particles travelling backwards in time

alistair

<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\nIn quantum field theory particles are said to travel backwards in\ntime.\nI assume this is allowable over quantum distance scales.Over what kind\nof distance scale does such particle behaviour stop?\nAnd if it happened when the universe as a whole had a radius equal to\nthe quantum distance scale, would a particle travelling backwards in\ntime still be acceptable to theorists? What was the motivation for\nhaving particles travelling backwards in time in the first place? And\nhow is this sort of time travel compatible with the fact that I always\nsee a clock travelling forwards in time?\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>In quantum field theory particles are said to travel backwards in
time.
I assume this is allowable over quantum distance scales.Over what kind
of distance scale does such particle behaviour stop?
And if it happened when the universe as a whole had a radius equal to
the quantum distance scale, would a particle travelling backwards in
time still be acceptable to theorists? What was the motivation for
having particles travelling backwards in time in the first place? And
how is this sort of time travel compatible with the fact that I always
see a clock travelling forwards in time?

Patrick Van Esch

<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\nalistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407201220.b474e1c@posting.google.com>...\n> In quantum field theory particles are said to travel backwards in\n> time.\n> I assume this is allowable over quantum distance scales.Over what kind\n> of distance scale does such particle behaviour stop?\n\nNo, it is not limited to small time scales. In fact, a particle\ntravelling backwards in time is indistinguishable from its\nantiparticle travelling forward in time. This is actually the\nmechanism by which QFT predicts the existence of anti-particles.\n\ncheers,\nPatrick.\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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407201220.b474e1c@po...google.com>...
> In quantum field theory particles are said to travel backwards in
> time.
> I assume this is allowable over quantum distance scales.Over what kind
> of distance scale does such particle behaviour stop?

No, it is not limited to small time scales. In fact, a particle
travelling backwards in time is indistinguishable from its
antiparticle travelling forward in time. This is actually the
mechanism by which QFT predicts the existence of anti-particles.

cheers,
Patrick.

Alfred Einstead

<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\nalistair@goforit64.fsnet.co.uk (alistair) wrote:\n> In quantum field theory particles are said to travel backwards in\n> time.\n\nNothing\'s moving or travelling. Those are 3-dimensional concepts.\nEverything\'s already all there in 4 dimensions. The particles\nare just worldlines plastered on a Minkowski framework to produce\na tapestry.\n\nThe directionality of the arrow in diagrams is just a graphic\nrepresentation of the C operator; distinguishing fermions from\ntheir anti-fermion states. Time-reveral, the T operator,\non the other hand is something entirely different.\n\nThe underlying theory (that is: the interactions) is\ninvariant under PCT (P = parity), so effecting a T is the\nsame as effecting a PC. But the particles themselves don\'t\nhave this relation. A particle under T is not the same as\nthe particle acted on by PC. In detail, P[C[T[psi]]] != psi.\nSo, a positron is not the mirror image of an electron "moving\nbackwards in time" (whatever "moving in time" is supposed to\nmean), as is commonly stated.\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>alistair@goforit64.fsnet.co.uk (alistair) wrote:
> In quantum field theory particles are said to travel backwards in
> time.

Nothing's moving or travelling. Those are 3-dimensional concepts.
Everything's already all there in 4 dimensions. The particles
are just worldlines plastered on a Minkowski framework to produce
a tapestry.

The directionality of the arrow in diagrams is just a graphic
representation of the C operator; distinguishing fermions from
their anti-fermion states. Time-reveral, the T operator,
on the other hand is something entirely different.

The underlying theory (that is: the interactions) is
invariant under PCT [itex](P =[/itex] parity), so effecting a T is the
same as effecting a PC. But the particles themselves don't
have this relation. A particle under T is not the same as
the particle acted on by PC. In detail, [itex]P[C[T[\psi]]] != \psi[/itex].
So, a positron is not the mirror image of an electron "moving
backwards in time" (whatever "moving in time" is supposed to
mean), as is commonly stated.

alistair

<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>\nnews:<861c1b21.0407201220.b474e1c@p....googl e.com>...\n> In quantum field theory particles are said to travel backwards in\n> time.\n> I assume this is allowable over quantum distance scales.Over what kind\n> of distance scale does such particle behaviour stop?\n\n>No, it is not limited to small time scales. In fact, a particle\n>travelling backwards in time is indistinguishable from its\n>antiparticle travelling forward in time. This is actually the\n>mechanism by which QFT predicts the existence of anti-particles.\n\n>cheers,\n>Patrick.\n\nIt was Dirac\'s combination of special relativity and quantum mechanics\nthat predicted antiparticles.No doubt this made Feynman look out for\nsomething similar.Isn\'t the notion of travelling back in time just a\ncomputational aid in qft - particles don\'t really travel backwards in\ntime, do they?\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>news:<861c1b21.0407201220.b474e1c@p....google.com>...
> In quantum field theory particles are said to travel backwards in
> time.
> I assume this is allowable over quantum distance scales.Over what kind
> of distance scale does such particle behaviour stop?

>No, it is not limited to small time scales. In fact, a particle
>travelling backwards in time is indistinguishable from its
>antiparticle travelling forward in time. This is actually the
>mechanism by which QFT predicts the existence of anti-particles.

>cheers,
>Patrick.

It was Dirac's combination of special relativity and quantum mechanics
that predicted antiparticles.No doubt this made Feynman look out for
something similar.Isn't the notion of travelling back in time just a
computational aid in qft - particles don't really travel backwards in
time, do they?

Oz

<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\nAlfred Einstead <whopkins@csd.uwm.edu> writes\n\n>Nothing\'s moving or travelling. Those are 3-dimensional concepts.\n>Everything\'s already all there in 4 dimensions. The particles\n>are just worldlines plastered on a Minkowski framework to produce\n>a tapestry.\n\nI have a problem with this when one gets to quantum mechanics.\nBecause there is an inherent uncertainty under QM even \'running\nforwards\' will not produce the same result after a period of time even\nfor a system starting in the same state. Perhaps I should add \'if the\nsystem is chaotic\'.\n\nNow that being so (I think) its hard to equate this with a static 4D\nspacetime under many common situations.\n\nOr, put another way, in a *macroscopic* system that is adequately\nchaotic even if you set a system up to be identical to another, the\nresult will not be the same after a period of time.\n\nOr, and this is the key, it is in general possible to distinguish and\narrow of time, its basically entropy driven. That is, in teds example\nusing a non-chaotic system (eg a pendulum, but can be much more complex)\nits not possible to determine the direction of time, but in others (eg a\ngas expanding into a vacuum) it is.\n\nSo the question is, IFF (and you dispute this, but I haven\'t fully\ngrasped your argument) antiparticles travel \'backwards in time\' how will\ntheir bulk properties differ, if at all? One can argue this both ways.\n\n1) They will see entropy increasing in the -t direction and so think\nnon-antiparticles having a decreasing entropy.\n\n2) They see entropy decreasing in the -t direction and so behave\n(statistically) like non-antiparticles in the +t direction.\n\nPersonally I am inclined towards option 2.\n\nAnyway my main point is an extension to this.\n\nIf one assumes option (2) then spacetime isn\'t rigid and fixed. Its more\nlike a flexible option at short distances/times (one could probably\nmutter about entanglement and stuff). At longer distances/times, where\nentropy smoothes everything out, it looks rigid and fixed largely\nbecause of the overwhelming abundance of non-antiparticles.\n\nOr, put another way, locally spacetime is a 4D flexible structure\n(although because of this its pretty complicated) but on large\nscales/long times its a rigid fixed structure.\n\nBearing this in mind that, as I understand it, on small scales\nantiparticles are rather common (the only way to change a particle?)\nthis would itself suggest a deep schism between GR and QM. But, looked\nat in this way, a fix doesn\'t seem impossible.\n\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\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>Alfred Einstead <whopkins@csd.uwm.edu> writes

>Nothing's moving or travelling. Those are 3-dimensional concepts.
>Everything's already all there in 4 dimensions. The particles
>are just worldlines plastered on a Minkowski framework to produce
>a tapestry.

I have a problem with this when one gets to quantum mechanics.
Because there is an inherent uncertainty under QM even 'running
forwards' will not produce the same result after a period of time even
for a system starting in the same state. Perhaps I should add 'if the
system is chaotic'.

Now that being so (I think) its hard to equate this with a static 4D
spacetime under many common situations.

Or, put another way, in a *macroscopic* system that is adequately
chaotic even if you set a system up to be identical to another, the
result will not be the same after a period of time.

Or, and this is the key, it is in general possible to distinguish and
arrow of time, its basically entropy driven. That is, in teds example
using a non-chaotic system (eg a pendulum, but can be much more complex)
its not possible to determine the direction of time, but in others (eg a
gas expanding into a vacuum) it is.

So the question is, IFF (and you dispute this, but I haven't fully
grasped your argument) antiparticles travel 'backwards in time' how will
their bulk properties differ, if at all? One can argue this both ways.

1) They will see entropy increasing in the -t direction and so think
non-antiparticles having a decreasing entropy.

2) They see entropy decreasing in the -t direction and so behave
(statistically) like non-antiparticles in the +t direction.

Personally I am inclined towards option 2.

Anyway my main point is an extension to this.

If one assumes option (2) then spacetime isn't rigid and fixed. Its more
like a flexible option at short distances/times (one could probably
mutter about entanglement and stuff). At longer distances/times, where
entropy smoothes everything out, it looks rigid and fixed largely
because of the overwhelming abundance of non-antiparticles.

Or, put another way, locally spacetime is a 4D flexible structure
(although because of this its pretty complicated) but on large
scales/long times its a rigid fixed structure.

Bearing this in mind that, as I understand it, on small scales
antiparticles are rather common (the only way to change a particle?)
this would itself suggest a deep schism between GR and QM. But, looked
at in this way, a fix doesn't seem impossible.

--
Oz
This post is worth absolutely nothing and is probably fallacious.

BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.

Patrick Van Esch

<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\nwhopkins@csd.uwm.edu (Alfred Einstead) wrote in message news:<e58d56ae.0407211511.47be9d57@posting.google.com>...\n\n> The underlying theory (that is: the interactions) is\n> invariant under PCT (P = parity), so effecting a T is the\n> same as effecting a PC. But the particles themselves don\'t\n> have this relation. A particle under T is not the same as\n> the particle acted on by PC. In detail, P[C[T[psi]]] != psi.\n> So, a positron is not the mirror image of an electron "moving\n> backwards in time" (whatever "moving in time" is supposed to\n> mean), as is commonly stated.\n\nWell, almost so !\nLooking at Peskin and Schroeder, chapter 3, we find that applying P to\na fermion field gives us gamma_0 psi(t,-x) ;\napplying T to it gives us gamma_1 gamma_3 psi(-t,x) and finally\napplying C gives us -i gamma_2 psi_star(t,x).\n\nSo doing the three in a row, C P T, we have:\npsi(x,t) -> -i gamma_2 (gamma_0 gamma_1 gamma_3 psi(-t,-x) )*\n\nWhich results in [ 1 0 0 0 ; 0 1 0 0 ; 0 0 -1 0 ; 0 0 0 -1] psi(-t,\n-x)*\n\nNow when looking at an individual Fourier mode (a single excitation),\nwe see that psi(-t,-x)* = psi(t,x) (for each individual mode). It is\nonly when they are combined with complex coefficients that we have to\nconjugate those coefficients.\n\nSo it is true that strictly speaking, there are phase differences\nbetween C P T psi and psi when considering the different modes, but\nfor one single mode, this does hold.\n\nSo, you DO can say that for a single electron, applying C P or\napplying T comes down to the same thing. This is btw verified by\ncrossing symmetry in Feynman diagrams, which comes down to saying that\nparticles incoming from the past can be exchanged (true, sometimes\nwith a minus sign or something like that) with its antiparticle going\nto the future.\n\ncheers,\nPatrick.\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>whopkins@csd.uwm.edu (Alfred Einstead) wrote in message news:<e58d56ae.0407211511.47be9d57@p...google.com>...

> The underlying theory (that is: the interactions) is
> invariant under PCT [itex](P =[/itex] parity), so effecting a T is the
> same as effecting a PC. But the particles themselves don't
> have this relation. A particle under T is not the same as
> the particle acted on by PC. In detail, [itex]P[C[T[\psi]]] != \psi[/itex].
> So, a positron is not the mirror image of an electron "moving
> backwards in time" (whatever "moving in time" is supposed to
> mean), as is commonly stated.

Well, almost so !
Looking at Peskin and Schroeder, chapter 3, we find that applying P to
a fermion field gives [itex]us \gamma_0 \psi(t,-x) ;[/itex]
applying T to it gives [itex]us \gamma_1 \gamma_3 \psi(-t,x)[/itex] and finally
applying C gives [itex]us -i \gamma_2 \psi_star(t,x)[/itex].

So doing the three in a row, C P T, we have:
[itex]\psi(x,t) -> -i \gamma_2 (\gamma_0 \gamma_1 \gamma_3 \psi(-t,-x) )*[/itex]

Which results in [ 1 ; 1 ; -1 ; [itex]-1] \psi(-t,-x)*[/itex]

Now when looking at an individual Fourier mode (a single excitation),
we see that [itex]\psi(-t,-x)* = \psi(t,x)[/itex] (for each individual mode). It is
only when they are combined with complex coefficients that we have to
conjugate those coefficients.

So it is true that strictly speaking, there are phase differences
between [itex]C P T \psi[/itex] and [itex]\psi[/itex] when considering the different modes, but
for one single mode, this does hold.

So, you DO can say that for a single electron, applying C P or
applying T comes down to the same thing. This is btw verified by
crossing symmetry in Feynman diagrams, which comes down to saying that
particles incoming from the past can be exchanged (true, sometimes
with a minus sign or something like that) with its antiparticle going
to the future.

cheers,
Patrick.

Ulmo

<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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407220202.795cfa58@posting.google.com>...\n> news:<861c1b21.0407201220.b474e1c@p....google.com>...\n> > In quantum field theory particles are said to travel backwards in\n> > time.\n> > I assume this is allowable over quantum distance scales.Over what kind\n> > of distance scale does such particle behaviour stop?\n>\n> >No, it is not limited to small time scales. In fact, a particle\n> >travelling backwards in time is indistinguishable from its\n> >antiparticle travelling forward in time. This is actually the\n> >mechanism by which QFT predicts the existence of anti-particles.\n>\n> >cheers,\n> >Patrick.\n>\n> It was Dirac\'s combination of special relativity and quantum mechanics\n> that predicted antiparticles.No doubt this made Feynman look out for\n> something similar.Isn\'t the notion of travelling back in time just a\n> computational aid in qft - particles don\'t really travel backwards in\n> time, do they?\n\nOf they don\'t really travel backwards in time. It\'s unfortunate that\nlay people come away with that impression.\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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407220202.795cfa58@p...google.com>...
> news:<861c1b21.0407201220.b474e1c@p....google.com>...
> > In quantum field theory particles are said to travel backwards in
> > time.
> > I assume this is allowable over quantum distance scales.Over what kind
> > of distance scale does such particle behaviour stop?
>
> >No, it is not limited to small time scales. In fact, a particle
> >travelling backwards in time is indistinguishable from its
> >antiparticle travelling forward in time. This is actually the
> >mechanism by which QFT predicts the existence of anti-particles.
>
> >cheers,
> >Patrick.
>
> It was Dirac's combination of special relativity and quantum mechanics
> that predicted antiparticles.No doubt this made Feynman look out for
> something similar.Isn't the notion of travelling back in time just a
> computational aid in qft - particles don't really travel backwards in
> time, do they?

Of they don't really travel backwards in time. It's unfortunate that
lay people come away with that impression.

Arnold Neumaier

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nPatrick Van Esch wrote:\n> alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407201220.b474e1c@posting.google.com>...\n>\n& gt;>In quantum field theory particles are said to travel backwards in\n>>time.\n>>I assume this is allowable over quantum distance scales.Over what kind\n>>of distance scale does such particle behaviour stop?\n>\n> No, it is not limited to small time scales. In fact, a particle\n> travelling backwards in time is indistinguishable from its\n> antiparticle travelling forward in time. This is actually the\n> mechanism by which QFT predicts the existence of anti-particles.\nNo; this is the way the old QM predicted antiparticles.\nOne can go some way with it (as in Volume 1 of Bjorken and Drell),\nbut more sophisticated stuff requires the QFT picture\n(as in their Volume 2).\n\nIn QFT there are _only_ particles (and antiparticles) traveling forward\nin time, corresponding to timelike or lightlike momenta.\n(Only \'virtual\' particles may have unrestricted momenta; but these are\nunobservable artifacts of perturbation theory.)\nThe need for antiparticles is in QFT instead revealed by the fact that\nthey are necessary to constract operators with causal (anti)commutation\nrelations, in connection with the spin-statistic theorem. See, e.g.,\nVolume 1 of Weinberg\'s QFT book.\n\nThus talking about particles traveling backward in time is outdated\nand more misleading than it does good.\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>Patrick Van Esch wrote:
> alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407201220.b474e1c@po...google.com>...
>
>>In quantum field theory particles are said to travel backwards in
>>time.
>>I assume this is allowable over quantum distance scales.Over what kind
>>of distance scale does such particle behaviour stop?
>
> No, it is not limited to small time scales. In fact, a particle
> travelling backwards in time is indistinguishable from its
> antiparticle travelling forward in time. This is actually the
> mechanism by which QFT predicts the existence of anti-particles.
No; this is the way the old QM predicted antiparticles.
One can go some way with it (as in Volume 1 of Bjorken and Drell),
but more sophisticated stuff requires the QFT picture
(as in their Volume 2).

In QFT there are _only_ particles (and antiparticles) traveling forward
in time, corresponding to timelike or lightlike momenta.
(Only 'virtual' particles may have unrestricted momenta; but these are
unobservable artifacts of perturbation theory.)
The need for antiparticles is in QFT instead revealed by the fact that
they are necessary to constract operators with causal (anti)commutation
relations, in connection with the spin-statistic theorem. See, e.g.,
Volume 1 of Weinberg's QFT book.

Thus talking about particles traveling backward in time is outdated
and more misleading than it does good.

Arnold Neumaier

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