varying as the inverse fourth power of the separation, as "just a
>>calculational device?"
>>
>>
>
>Of course, physicists would not talk of virtual particles if the concept
>had no relevance at all. However, in terms of real particles, the
>above effects all show up as a consequence of renormalized, effective
>interactions. Only these have a real meaning in terms of observable
>effects.
>
>
>Arnold Neumaier
>
>
>
>
>
Arnold Neumaier
Oct27-04, 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\n\n\nJesse Mazer wrote:\n> Arnold Neumaier wrote:\n>\n>>This is explained at length in the secition\n>>\'\'How real are \'virtual particles\'?\'\' of my theoretical physics FAQ at\n>> http://www.mat.univie.ac.at/~neum/physics-faq.txt\n>>\n>>If you don\'t find this convincing, please state your reasons, and\n>>I\'ll improve the argumentation.\n>\n> From popular descriptions I had been under the impression that Feynman\n> diagrams of virtual particle interactions were the quantum field theory\n> equivalent of different possible paths in the path integral approach to\n> nonrelativistic quantum mechanics--i.e. you take the conditions found by\n> your initial measurement and then sum all possible paths/Feynman\n> diagrams to find the probability of various possible outcomes when you\n> make your next measurement.\n\nHmm. The paths in the Feynman picture of QM are not real either.\nAll possible paths are about as real as all possible items in a\nstatistical ensemble modeling a classical ideal gas. Of course only one\nstate is realized, not all conceivable ones; all others are just there\nto compare to and compute proabilities. In QM things are slightly\nmore complicated, however, since the \'true\' path is smeared by the\nuncertainty principle.\n\n\n> But reading your FAQ answer it seems things\n> are more complicated--would you say the Feynman diagrams of virtual\n> particle interactions should be seen as even less "real" in some sense\n> than the paths in the path integral?\n\nBoth are just calculational devices that stop to exist once a\ndifferent approach to computations are taken. This is why I don\'t\nascribe any reality to them. The real objects remain present in\nany sensible description; the unreal one\'s don\'t.\n\n\n> For example, would the many-worlds\n> interpretation say that the paths in the path integral represent the\n> actual paths of alternate versions of the same particle, but not\n> necessarily say the same thing about Feynman diagrams?\n\nNeither. Even in the many-wolds interpretation, quantum objects have no\nsharp paths, while those integrated over in a path integral are\nperfectly accurate.\n\n\nArnold Neumaier\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>Jesse Mazer wrote:
> Arnold Neumaier wrote:
>
>>This is explained at length in the secition
>>''How real are 'virtual particles'?'' of my theoretical physics FAQ at
>> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>>
>>If you don't find this convincing, please state your reasons, and
>>I'll improve the argumentation.
>
> From popular descriptions I had been under the impression that Feynman
> diagrams of virtual particle interactions were the quantum field theory
> equivalent of different possible paths in the path integral approach to
> nonrelativistic quantum mechanics--i.e. you take the conditions found by
> your initial measurement and then sum all possible paths/Feynman
> diagrams to find the probability of various possible outcomes when you
> make your next measurement.
Hmm. The paths in the Feynman picture of QM are not real either.
All possible paths are about as real as all possible items in a
statistical ensemble modeling a classical ideal gas. Of course only one
state is realized, not all conceivable ones; all others are just there
to compare to and compute proabilities. In QM things are slightly
more complicated, however, since the 'true' path is smeared by the
uncertainty principle.
> But reading your FAQ answer it seems things
> are more complicated--would you say the Feynman diagrams of virtual
> particle interactions should be seen as even less "real" in some sense
> than the paths in the path integral?
Both are just calculational devices that stop to exist once a
different approach to computations are taken. This is why I don't
ascribe any reality to them. The real objects remain present in
any sensible description; the unreal one's don't.
> For example, would the many-worlds
> interpretation say that the paths in the path integral represent the
> actual paths of alternate versions of the same particle, but not
> necessarily say the same thing about Feynman diagrams?
Neither. Even in the many-wolds interpretation, quantum objects have no
sharp paths, while those integrated over in a path integral are
perfectly accurate.
Arnold Neumaier
Doug Sweetser
Nov3-04, 09:59 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>Hello:\n\nThis does not sound right to me:\n\n> One thing about the sum-over-histories model is\n> that it assumes virtual photons travelling between\n> electric charges can do so at every possible speed\n> from zero up to infinity.\n\nI believe it is the sum-over-all-possible histories. There is a fun\nstreaming lecture on the web by Feynman where he talks about light\nbouncing off a mirror. Which photon in the diagram below contributes\nto the reflection?\n\nsource observer\n. o\n|\\\nA| \\B\n| \\\n--------\n\nThe correct answer is both A and B do. The difference is that the\nprobability amplitude for traveling the path of photon A that reaches\nthe observer is changing rapidly in time. Its contribution to the\nsquared amplitude is quickly canceled by a path the smallest step away.\nFor path B, the probability is changing very slowly. Paths near B\ntherefore all contribute to the same effect, the equal angle\nreflection. Doing the calculation correctly involves adding up all\npossible means of bouncing and re-emission to the observer.\n\nPhotons are defined in part as traveling at the speed of light. That\ncharacteristic stays in force for the sum-over-all-possible histories\nmethod. I think standard interpretation will not allow one to add in a\ncontribution from a pion traveling infinitely fast.\n\ndoug\nquaternions.com\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>Hello:
This does not sound right to me:
> One thing about the sum-over-histories model is
> that it assumes virtual photons travelling between
> electric charges can do so at every possible speed
> from zero up to infinity.
I believe it is the sum-over-all-possible histories. There is a fun
streaming lecture on the web by Feynman where he talks about light
bouncing off a mirror. Which photon in the diagram below contributes
to the reflection?
source observer
. o
|\
A| \B| \
--------
The correct answer is both A and B do. The difference is that the
probability amplitude for traveling the path of photon A that reaches
the observer is changing rapidly in time. Its contribution to the
squared amplitude is quickly canceled by a path the smallest step away.
For path B, the probability is changing very slowly. Paths near B
therefore all contribute to the same effect, the equal angle
reflection. Doing the calculation correctly involves adding up all
possible means of bouncing and re-emission to the observer.
Photons are defined in part as traveling at the speed of light. That
characteristic stays in force for the sum-over-all-possible histories
method. I think standard interpretation will not allow one to add in a
contribution from a pion traveling infinitely fast.
doug
quaternions.com
FrediFizzx
Nov3-04, 10:03 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>"Igor Khavkine" <k_igor_k@lycos.com> wrote in message\nnews:pan.2004.09.29.14.07.24.452560@lycos .com...\n\n[snip]\n| 1) Do some perturbative calculations that involve scribbling diagrams on\n| paper with solid and wavy lines that look awful lot like photons and\n| electrons, and evaluating integrals associated with them.\n|\n| 2) Concoct some large matrix representation of your states and operators,\n| then go to your futuristic supercomputer and make it solve some matrix\n| differential equations.\n|\n| 3) Write down the path integral formulation of the same problem and go off\n| to another futuristic supercomputer and make it crunch some numbers to\n| evaluate this integral.\n|\n| If you did your calculations right in the end you get the same answer with\n| all of the above. However, virtual particles only come up in method (1),\n| they are an interpretation of the calculation steps that conveniently\n| involve drawing very suggestive diagrams. But other methods have their own\n| interpretations. In (3) you picture a particle wandering around in all\n| possible paths and averaging contributions from each path you arrive at\n| something close to the classical path with some corrections. In (2) you\n| note that as the state (wave function if you will) evolves with time it\n| becomes a superposition of states representing classically exclusive\n| alternatives, but only finitely many of them since you matrix\n| representation is necessarily finite-dimensional.\n|\n| I\'m sure you\'ve at least heard of the above interpretations of\n| quantum-mechanical and field-theoretical calculations. So if you start\n| asking yourself about the reality of virtual particles, I think you\n| should start asking yourself whether the paths taken by electrons in the\n| path integral and the superpositions and finite dimensionality of the\n| matrix approximation are real.\n|\n| Well, are they?\n\nIf they are all representing the same thing and get the same answer, why\nwouldn\'t they be real? IMHO, (1) can explain all three. Can a real\nelectron swap with a virtual one? If so; this explains (3). Is there an\ninfinite number of virtual particles per small volume of space? Doubtful.\nThis explains (2).\n\nFrediFizzx\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>"Igor Khavkine" <k_{igor_k}@lycos.com> wrote in message
news:pan.2004.09.29.14.07.24.452560@lycos.com...
[snip]
| 1) Do some perturbative calculations that involve scribbling diagrams on
| paper with solid and wavy lines that look awful lot like photons and
| electrons, and evaluating integrals associated with them.
|
| 2) Concoct some large matrix representation of your states and operators,
| then go to your futuristic supercomputer and make it solve some matrix
| differential equations.
|
| 3) Write down the path integral formulation of the same problem and go off
| to another futuristic supercomputer and make it crunch some numbers to
| evaluate this integral.
|
| If you did your calculations right in the end you get the same answer with
| all of the above. However, virtual particles only come up in method (1),
| they are an interpretation of the calculation steps that conveniently
| involve drawing very suggestive diagrams. But other methods have their own
| interpretations. In (3) you picture a particle wandering around in all
| possible paths and averaging contributions from each path you arrive at
| something close to the classical path with some corrections. In (2) you
| note that as the state (wave function if you will) evolves with time it
| becomes a superposition of states representing classically exclusive
| alternatives, but only finitely many of them since you matrix
| representation is necessarily finite-dimensional.
|
| I'm sure you've at least heard of the above interpretations of
| quantum-mechanical and field-theoretical calculations. So if you start
| asking yourself about the reality of virtual particles, I think you
| should start asking yourself whether the paths taken by electrons in the
| path integral and the superpositions and finite dimensionality of the
| matrix approximation are real.
|
| Well, are they?
If they are all representing the same thing and get the same answer, why
wouldn't they be real? IMHO, (1) can explain all three. Can a real
electron swap with a virtual one? If so; this explains (3). Is there an
infinite number of virtual particles per small volume of space? Doubtful.
This explains (2).
FrediFizzx
Igor Khavkine
Nov4-04, 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>On Wed, 03 Nov 2004 16:03:01 +0000, FrediFizzx wrote:\n\n> "Igor Khavkine" <k_igor_k@lycos.com> wrote in message\n> news:pan.2004.09.29.14.07.24.452560@lycos.com...\n >\n> [snip]\n> | 1) Do some perturbative calculations that involve scribbling diagrams on\n> | paper with solid and wavy lines that look awful lot like photons and\n> | electrons, and evaluating integrals associated with them.\n> |\n> | 2) Concoct some large matrix representation of your states and\n> | operators,\n> | then go to your futuristic supercomputer and make it solve some\n> | matrix differential equations.\n> |\n> | 3) Write down the path integral formulation of the same problem and go\n> | off\n> | to another futuristic supercomputer and make it crunch some numbers\n> | to evaluate this integral.\n> |\n> | If you did your calculations right in the end you get the same answer\n> | with all of the above. However, virtual particles only come up in method\n> | (1), they are an interpretation of the calculation steps that\n> | conveniently involve drawing very suggestive diagrams. But other methods\n> | have their own interpretations. In (3) you picture a particle wandering\n> | around in all possible paths and averaging contributions from each path\n> | you arrive at something close to the classical path with some\n> | corrections. In (2) you note that as the state (wave function if you\n> | will) evolves with time it becomes a superposition of states\n> | representing classically exclusive alternatives, but only finitely many\n> | of them since you matrix representation is necessarily\n> | finite-dimensional.\n> |\n> | I\'m sure you\'ve at least heard of the above interpretations of\n> | quantum-mechanical and field-theoretical calculations. So if you start\n> | asking yourself about the reality of virtual particles, I think you\n> | should start asking yourself whether the paths taken by electrons in the\n> | path integral and the superpositions and finite dimensionality of the\n> | matrix approximation are real.\n> |\n> | Well, are they?\n>\n> If they are all representing the same thing and get the same answer, why\n> wouldn\'t they be real?\n\nSince they are approximations they don\'t generally give the same answer\nuntil you take each approximation to the theoretical extreme in which it\ngives the right answer. You can make each approximation give the\nsame answer within some fixed error bars, but the amount of effort\nexpended in each case will be different.\n\n> IMHO, (1) can explain all three.\n\nAll three what? And how?\n\n> Can a real\n> electron swap with a virtual one? If so; this explains (3).\n\nThis question is already ill defined. It may indeed be possible to\nestablish links between different interpretations of the same calculation.\nBut I\'m not sure if this is what you are trying to do and how.\n\n> Is there an\n> infinite number of virtual particles per small volume of space? Doubtful.\n> This explains (2).\n\nReducing the Hilbert space of states to a finite number of dimensions does\nnot translate into a finite number of particles, but into a finitely many\npossible states of the total system. A single particle, e.g. the harmonic\noscillator, may have infinitely many possible states or not, e.g. a\nstationary spin 1/2 particle.\n\nIgor\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>On Wed, 03 Nov 2004 16:03:01 +0000, FrediFizzx wrote:
> "Igor Khavkine" <k_{igor_k}@lycos.com> wrote in message
> news:pan.2004.09.29.14.07.24.452560@lycos.com...
>
> [snip]
> | 1) Do some perturbative calculations that involve scribbling diagrams on
> | paper with solid and wavy lines that look awful lot like photons and
> | electrons, and evaluating integrals associated with them.
> |
> | 2) Concoct some large matrix representation of your states and
> | operators,
> | then go to your futuristic supercomputer and make it solve some
> | matrix differential equations.
> |
> | 3) Write down the path integral formulation of the same problem and go
> | off
> | to another futuristic supercomputer and make it crunch some numbers
> | to evaluate this integral.
> |
> | If you did your calculations right in the end you get the same answer
> | with all of the above. However, virtual particles only come up in method
> | (1), they are an interpretation of the calculation steps that
> | conveniently involve drawing very suggestive diagrams. But other methods
> | have their own interpretations. In (3) you picture a particle wandering
> | around in all possible paths and averaging contributions from each path
> | you arrive at something close to the classical path with some
> | corrections. In (2) you note that as the state (wave function if you
> | will) evolves with time it becomes a superposition of states
> | representing classically exclusive alternatives, but only finitely many
> | of them since you matrix representation is necessarily
> | finite-dimensional.
> |
> | I'm sure you've at least heard of the above interpretations of
> | quantum-mechanical and field-theoretical calculations. So if you start
> | asking yourself about the reality of virtual particles, I think you
> | should start asking yourself whether the paths taken by electrons in the
> | path integral and the superpositions and finite dimensionality of the
> | matrix approximation are real.
> |
> | Well, are they?
>
> If they are all representing the same thing and get the same answer, why
> wouldn't they be real?
Since they are approximations they don't generally give the same answer
until you take each approximation to the theoretical extreme in which it
gives the right answer. You can make each approximation give the
same answer within some fixed error bars, but the amount of effort
expended in each case will be different.
> IMHO, (1) can explain all three.
All three what? And how?
> Can a real
> electron swap with a virtual one? If so; this explains (3).
This question is already ill defined. It may indeed be possible to
establish links between different interpretations of the same calculation.
But I'm not sure if this is what you are trying to do and how.
> Is there an
> infinite number of virtual particles per small volume of space? Doubtful.
> This explains (2).
Reducing the Hilbert space of states to a finite number of dimensions does
not translate into a finite number of particles, but into a finitely many
possible states of the total system. A single particle, e.g. the harmonic
oscillator, may have infinitely many possible states or not, e.g. a
stationary spin 1/2 particle.
Igor
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