QED and the speed of light

Sep9-04, 03:06 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>Based on what I\'ve read by Feynman on QED he says there are ways of\nthe photon travelling faster or slower than the speed of light:\n\n<quote>\nIt may surprise you that there is an amplitude for a photon to go at\nspeeds faster or slower than the conventional speed, c. The amplitudes\nfor these possibilities are very small compared to the contribution\nfrom speed c; in fact, they cancel out when light travels over long\ndistances. However, when the distances are short...these other\nposibilities become vitally important and must be considered.\n</quote>\n\nThe question is, does this apply to all photons or just virtual\nphotons? In the context of this quote, there is nothing to suggest\nvirtual photons, but when I say that photons can travel at speeds\nother than c no one believes me.\n\nIf this is specific to virtual photons, can someone provide a cite or\nreference that makes this clear? Preferably can someone cite Feynman?\n\n--\nhttp://www.techmocracy.net/music/\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>Based on what I've read by Feynman on QED he says there are ways of
the photon travelling faster or slower than the speed of light:

<quote>
It may surprise you that there is an amplitude for a photon to go at
speeds faster or slower than the conventional speed, c. The amplitudes
for these possibilities are very small compared to the contribution
from speed c; in fact, they cancel out when light travels over long
distances. However, when the distances are short...these other
posibilities become vitally important and must be considered.
</quote>

The question is, does this apply to all photons or just virtual
photons? In the context of this quote, there is nothing to suggest
virtual photons, but when I say that photons can travel at speeds
other than c no one believes me.

If this is specific to virtual photons, can someone provide a cite or
reference that makes this clear? Preferably can someone cite Feynman?

--
http://www.techmocracy.net/music/

Sep12-04, 02:23 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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 Thu, 9 Sep 2004 20:06:46 +0000 (UTC), mobydikc@gmail.com (Mike\nHelland) wrote:\n>If this is specific to virtual photons, can someone provide a cite or\n>reference that makes this clear? Preferably can someone cite Feynman?\n\nForget about "virtual" photons, they are just a calculational tool\nwithout actual existence or attributes.\n\nEric\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 Thu, 9 Sep 2004 20:06:46

(UTC), mobydikc@gmail.com (Mike
Helland) wrote:
>If this is specific to virtual photons, can someone provide a cite or
>reference that makes this clear? Preferably can someone cite Feynman?

Forget about "virtual" photons, they are just a calculational tool
without actual existence or attributes.

Eric

**Hans de Vries** · Sep12-04, 02:24 AM

Originally Posted by Mike Helland

<quote>
It may surprise you that there is an amplitude for a photon to go at
speeds faster or slower than the conventional speed, c. The amplitudes
for these possibilities are very small compared to the contribution
from speed c; in fact, they cancel out when light travels over long
distances. However, when the distances are short...these other
posibilities become vitally important and must be considered.
</quote>

The question is, does this apply to all photons or just virtual
photons? In the context of this quote, there is nothing to suggest
virtual photons, but when I say that photons can travel at speeds
other than c no one believes me.

If this is specific to virtual photons, can someone provide a cite or
reference that makes this clear? Preferably can someone cite Feynman?

You can read more about Feynman arguments in:

Elementary Particles and the Laws of Physics.
Richard Feynman, Steven Weinberg
(Dirac Memorial Lectures 1986)

See page 7..10

His argument is based on the Fourier decomposition of
the wave function with positive energies only:

On page 8:
"If you start a series of waves from a particular point they can
not be confined to be inside the light cone if all the energies
are positive."

and on page 9:
"In other words, there is an amplitude for particles to travel
faster than the speed of light and no arrangement of super-
position (with only positive energies) can get around that."

Regards, Hans

Sep14-04, 12:24 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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"Hans de Vries" <hansdevries@chip-architect.com> wrote in message\nnews:Hans.de.Vries.1cds07@physicsforums.c om...\n>> There is an amplitude for a photon to go at speeds\n>> faster or slower than the conventional speed, c.\n>\n> You can read more about Feynman arguments in:\n>\n> Elementary Particles and the Laws of Physics.\n> Richard Feynman, Steven Weinberg\n> (Dirac Memorial Lectures 1986)\n>\n> See page 7..10\n\nI believe that Feynman\'s supposition is brilliant inspiration.\nHowever, the real talent would be in moving to the next\nlevel and knowing how to derive a quantum-based,\nprobabilistic generalization of the Lorentz Transformation\nGroup. Has that been done? Is anyone working on it? Has\nany progress been made?\n\nIt strikes me that an equation for the probabilistic amplitude\nof a photon velocity might be easy to write down. But how\ncould you derive generalized Lorentz Transformations from\nthat?\n\nEugene Shubert\nhttp://www.everythingimportant.org/relativity/special.pdf\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>"Hans de Vries" <hansdevries@chip-architect.com> wrote in message
news:Hans.de.Vries.1cds07@physicsforums.com...
>> There is an amplitude for a photon to go at speeds
>> faster or slower than the conventional speed, c.
>
> You can read more about Feynman arguments in:
>
> Elementary Particles and the Laws of Physics.
> Richard Feynman, Steven Weinberg
> (Dirac Memorial Lectures 1986)
>
> See page 7..10

I believe that Feynman's supposition is brilliant inspiration.
However, the real talent would be in moving to the next
level and knowing how to derive a quantum-based,
probabilistic generalization of the Lorentz Transformation
Group. Has that been done? Is anyone working on it? Has
any progress been made?

It strikes me that an equation for the probabilistic amplitude
of a photon velocity might be easy to write down. But how
could you derive generalized Lorentz Transformations from
that?

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf

Sep16-04, 07:09 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>\nHans de Vries <hansdevries@chip-architect.com> wrote in message news:<Hans.de.Vries.1cds07@physicsforums.com&gt ;...\n> Mike Helland Wrote:\n> >\n> > <quote>\n> > It may surprise you that there is an amplitude for a photon to go at\n> >\n> > speeds faster or slower than the conventional speed, c. The\n> > amplitudes\n> > for these possibilities are very small compared to the contribution\n> > from speed c; in fact, they cancel out when light travels over long\n> > distances. However, when the distances are short...these other\n> > posibilities become vitally important and must be considered.\n> > </quote>\n> >\n> > The question is, does this apply to all photons or just virtual\n> > photons? In the context of this quote, there is nothing to suggest\n> > virtual photons, but when I say that photons can travel at speeds\n> > other than c no one believes me.\n> >\n> > If this is specific to virtual photons, can someone provide a cite or\n> >\n> > reference that makes this clear? Preferably can someone cite Feynman?\n> >\n> >\n>\n>\n> You can read more about Feynman arguments in:\n>\n> Elementary Particles and the Laws of Physics.\n> Richard Feynman, Steven Weinberg\n> (Dirac Memorial Lectures 1986)\n>\n> See page 7..10\n>\n> His argument is based on the Fourier decomposition of\n> the wave function with positive energies only:\n>\n> On page 8:\n> "If you start a series of waves from a particular point they can\n> not be confined to be inside the light cone if all the energies\n> are positive."\n>\n> and on page 9:\n> "In other words, there is an amplitude for particles to travel\n> faster than the speed of light and no arrangement of super-\n> position (with only positive energies) can get around that."\n>\n>\n> Regards, Hans\n>\n> ------------------------------------------------------------------------\n> This post submitted through the LaTeX-enabled physicsforums.com\n> To view this post with LaTeX images:\n> http://www.physicsforums.com/showthread.php?t=42430#post308232\n\n\nThat\'s a very interesting reference. He essentially correlates the\nnon-vanishing amplitudes outside the light cone with the sense of\nreverse causality in that region and uses it as a justification for\nantiparticles. I\'m just curious what other implications can be\ncarefully derived from this result.\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>Hans de Vries <hansdevries@chip-architect.com> wrote in message news:<Hans.de.Vries.1cds07@physicsforums.com>...
> Mike Helland Wrote:
> >
> > <quote>
> > It may surprise you that there is an amplitude for a photon to go at
> >
> > speeds faster or slower than the conventional speed, c. The
> > amplitudes
> > for these possibilities are very small compared to the contribution
> > from speed c; in fact, they cancel out when light travels over long
> > distances. However, when the distances are short...these other
> > posibilities become vitally important and must be considered.
> > </quote>
> >
> > The question is, does this apply to all photons or just virtual
> > photons? In the context of this quote, there is nothing to suggest
> > virtual photons, but when I say that photons can travel at speeds
> > other than c no one believes me.
> >
> > If this is specific to virtual photons, can someone provide a cite or
> >
> > reference that makes this clear? Preferably can someone cite Feynman?
> >
> >
>
>
> You can read more about Feynman arguments in:
>
> Elementary Particles and the Laws of Physics.
> Richard Feynman, Steven Weinberg
> (Dirac Memorial Lectures 1986)
>
> See page 7..10
>
> His argument is based on the Fourier decomposition of
> the wave function with positive energies only:
>
> On page 8:
> "If you start a series of waves from a particular point they can
> not be confined to be inside the light cone if all the energies
> are positive."
>
> and on page 9:
> "In other words, there is an amplitude for particles to travel
> faster than the speed of light and no arrangement of super-
> position (with only positive energies) can get around that."
>
>
> Regards, Hans
>
> ------------------------------------------------------------------------
> This post submitted through the LaTeX-enabled physicsforums.com
> To view this post with LaTeX images:
> http://www.physicsforums.com/showthr...430#post308232

That's a very interesting reference. He essentially correlates the
non-vanishing amplitudes outside the light cone with the sense of
reverse causality in that region and uses it as a justification for
antiparticles. I'm just curious what other implications can be
carefully derived from this result.

**Hans de Vries** · Sep17-04, 05:32 AM

Originally Posted by Eugene Shubert

It strikes me that an equation for the probabilistic amplitude
of a photon velocity might be easy to write down. But how
could you derive generalized Lorentz Transformations from
that?

Actually, The Lorentz transformation can already be derived
from the earliest developments in Quantum Mechanics:

Energy = h * temporal_frequency,
Momentum = h * spacial_frequency

A particle at rest has no momentum but it has (rest) energy.
The QM phase changes in time but it doesn't change spatially.

Now let's see why the same particle seen from another reference
frame does have momentum:

First:

Say if you would have a little "freezing machine" then you could
freeze somebody who is flashing by at very high speed. You could
then walk around him and see that he's highly compressed.

The poor guy however would argue with you. He would say: Hey,
You first froze my front and only later froze my back. That's why
I'm in this awkward position.

So, simultaneity is shifted in his reference frame, Why? It needs
to be shifted because the particles in his body exchange forces
with the speed of light. If the speed of light would be different in
one direction than in another then all equilibriums would be disturbed.

The shift in simultaneity makes the speed of light the same again in
all directions. Equilibriums are restored and the laws of physics
work again, the same as they worked in the “frame-at-rest”

Now:

Instead of a guy passing by at very high speed take a particle with
a QM wave function. The particle in its own reference frame
doesn’t have momentum but it has (rest) energy. Its QM phase
changes in time but it doesn’t change spatially.

Now let’s freeze the particle passing by. From the particle’s view
point we first froze its front while its back was only frozen later.
Its QM wave function which only changes in time was stopped
first at the front but could continue for the rest.

Only after a while it was stopped changing at the back as well.
So what we get is a QM wave function with a phase changing
form the front to the back. That is: It’s changing spatially and
thus has momentum!

It's the shift in simultaneity which does it.

Regards, Hans

Sep19-04, 06:55 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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\nHans de Vries <hansdevries@chip-architect.com> writes\n\n>Energy = h * temporal_frequency,\n>Momentum = h * spacial_frequency\n>\n>A particle at rest has no momentum but it has (rest) energy.\n>The QM phase changes in time but it doesn\'t change spatially.\n\nOk, something I\'ve been wanting to discuss for ages and ages.\n\nI\'d like to see it in 4D.\nThen, just by using a lorentz transform I could see how it looked for\nany arbitrary momentum.\n\n>From your description I am looking at a 4D density that varies\nsinusoidally in each dimension. No, that\'s not right because it doesn\'t\nchange spatially.\n\nOk at any given time the phase over all space is the same.\nOK that\'s much simpler. In 2+1D its a (radially) corrugated tube.\n\nThere is an irresistible temptation to see time as a projection of\nsomething circling in a small circle using an extra dimension + time.\nThat\'ll probably get me shot.\n\nHmmm...\nHang on a minute though, don\'t we want the magnitude to be one at all\ntimes? Naively that would imply another dimension so we can have the\nparticle moving round a circle. It would be nice to have two time\ndimensions or equivalently have time as a complex number.\nI\'ll have a blindfold and final cigarette, please. Thank you.\n\nOh dear another conceptual problem.\nWe are viewing a stationary particle, right. The phase is the same\nthroughout space at any given time. But phase here looks like a scalar.\nIn a way that sort of implies the particle is everywhere in space, which\nis good. But I don\'t see how that can produce an essentially finite\nparticle with a lorentz transformation. One implication is that it takes\ntwo particles to define distance and momentum. Shouldn\'t we bring in\nzero point energy here somewhere?\n\n============\n\nI wrote a longish piece here, but quite honestly the above is confused\nenough and additions would just confuse matters more, so I <snipped> it.\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@despamm ed.com still functions.\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>Hans de Vries <hansdevries@chip-architect.com> writes

>Energy

>Momentum

>
>A particle at rest has no momentum but it has (rest) energy.
>The QM phase changes in time but it doesn't change spatially.

Ok, something I've been wanting to discuss for ages and ages.

I'd like to see it in 4D.
Then, just by using a lorentz transform I could see how it looked for
any arbitrary momentum.

>From your description I am looking at a 4D density that varies
sinusoidally in each dimension. No, that's not right because it doesn't
change spatially.

Ok at any given time the phase over all space is the same.
OK that's much simpler. In

its a (radially) corrugated tube.

There is an irresistible temptation to see time as a projection of
something circling in a small circle using an extra dimension + time.
That'll probably get me shot.

Hmmm...
Hang on a minute though, don't we want the magnitude to be one at all
times? Naively that would imply another dimension so we can have the
particle moving round a circle. It would be nice to have two time
dimensions or equivalently have time as a complex number.
I'll have a blindfold and final cigarette, please. Thank you.

Oh dear another conceptual problem.
We are viewing a stationary particle, right. The phase is the same
throughout space at any given time. But phase here looks like a scalar.
In a way that sort of implies the particle is everywhere in space, which
is good. But I don't see how that can produce an essentially finite
particle with a lorentz transformation. One implication is that it takes
two particles to define distance and momentum. Shouldn't we bring in
zero point energy here somewhere?

============

I wrote a longish piece here, but quite honestly the above is confused
enough and additions would just confuse matters more, so I <snipped> it.

--
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.

**zefram_c** · Sep20-04, 03:38 AM

Originally Posted by Hans de Vries

Today we have anti-hydrogen atoms. Maybe one day we'll have
anti-DNA. I personally won't expect anti-DNA to replicate back-
ward in time (although it's not entirely unlikely that an experi-
menter who sees his anti-DNA slowly disappear from 8 to 4 to
2 to 1 will make such a claim. :^)

It's not going to happen. Treating an anti-particle as the normal particle propagating backwards in time is just a useful mathematical trick to derive results in field theory. When it comes to making actual observations, however, all you will see is particles and antiparticles moving forward in time. One will not see anti-DNA slowly disappear.

Sep20-04, 01:43 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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\nMike Helland wrote:\n> Based on what I\'ve read by Feynman on QED he says there are ways of\n> the photon travelling faster or slower than the speed of light:\n>\n> <quote>\n> It may surprise you that there is an amplitude for a photon to go at\n> speeds faster or slower than the conventional speed, c. The amplitudes\n> for these possibilities are very small compared to the contribution\n> from speed c; in fact, they cancel out when light travels over long\n> distances. However, when the distances are short...these other\n> posibilities become vitally important and must be considered.\n> </quote>\n>\n> The question is, does this apply to all photons or just virtual\n> photons? In the context of this quote, there is nothing to suggest\n> virtual photons,\n\nWhat suggests virtual photons are the \'amplitudes\'.\nIn Feynman\'s approach, the transition probabilities come about by\nsumming amplitudes of virtual processes, and at the end taking the\nabsolute square.\n\nReal (on-shell) photons - i.e., those in the in- and out-states\non which the S-matrix acts - are lightlike and hence travel at the\nspeed of light.\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>Mike Helland wrote:
> Based on what I've read by Feynman on QED he says there are ways of
> the photon travelling faster or slower than the speed of light:
>
> <quote>
> It may surprise you that there is an amplitude for a photon to go at
> speeds faster or slower than the conventional speed, c. The amplitudes
> for these possibilities are very small compared to the contribution
> from speed c; in fact, they cancel out when light travels over long
> distances. However, when the distances are short...these other
> posibilities become vitally important and must be considered.
> </quote>
>
> The question is, does this apply to all photons or just virtual
> photons? In the context of this quote, there is nothing to suggest
> virtual photons,

What suggests virtual photons are the 'amplitudes'.
In Feynman's approach, the transition probabilities come about by
summing amplitudes of virtual processes, and at the end taking the
absolute square.

Real (on-shell) photons - i.e., those in the in- and out-states
on which the S-matrix acts - are lightlike and hence travel at the
speed of light.

Arnold Neumaier

Sep24-04, 08:08 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Eugene Shubert wrote:\n> how to derive a quantum-based,\n> probabilistic generalization of the Lorentz transformation Group.\n\nThis is not the right question. It is similar as to ask for a probabilistic\ngeneralization of the time translation group...\n\nThe right question to ask is about Lorentz-invariant stochastic\ndifferential equations, and these exist both in a classical and in a\nquantum version:\n\nR. M. Dudley.\nLorentz-invariant Markov processes in relativistic phase space.\nArk. Mat., 6:241-268, 1966.\n[For relations to discrete gravity, see gr-qc/0311055]\n\nFor the quantum case, see, e.g: quant-ph/0207053\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Eugene Shubert wrote:
> how to derive a quantum-based,
> probabilistic generalization of the Lorentz Transformation Group.

This is not the right question. It is similar as to ask for a probabilistic
generalization of the time translation group...

The right question to ask is about Lorentz-invariant stochastic
differential equations, and these exist both in a classical and in a
quantum version:

R. M. Dudley.
Lorentz-invariant Markov processes in relativistic phase space.
Ark. Mat.

1966.
[For relations to discrete gravity, see http://www.arxiv.org/abs/gr-qc/0311055]

For the quantum case, see, e.g: http://www.arxiv.org/abs/quant-ph/0207053

Arnold Neumaier

Sep27-04, 03:31 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nArnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<414F10A6.50604@univie.ac.at>...\n> Eugene Shubert wrote:\n> > how to derive a quantum-based, probabilistic generalization\n> > of the Lorentz transformation Group.\n>\n> This is not the right question. ...\n>\n> The right question to ask is about Lorentz-invariant stochastic\n> differential equations, ...\n>\n> R. M. Dudley.\n> Lorentz-invariant Markov processes in relativistic phase space.\n> Ark. Mat., 6:241-268, 1966.\n\nIn special relativity the speed of light is a constant. In Feynman\'s\ntheory "there is an amplitude for a photon to go at speeds faster or\nslower than the conventional speed, c." It strikes me as a difficult\nand remarkable transition to go from the greatest possible speed being\na constant to a non-constant probability amplitude. Why do you believe\nthat Feynman\'s theory preserves Lorentz invariance and that, if we\nassume that Feynman\'s theory is correct, then a modified Lorentz\ntransformation is not required?\n\nEugene Shubert\nhttp://www.everythingimportant.org/relativity/special.pdf\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<414F10A6.50604@univie.ac.at>...
> Eugene Shubert wrote:
> > how to derive a quantum-based, probabilistic generalization
> > of the Lorentz Transformation Group.
>
> This is not the right question. ...
>
> The right question to ask is about Lorentz-invariant stochastic
> differential equations, ...
>
> R. M. Dudley.
> Lorentz-invariant Markov processes in relativistic phase space.
> Ark. Mat.

1966.

In special relativity the speed of light is a constant. In Feynman's
theory "there is an amplitude for a photon to go at speeds faster or
slower than the conventional speed, c." It strikes me as a difficult
and remarkable transition to go from the greatest possible speed being
a constant to a non-constant probability amplitude. Why do you believe
that Feynman's theory preserves Lorentz invariance and that, if we
assume that Feynman's theory is correct, then a modified Lorentz
transformation is not required?

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf

Sep27-04, 10:20 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>\nEugene Shubert wrote:\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<414F10A6.50604@univie.ac.at>...\n>\ n>>Eugene Shubert wrote:\n>>\n>>>how to derive a quantum-based, probabilistic generalization\n>>>of the Lorentz transformation Group.\n>>\n>>This is not the right question. ...\n>>\n>>The right question to ask is about Lorentz-invariant stochastic\n>>differential equations, ...\n>>\n>>R. M. Dudley.\n>>Lorentz-invariant Markov processes in relativistic phase space.\n>>Ark. Mat., 6:241-268, 1966.\n>\n>\n> In special relativity the speed of light is a constant. In Feynman\'s\n> theory "there is an amplitude for a photon to go at speeds faster or\n> slower than the conventional speed, c." It strikes me as a difficult\n> and remarkable transition to go from the greatest possible speed being\n> a constant to a non-constant probability amplitude. Why do you believe\n> that Feynman\'s theory preserves Lorentz invariance and that, if we\n> assume that Feynman\'s theory is correct, then a modified Lorentz\n> transformation is not required?\n\nBecause Feynman\'s quote above only concerns virtual photons, which are\nartifacts of the perturbation expansion of the green\'s functions.\nHe derived statement by formal manipulations within standard QED, which\nis invariant under the standard Lorentz group. So why should any change\nbe needed??\n\n\nArnold Neumaier\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>Eugene Shubert wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<414F10A6.50604@univie.ac.at>...
>
>>Eugene Shubert wrote:
>>
>>>how to derive a quantum-based, probabilistic generalization
>>>of the Lorentz Transformation Group.
>>
>>This is not the right question. ...
>>
>>The right question to ask is about Lorentz-invariant stochastic
>>differential equations, ...
>>
>>R. M. Dudley.
>>Lorentz-invariant Markov processes in relativistic phase space.
>>Ark. Mat.

1966.
>
>
> In special relativity the speed of light is a constant. In Feynman's
> theory "there is an amplitude for a photon to go at speeds faster or
> slower than the conventional speed, c." It strikes me as a difficult
> and remarkable transition to go from the greatest possible speed being
> a constant to a non-constant probability amplitude. Why do you believe
> that Feynman's theory preserves Lorentz invariance and that, if we
> assume that Feynman's theory is correct, then a modified Lorentz
> transformation is not required?

Because Feynman's quote above only concerns virtual photons, which are
artifacts of the perturbation expansion of the green's functions.
He derived statement by formal manipulations within standard QED, which
is invariant under the standard Lorentz group. So why should any change
be needed??

Arnold Neumaier

Sep28-04, 10:20 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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\nHans de Vries <hansdevries@chip-architect.com> wrote in message\n>\n> On page 8:\n> "If you start a series of waves from a particular point they can\n> not be confined to be inside the light cone if all the energies\n> are positive."\n>\n> and on page 9:\n> "In other words, there is an amplitude for particles to travel\n> faster than the speed of light and no arrangement of super-\n> position (with only positive energies) can get around that."\n\n\nWell, one could also conclude that this implies one cannot achieve\nphysically a superposition of states with only positive energy states,\nunless im missing the obvious?\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>Hans de Vries <hansdevries@chip-architect.com> wrote in message
>
> On page 8:
> "If you start a series of waves from a particular point they can
> not be confined to be inside the light cone if all the energies
> are positive."
>
> and on page 9:
> "In other words, there is an amplitude for particles to travel
> faster than the speed of light and no arrangement of super-
> position (with only positive energies) can get around that."

Well, one could also conclude that this implies one cannot achieve
physically a superposition of states with only positive energy states,
unless im missing the obvious?