View Full Version : Virtual Photon?
Curious
Apr15-04, 04:03 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>\n\n\n\nWhat is a "virtual" photon?\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>What is a "virtual" photon?
Arnold Neumaier
Apr15-04, 11:38 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Curious wrote:\n> What is a "virtual" photon?\n\nAn artifice of perturbation theory invented to give an intuitive\n(but if taken too far, misleading) interpretation for Feynman\ndiagrams. More precisely, it is an internal photon line in one of the\nFeynman diagrams. But there is nothing real associated with it.\nDetectable photons are always real, \'dressed\' photons.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Curious wrote:
> What is a "virtual" photon?
An artifice of perturbation theory invented to give an intuitive
(but if taken too far, misleading) interpretation for Feynman
diagrams. More precisely, it is an internal photon line in one of the
Feynman diagrams. But there is nothing real associated with it.
Detectable photons are always real, 'dressed' photons.
Arnold Neumaier
Rahul Jain
Apr18-04, 03:51 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>(I don\'t read this group often and tend to skip over quite a bit of\ndiscussion, so copying an email to me is probably a good idea if you\'d\nlike to respond to me.)\n\nArnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n\n> Curious wrote:\n>> What is a "virtual" photon?\n>\n> An artifice of perturbation theory invented to give an intuitive\n> (but if taken too far, misleading) interpretation for Feynman\n> diagrams. More precisely, it is an internal photon line in one of the\n> Feynman diagrams. But there is nothing real associated with it.\n> Detectable photons are always real, \'dressed\' photons.\n\nWhat if virtual phtotons were merely photons which passed between the\ntwo endpoints of their photon line before quantum decoherence occurred?\n\nJust a random thought from an ----+\nv\n--\nRahul Jain\nrjain@nyct.net\nProfessional Software Developer, Amateur Quantum Mechanicist\n\n\nP.S. OK, I\'ve actually given this issue an enormous amount of thought\n(for an amateur, at least :) and there are some preconditions on the\nvalidity of this idea:\n\n1. Quantum decoherence must occur "instantaneously" and the moment of\ndecoherence must be the moment that all (some?) conservation laws are\n"enforced".\n\n2. However, since the individual particles can only move at speeds up to\nand including c, the magnitude of forces will propagate at speeds up to\nand including c, while the direction of forces will propagate at\n"infinite" speed.\n\nNote that what I mean by "magnitude" is really the average\n(probabalistically expected outcome?) magnitude. The force remains as\nquantum mechanics explains it: the result of the transfer of momentum\nbetween the two endpoints, using the virtual particle as an\nintermediary.\n\nThis "infinite" speed "paradox" can be reconciled with relativity if we\nconsider decoherence to be an operation of space-time itself. The\nmovement of particles through space-time could be considered a\npropagation of a wave through space time. By analogy to sound, an air\nmolecule can move faster than the speed of sound (at least\ntheoretically, even if they don\'t actually have any force applied to\nthem that moves them this fast). A sound wave, on the other hand, is\nlimited to a much lower speed.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>(I don't read this group often and tend to skip over quite a bit of
discussion, so copying an email to me is probably a good idea if you'd
like to respond to me.)
Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
> Curious wrote:
>> What is a "virtual" photon?
>
> An artifice of perturbation theory invented to give an intuitive
> (but if taken too far, misleading) interpretation for Feynman
> diagrams. More precisely, it is an internal photon line in one of the
> Feynman diagrams. But there is nothing real associated with it.
> Detectable photons are always real, 'dressed' photons.
What if virtual phtotons were merely photons which passed between the
two endpoints of their photon line before quantum decoherence occurred?
Just a random thought from an ----+
v
--
Rahul Jain
rjain@nyct.net
Professional Software Developer, Amateur Quantum Mechanicist
P.S. OK, I've actually given this issue an enormous amount of thought
(for an amateur, at least :) and there are some preconditions on the
validity of this idea:
1. Quantum decoherence must occur "instantaneously" and the moment of
decoherence must be the moment that all (some?) conservation laws are
"enforced".
2. However, since the individual particles can only move at speeds up to
and including c, the magnitude of forces will propagate at speeds up to
and including c, while the direction of forces will propagate at
"infinite" speed.
Note that what I mean by "magnitude" is really the average
(probabalistically expected outcome?) magnitude. The force remains as
quantum mechanics explains it: the result of the transfer of momentum
between the two endpoints, using the virtual particle as an
intermediary.
This "infinite" speed "paradox" can be reconciled with relativity if we
consider decoherence to be an operation of space-time itself. The
movement of particles through space-time could be considered a
propagation of a wave through space time. By analogy to sound, an air
molecule can move faster than the speed of sound (at least
theoretically, even if they don't actually have any force applied to
them that moves them this fast). A sound wave, on the other hand, is
limited to a much lower speed.
Charles Francis
Apr19-04, 02:10 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In article <34a4f456.0404142355.48961556@posting.google.com >, Curious\n<curious11112001@yahoo.com> writes\n>\n>\n>\n>\n>What is a "virtual" photon?\n\nThe electromagnetic force is transmitted by "virtual" photons. They are\ncalled virtual because they are not directly detected, but they have a\nreal effect and may be regarded as real.\n\n\nRegards\n\n--\nCharles Francis\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <34a4f456.0404142355.48961556@posting.google.com>, Curious
<curious11112001@yahoo.com> writes
>
>
>
>
>What is a "virtual" photon?
The electromagnetic force is transmitted by "virtual" photons. They are
called virtual because they are not directly detected, but they have a
real effect and may be regarded as real.
Regards
--
Charles Francis
Arnold Neumaier
Apr19-04, 02:15 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>Rahul Jain wrote:\n>\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>\n>>Curious wrote:\n>>\n>>>What is a "virtual" photon?\n>>\n>>An artifice of perturbation theory invented to give an intuitive\n>>(but if taken too far, misleading) interpretation for Feynman\n>>diagrams. More precisely, it is an internal photon line in one of the\n>>Feynman diagrams. But there is nothing real associated with it.\n>>Detectable photons are always real, \'dressed\' photons.\n>\n>\n> What if virtual phtotons were merely photons which passed between the\n> two endpoints of their photon line before quantum decoherence occurred?\n>\n> 2. However, since the individual particles can only move at speeds up to\n> and including c, the magnitude of forces will propagate at speeds up to\n> and including c, while the direction of forces will propagate at\n> "infinite" speed.\n\nVirtual photons mediating the Coulomb repulsion between electrons\nhave spacelike momenta and hence would proceed faster than light\nif there were any reality to them. But there cannot be; you\'d need\ninfinitely many of them, and infinitely many virtual electron-positron\npairs (and then superpositions of any numbers of these) to match exactly\na real, dressed object or interaction.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Rahul Jain wrote:
>
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>
>>Curious wrote:
>>
>>>What is a "virtual" photon?
>>
>>An artifice of perturbation theory invented to give an intuitive
>>(but if taken too far, misleading) interpretation for Feynman
>>diagrams. More precisely, it is an internal photon line in one of the
>>Feynman diagrams. But there is nothing real associated with it.
>>Detectable photons are always real, 'dressed' photons.
>
>
> What if virtual phtotons were merely photons which passed between the
> two endpoints of their photon line before quantum decoherence occurred?
>
> 2. However, since the individual particles can only move at speeds up to
> and including c, the magnitude of forces will propagate at speeds up to
> and including c, while the direction of forces will propagate at
> "infinite" speed.
Virtual photons mediating the Coulomb repulsion between electrons
have spacelike momenta and hence would proceed faster than light
if there were any reality to them. But there cannot be; you'd need
infinitely many of them, and infinitely many virtual electron-positron
pairs (and then superpositions of any numbers of these) to match exactly
a real, dressed object or interaction.
Arnold Neumaier
Patrick Van Esch
Apr20-04, 02:33 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>Rahul Jain <rjain@nyct.net> wrote in message news:<87y8otyjxf.fsf@nyct.net>...\n\n> What if virtual phtotons were merely photons which passed between the\n> two endpoints of their photon line before quantum decoherence occurred?\n>\n>\n> 1. Quantum decoherence must occur "instantaneously" and the moment of\n> decoherence must be the moment that all (some?) conservation laws are\n> "enforced".\n\nYou seem to confuse quantum decoherence with wave function collapse.\nQuantum decoherence is a gradual process as described with orthodox\nquantum theory when taking into account inevitable couplings to the\nenvironment. There are hence no "moments" where "conservation laws\nare enforced".\n\n\n\n> This "infinite" speed "paradox" can be reconciled with relativity if we\n> consider decoherence to be an operation of space-time itself.\n\nThe "paradox" is only a paradox induced by taking too far popular\ndescriptions of quantum field theory. But quantum field theory (the\ntheory at the origin of the concept of "virtual particle" ; or at\nleast when you devellop it in a power series) IS reconciled with\nrelativity.\nWhat you do here is typically the error committed when attaching too\nmuch importance (= classical existence) to "virtual particles",\nsomething I tried to point out in another thread a few weeks ago on\nthis forum.\n\nWhat happens in Quantum Field theory is the following (in perturbative\napproach).\nLet us consider electron-electron scattering in QED. The asymptotic\nquantum amplitude to find a particle at angle theta and phi after\ncollision (also called the S-matrix element) can be written as a power\nseries in the coupling constant, alpha:\n\nS = T0 + alpha T1 + alpha^2 T2 + alpha^3 T3 + ...\n\nIt turns out that T0 = 0, which is normal: T0 is what we would scatter\nif there\'s no interaction (alpha = 0), and then we don\'t scatter\nanything.\n\nIt turns out that the coefficients T1, T2 etc... can be written as\nfollows:\n\nT1 = (factor depending on incoming particles) x (virtual photon\nfactor) x (factor depending on desired outgoing particles)\n\nT2 = (factor depending on incoming particles) x integral of [ (virtual\nphoton 1 factor and virtual photon 2 fator)] x (factor depending on\ndesired outgoing particles)\n\n....\n\nI make a slight error in T2 because there are actually several\ncontributions possible and I only consider 1 case and it should be a\nsum.\n\nThe virtual photon factor in T1 is simply an expression that\ncorresponds to what is called a virtual photon, and takes on the form\n1/q^2 where q is the 4-momentum of what is transferred between the two\nparticles, so we say that there has been a virtual photon exchanged.\nBut in fact it is just a mathematical expression with a 1/q^2 factor\nin it, as a term in a series devellopment.\n\nThe integral in T2 is more complicated: it can contain factors of the\nform 1/q^2 and then factors of the form 1/(k-slash + m). We call the\nfirst factor a virtual photon and the second one a virtual electron.\nIt can be pictorally represented by the exchange of two virtual\nphotons: that\'s then a Feynman diagram. In fact, Feynman invented his\ndiagrams as a mnemonic to write down the series devellopment above,\nand it goes roughly as follows:\n\ndraw the incoming and outgoing particles as full lines. We have hence\n4 lines. Now connect them in all possible ways using internal full\nlines and wiggled lines, such that a full line has no end except for\nan incoming or outgoing particle, they also do not connect to\neachother, but they do connect in a vertex (a point on a full line) to\na wiggle line. Wiggle lines are only to be drawn between vertices on\nfull lines, and to a vertex can only connect one single wiggle line.\nThe number of vertices (which is always an even number) divided by two\ngives you then the power of alpha to which we are going to have a\ncontribution.\n\nThe full lines internally are called virtual electrons (in between\nvertices), and the wiggle lines are called virtual photons. We assign\na 4-momentum to each of those internal pieces, and we require\n4-momentum conservation at each vertex (a bit as in an electrical\ncircuit). This can completely fix all 4-momenta, or still leave some\nfree choices. We now write the factors corresponding to each virtual\nparticle: 1/q^2 for the photons, 1/(k-slash + m) for the virtual\nelectrons. If there are some free momentum choices, we integrate over\nall of them. This expression is a contribution to the T_n term\nmentioned above.\nWe sum over all contributions of all different diagrams we can draw\naccording to this principle.\n\nThis was Feynman\'s trick to write these expressions, which can be\nobtained also by develloping in a series what \'s called the fully\ncontracted interaction hamiltonian (in an exponential). The\nrelationship between this graphical trick and this contraction is\nfully understood and explained in a good QFT text.\nThere are two nice features to Feynman\'s trick: first of all, for a\nhuman being it is MUCH easier to draw the diagrams and to write down\nthe corresponding expressions than to do the series devellopment of\nthe full contraction (for a computer, that\'s not necessarily true !).\nThe second one is that you have the impression to "see" the reaction\nbefore your eyes in each of these diagrams. And that\'s what gives\nrise to an almost physical interpretation of these "virtual\nparticles". The problem is that popularizing works stress this too\nmuch, and if you only read those works, you get the false impression\nof independent existance of billiard balls which are thrown out and\ncaught continuously between particles. But there are difficulties\nwith this picture. Let us consider the basic diagram of the exchange\nof a virtual photon between two electrons. It seems to indicate a\nkind of sending out of the virtual photon, and, after a finite time of\ntravelling, a reception on the other side. But do me a favor and\ncalculate the 4-momentum of that virtual photon: you\'ll see that its\nmass squared is a negative real number !\nMoreover, we\'re working here with Fourier transforms, so this process\nis timeless. In fact, working out what it means, you find back the\nstandard Coulomb interaction. So you can picture a "virtual photon"\nas "one classical coulomb interaction". Nobody associates a billiard\nball to "coulomb interaction" but rather a continuous pulling or\npushing. Nevertheless, this is what is mathematically represented by\none virtual photon in this case.\n\ncheers,\nPatrick.\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>Rahul Jain <rjain@nyct.net> wrote in message news:<87y8otyjxf.fsf@nyct.net>...
> What if virtual phtotons were merely photons which passed between the
> two endpoints of their photon line before quantum decoherence occurred?
>
>
> 1. Quantum decoherence must occur "instantaneously" and the moment of
> decoherence must be the moment that all (some?) conservation laws are
> "enforced".
You seem to confuse quantum decoherence with wave function collapse.
Quantum decoherence is a gradual process as described with orthodox
quantum theory when taking into account inevitable couplings to the
environment. There are hence no "moments" where "conservation laws
are enforced".
> This "infinite" speed "paradox" can be reconciled with relativity if we
> consider decoherence to be an operation of space-time itself.
The "paradox" is only a paradox induced by taking too far popular
descriptions of quantum field theory. But quantum field theory (the
theory at the origin of the concept of "virtual particle" ; or at
least when you devellop it in a power series) IS reconciled with
relativity.
What you do here is typically the error committed when attaching too
much importance (= classical existence) to "virtual particles",
something I tried to point out in another thread a few weeks ago on
this forum.
What happens in Quantum Field theory is the following (in perturbative
approach).
Let us consider electron-electron scattering in QED. The asymptotic
quantum amplitude to find a particle at angle \theta and \phi after
collision (also called the S-matrix element) can be written as a power
series in the coupling constant, \alpha:S = T0 + \alpha T1 + \alpha^2 T2 + \alpha^3 T3 + ...
It turns out that T0 = 0, which is normal: T0 is what we would scatter
if there's no interaction (\alpha = 0), and then we don't scatter
anything.
It turns out that the coefficients T1, T2 etc... can be written as
follows:
T1 = (factor depending on incoming particles) x (virtual photon
factor) x (factor depending on desired outgoing particles)
T2 = (factor depending on incoming particles) x integral of [ (virtual
photon 1 factor and virtual photon 2 fator)] x (factor depending on
desired outgoing particles)
....
I make a slight error in T2 because there are actually several
contributions possible and I only consider 1 case and it should be a
sum.
The virtual photon factor in T1 is simply an expression that
corresponds to what is called a virtual photon, and takes on the form
1/q^2 where q is the 4-momentum of what is transferred between the two
particles, so we say that there has been a virtual photon exchanged.
But in fact it is just a mathematical expression with a 1/q^2 factor
in it, as a term in a series devellopment.
The integral in T2 is more complicated: it can contain factors of the
form 1/q^2 and then factors of the form 1/(k-slash + m). We call the
first factor a virtual photon and the second one a virtual electron.
It can be pictorally represented by the exchange of two virtual
photons: that's then a Feynman diagram. In fact, Feynman invented his
diagrams as a mnemonic to write down the series devellopment above,
and it goes roughly as follows:
draw the incoming and outgoing particles as full lines. We have hence
4 lines. Now connect them in all possible ways using internal full
lines and wiggled lines, such that a full line has no end except for
an incoming or outgoing particle, they also do not connect to
eachother, but they do connect in a vertex (a point on a full line) to
a wiggle line. Wiggle lines are only to be drawn between vertices on
full lines, and to a vertex can only connect one single wiggle line.
The number of vertices (which is always an even number) divided by two
gives you then the power of \alpha to which we are going to have a
contribution.
The full lines internally are called virtual electrons (in between
vertices), and the wiggle lines are called virtual photons. We assign
a 4-momentum to each of those internal pieces, and we require
4-momentum conservation at each vertex (a bit as in an electrical
circuit). This can completely fix all 4-momenta, or still leave some
free choices. We now write the factors corresponding to each virtual
particle: 1/q^2 for the photons, 1/(k-slash + m) for the virtual
electrons. If there are some free momentum choices, we integrate over
all of them. This expression is a contribution to the T_n term
mentioned above.
We sum over all contributions of all different diagrams we can draw
according to this principle.
This was Feynman's trick to write these expressions, which can be
obtained also by develloping in a series what 's called the fully
contracted interaction hamiltonian (in an exponential). The
relationship between this graphical trick and this contraction is
fully understood and explained in a good QFT text.
There are two nice features to Feynman's trick: first of all, for a
human being it is MUCH easier to draw the diagrams and to write down
the corresponding expressions than to do the series devellopment of
the full contraction (for a computer, that's not necessarily true !).
The second one is that you have the impression to "see" the reaction
before your eyes in each of these diagrams. And that's what gives
rise to an almost physical interpretation of these "virtual
particles". The problem is that popularizing works stress this too
much, and if you only read those works, you get the false impression
of independent existance of billiard balls which are thrown out and
caught continuously between particles. But there are difficulties
with this picture. Let us consider the basic diagram of the exchange
of a virtual photon between two electrons. It seems to indicate a
kind of sending out of the virtual photon, and, after a finite time of
travelling, a reception on the other side. But do me a favor and
calculate the 4-momentum of that virtual photon: you'll see that its
mass squared is a negative real number !
Moreover, we're working here with Fourier transforms, so this process
is timeless. In fact, working out what it means, you find back the
standard Coulomb interaction. So you can picture a "virtual photon"
as "one classical coulomb interaction". Nobody associates a billiard
ball to "coulomb interaction" but rather a continuous pulling or
pushing. Nevertheless, this is what is mathematically represented by
one virtual photon in this case.
cheers,
Patrick.
Arnold Neumaier
Apr21-04, 04:22 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Patrick Van Esch wrote:\n\n> Moreover, we\'re working here with Fourier transforms, so this process\n> is timeless. In fact, working out what it means, you find back the\n> standard Coulomb interaction. So you can picture a "virtual photon"\n> as "one classical coulomb interaction".\n\nThis is not quite correct. The Coulomb interaction is a ladder\napproximation, and hence corresponds to summing all diagrams with\n0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.\n\nSingle exchanged photons are completely meaningless.\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:
> Moreover, we're working here with Fourier transforms, so this process
> is timeless. In fact, working out what it means, you find back the
> standard Coulomb interaction. So you can picture a "virtual photon"
> as "one classical coulomb interaction".
This is not quite correct. The Coulomb interaction is a ladder
approximation, and hence corresponds to summing all diagrams with
0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.
Single exchanged photons are completely meaningless.
Arnold Neumaier
Charles Francis
Apr22-04, 03:31 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>In article <c61502\\$d24\\$1@lfa222122.richmond.edu>, Arnold Neumaier\n<Arnold.Neumaier@univie.ac.at> writes\n>Rahul Jain wrote:\n>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:\n>>\n>>>Curious wrote:\n>>>\n>>>>What is a "virtual" photon?\n>>>\n>>>An artifice of perturbation theory invented to give an intuitive\n>>>(but if taken too far, misleading) interpretation for Feynman\n>>>diagrams. More precisely, it is an internal photon line in one of the\n>>>Feynman diagrams. But there is nothing real associated with it.\n>>>Detectable photons are always real, \'dressed\' photons.\n>> What if virtual phtotons were merely photons which passed between\n>>the\n>> two endpoints of their photon line before quantum decoherence occurred?\n>> 2. However, since the individual particles can only move at speeds\n>>up to\n>> and including c, the magnitude of forces will propagate at speeds up to\n>> and including c, while the direction of forces will propagate at\n>> "infinite" speed.\n>\n>Virtual photons mediating the Coulomb repulsion between electrons\n>have spacelike momenta and hence would proceed faster than light\n>if there were any reality to them.\n\nYes, that is fine. Only information cannot travel faster than light.\n\n>But there cannot be; you\'d need\n>infinitely many of them, and infinitely many virtual electron-positron\n>pairs (and then superpositions of any numbers of these) to match exactly\n>a real, dressed object or interaction.\n\nNot an infinity, just a large enough population to be accurately\nmodelled as an infinity.\n\n\n\nRegards\n\n--\nCharles Francis\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <c61502$d24$1@lfa222122.richmond.edu>, Arnold Neumaier
<Arnold.Neumaier@univie.ac.at> writes
>Rahul Jain wrote:
>> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> writes:
>>
>>>Curious wrote:
>>>
>>>>What is a "virtual" photon?
>>>
>>>An artifice of perturbation theory invented to give an intuitive
>>>(but if taken too far, misleading) interpretation for Feynman
>>>diagrams. More precisely, it is an internal photon line in one of the
>>>Feynman diagrams. But there is nothing real associated with it.
>>>Detectable photons are always real, 'dressed' photons.
>> What if virtual phtotons were merely photons which passed between
>>the
>> two endpoints of their photon line before quantum decoherence occurred?
>> 2. However, since the individual particles can only move at speeds
>>up to
>> and including c, the magnitude of forces will propagate at speeds up to
>> and including c, while the direction of forces will propagate at
>> "infinite" speed.
>
>Virtual photons mediating the Coulomb repulsion between electrons
>have spacelike momenta and hence would proceed faster than light
>if there were any reality to them.
Yes, that is fine. Only information cannot travel faster than light.
>But there cannot be; you'd need
>infinitely many of them, and infinitely many virtual electron-positron
>pairs (and then superpositions of any numbers of these) to match exactly
>a real, dressed object or interaction.
Not an infinity, just a large enough population to be accurately
modelled as an infinity.
Regards
--
Charles Francis
Jerzy Karczmarczuk
Apr22-04, 03:46 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>Patrick Van Esch wrote:\n\n/many things about virtuality, incoherence, etc...\nAnd about the dangers of taking virtual particles too seriously.\n/\n\n\n....\n> The second one is that you have the impression to "see" the reaction\n> before your eyes in each of these diagrams. And that\'s what gives\n> rise to an almost physical interpretation of these "virtual\n> particles". The problem is that popularizing works stress this too\n> much, and if you only read those works, you get the false impression\n> of independent existance of billiard balls which are thrown out and\n> caught continuously between particles. But there are difficulties\n> with this picture. Let us consider the basic diagram of the exchange\n> of a virtual photon between two electrons. It seems to indicate a\n> kind of sending out of the virtual photon, and, after a finite time of\n> travelling, a reception on the other side. But do me a favor and\n> calculate the 4-momentum of that virtual photon: you\'ll see that its\n> mass squared is a negative real number !\n\nI have the impression that most people here - and PVE in particular, when\nfighting "against virtual particles" fight against mythology. One CAN\ntake those entities seriously without committing any sin against common\nsense. It is not a question of seeing virtual photons, mesons, etc. as\nbillard balls. Properly educated people know that REAL particles are\nneither !\n\nIt is the question: does the perturbation theory reflects somehow the\n"reality"? In my opinion yes. It works numerically. In a dense matter, where\nphoton exchange are dense, one sees that ladder approximations (or Random\nPhase, or Hartree-Fock, etc.) work reasonably, and "particles" give some\nintuitive picture. Summing a geometric series of 1/q^2 propagators gives\na "dressed" one 1/(q^2 + c) - a plasmon, a "photon with mass". Replacing\nan infinite sum of ladder diagrams, of many photon exchanges by one quasi-\nparticle is intuitively appealing. You have also polarons, etc. All that is\nas "physical" as anything else, WITHIN THE QFT FRAMEWORK.\n\nFor the theory itself, the difference between asymptotic states, on-shell,\nand Green\'s functions, the propagators off-shell is not as cardinal as\nthat; out OBSERVATION framework introduces the difference.\n\nI strongly believe that instead of crying "virtal particles do not exist,\nthey are dybbuks in your head", one should instead teach WELL their properties.\n\n\n\n> Moreover, we\'re working here with Fourier transforms, so this process\n> is timeless. In fact, working out what it means, you find back the\n> standard Coulomb interaction. So you can picture a "virtual photon"\n> as "one classical coulomb interaction". Nobody associates a billiard\n> ball to "coulomb interaction" but rather a continuous pulling or\n> pushing. Nevertheless, this is what is mathematically represented by\n> one virtual photon in this case.\n\n\nNow, there are curious methodological sins above. Saying "we are working\nin Fourier space, so the process is timeless" is - with my full respect -\nan absurdity. If you analyse the spectrum of musical instruments, and you\npass to the frequency domain, you will do the same. Will you claim that\n"music is a timeless process"??\n\nSecond, while 1/q^2 is the Fourier transform of 1/r (in 3D), the *classical*\nCoulomb attraction/repulsion, as we can see on macroscopic bodies is FAR\nfrom being ONE virtual photon. It is well known that we have to go to\nthe infra-red limit; the classical force will result from an infinite number\nof wee photons, with infinite wavelength... So, first of all, one should\nrefrain from imagining a classical, macroscopical interaction as the exchange\nof virtual particles, unless one knows that one has to descend to a delicate\ncoherent limit.\n\n\n\nJerzy Karczmarczuk\nCaen, France.\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>Patrick Van Esch wrote:
/many things about virtuality, incoherence, etc...
And about the dangers of taking virtual particles too seriously.
/
....
> The second one is that you have the impression to "see" the reaction
> before your eyes in each of these diagrams. And that's what gives
> rise to an almost physical interpretation of these "virtual
> particles". The problem is that popularizing works stress this too
> much, and if you only read those works, you get the false impression
> of independent existance of billiard balls which are thrown out and
> caught continuously between particles. But there are difficulties
> with this picture. Let us consider the basic diagram of the exchange
> of a virtual photon between two electrons. It seems to indicate a
> kind of sending out of the virtual photon, and, after a finite time of
> travelling, a reception on the other side. But do me a favor and
> calculate the 4-momentum of that virtual photon: you'll see that its
> mass squared is a negative real number !
I have the impression that most people here - and PVE in particular, when
fighting "against virtual particles" fight against mythology. One CAN
take those entities seriously without committing any sin against common
sense. It is not a question of seeing virtual photons, mesons, etc. as
billard balls. Properly educated people know that REAL particles are
neither !
It is the question: does the perturbation theory reflects somehow the
"reality"? In my opinion yes. It works numerically. In a dense matter, where
photon exchange are dense, one sees that ladder approximations (or Random
Phase, or Hartree-Fock, etc.) work reasonably, and "particles" give some
intuitive picture. Summing a geometric series of 1/q^2 propagators gives
a "dressed" one 1/(q^2 + c) - a plasmon, a "photon with mass". Replacing
an infinite sum of ladder diagrams, of many photon exchanges by one quasi-
particle is intuitively appealing. You have also polarons, etc. All that is
as "physical" as anything else, WITHIN THE QFT FRAMEWORK.
For the theory itself, the difference between asymptotic states, on-shell,
and Green's functions, the propagators off-shell is not as cardinal as
that; out OBSERVATION framework introduces the difference.
I strongly believe that instead of crying "virtal particles do not exist,
they are dybbuks in your head", one should instead teach WELL their properties.
> Moreover, we're working here with Fourier transforms, so this process
> is timeless. In fact, working out what it means, you find back the
> standard Coulomb interaction. So you can picture a "virtual photon"
> as "one classical coulomb interaction". Nobody associates a billiard
> ball to "coulomb interaction" but rather a continuous pulling or
> pushing. Nevertheless, this is what is mathematically represented by
> one virtual photon in this case.
Now, there are curious methodological sins above. Saying "we are working
in Fourier space, so the process is timeless" is - with my full respect -
an absurdity. If you analyse the spectrum of musical instruments, and you
pass to the frequency domain, you will do the same. Will you claim that
"music is a timeless process"??
Second, while 1/q^2 is the Fourier transform of 1/r (in 3D), the *classical*
Coulomb attraction/repulsion, as we can see on macroscopic bodies is FAR
from being ONE virtual photon. It is well known that we have to go to
the infra-red limit; the classical force will result from an infinite number
of wee photons, with infinite wavelength... So, first of all, one should
refrain from imagining a classical, macroscopical interaction as the exchange
of virtual particles, unless one knows that one has to descend to a delicate
coherent limit.
Jerzy Karczmarczuk
Caen, France.
Alejandro
Apr22-04, 04:07 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Charles Francis <charles@clef.demon.co.uk> wrote in message news:<c614n3\\$d1r\\$1@lfa222122.richmond.edu>...\ n> In article <34a4f456.0404142355.48961556@posting.google.com >, Curious\n> <curious11112001@yahoo.com> writes\n> >What is a "virtual" photon?\n>\n> The electromagnetic force is transmitted by "virtual" photons. They are\n> called virtual because they are not directly detected, but they have a\n> real effect and may be regarded as real.\n\nYes, let me keep going on this. The virtual photons can be considered\nreal in virtue of the incertainty principle. The equation E=p is violated,\nbut this violation is possible in quantum mechanics for a short time\nt = h/E or around a short spacing x=h/p.\n\nConsider for instance a particle in a circular orbit on a central spherical\npotential. Its momentum changes, but its energy is constant. So the\nvirtual photons transmit momenta but they do not transmit energy.\n\nto avoid the philosophical implications of real/virtual, the practicioners\nof perturbative theory prefer to speak of on-shell and off-shell particles.\n\n\nAlejandro\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>Charles Francis <charles@clef.demon.co.uk> wrote in message news:<c614n3$d1r$1@lfa222122.richmond.edu>...
> In article <34a4f456.0404142355.48961556@posting.google.com>, Curious
> <curious11112001@yahoo.com> writes
> >What is a "virtual" photon?
>
> The electromagnetic force is transmitted by "virtual" photons. They are
> called virtual because they are not directly detected, but they have a
> real effect and may be regarded as real.
Yes, let me keep going on this. The virtual photons can be considered
real in virtue of the incertainty principle. The equation E=p is violated,
but this violation is possible in quantum mechanics for a short time
t = h/E or around a short spacing x=h/p.
Consider for instance a particle in a circular orbit on a central spherical
potential. Its momentum changes, but its energy is constant. So the
virtual photons transmit momenta but they do not transmit energy.
to avoid the philosophical implications of real/virtual, the practicioners
of perturbative theory prefer to speak of on-shell and off-shell particles.
Alejandro
Alejandro
Apr22-04, 04:07 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<c61502\\$d24\\$1@lfa222122.richmond.edu>...\ n\n> Virtual photons mediating the Coulomb repulsion between electrons\n> have spacelike momenta and hence would proceed faster than light\n> if there were any reality to them. But there cannot be; you\'d need\n> infinitely many of them, and infinitely many virtual electron-positron\n> pairs (and then superpositions of any numbers of these) to match exactly\n> a real, dressed object or interaction.\n\nI am not sure of iy. If you are meaning that you need to sum the\nfull perturbative series, then you should explain how the divergence\nproblem is avoided.\n\nAlso I don\'t get what a "dressed interaction" is.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<c61502$d24$1@lfa222122.richmond.edu>...
> Virtual photons mediating the Coulomb repulsion between electrons
> have spacelike momenta and hence would proceed faster than light
> if there were any reality to them. But there cannot be; you'd need
> infinitely many of them, and infinitely many virtual electron-positron
> pairs (and then superpositions of any numbers of these) to match exactly
> a real, dressed object or interaction.
I am not sure of iy. If you are meaning that you need to sum the
full perturbative series, then you should explain how the divergence
problem is avoided.
Also I don't get what a "dressed interaction" is.
Patrick Van Esch
Apr24-04, 12:16 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4084FD9F.4090602@univie.ac.at>...\n> Patrick Van Esch wrote:\n>\n> > Moreover, we\'re working here with Fourier transforms, so this process\n> > is timeless. In fact, working out what it means, you find back the\n> > standard Coulomb interaction. So you can picture a "virtual photon"\n> > as "one classical coulomb interaction".\n>\n> This is not quite correct. The Coulomb interaction is a ladder\n> approximation, and hence corresponds to summing all diagrams with\n> 0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.\n>\n> Single exchanged photons are completely meaningless.\n\nWell, I had in mind the fact that in the non-relativistic limit, the\ntree diagram of an electron-electron interaction gives rise to a\nscattering amplitude. This scattering amplitude can then be\ninterpreted in the Born approximation as potential scattering, and\nwhen one extracts the potential, it gives rise to the Coulomb\npotential. So to me, the whole Coulomb potential was already\ndescribed by that tree diagram.\n\ncheers,\nPatrick.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4084FD9F.4090602@univie.ac.at>...
> Patrick Van Esch wrote:
>
> > Moreover, we're working here with Fourier transforms, so this process
> > is timeless. In fact, working out what it means, you find back the
> > standard Coulomb interaction. So you can picture a "virtual photon"
> > as "one classical coulomb interaction".
>
> This is not quite correct. The Coulomb interaction is a ladder
> approximation, and hence corresponds to summing all diagrams with
> 0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.
>
> Single exchanged photons are completely meaningless.
Well, I had in mind the fact that in the non-relativistic limit, the
tree diagram of an electron-electron interaction gives rise to a
scattering amplitude. This scattering amplitude can then be
interpreted in the Born approximation as potential scattering, and
when one extracts the potential, it gives rise to the Coulomb
potential. So to me, the whole Coulomb potential was already
described by that tree diagram.
cheers,
Patrick.
Arnold Neumaier
Apr24-04, 12:17 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Alejandro wrote:\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<c61502\\$d24\\$1@lfa222122.richmond.edu>...\ n>\n>\n>>Virtual photons mediating the Coulomb repulsion between electrons\n>>have spacelike momenta and hence would proceed faster than light\n>>if there were any reality to them. But there cannot be; you\'d need\n>>infinitely many of them, and infinitely many virtual electron-positron\n>>pairs (and then superpositions of any numbers of these) to match exactly\n>>a real, dressed object or interaction.\n>\n>\n> I am not sure of iy. If you are meaning that you need to sum the\n> full perturbative series, then you should explain how the divergence\n> problem is avoided.\n\nYou need to sum all ladder diagrams - and then solve an approximate\nBethe-Salpeter equation to get the result. These are nonperturbative\ntechniques. The computations are still done at few loops only,\nwhich means that questions of convergence never enter.\n\n\n> Also I don\'t get what a "dressed interaction" is.\n\nThe dressed object is the renormalized, physical object,\ndescribed perturbatively as the bare object \'clothed\' by the\ncloud of virtual particles. The dressed interaction is the \'screened\'\nphysical interaction between these dress objects.\n\nTo draw an analogy in nonrelativistic QM\nthink of nuclei as bare atoms, electrons as virtual particles,\natoms as dressed nuclei and the residual interaction between atoms,\ncomputed in the Born-Oppenheimer approximation, as the dressed\ninteraction. Thus, for Argon atoms, the dressed interaction is\nsomething close to a Lennard-Jones potential, while the bare\ninteraction is Coulomb repulsion. This is the situation physicists\nhad in mind when they invented the notions of bare and dressed\nparticles.\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>Alejandro wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<c61502$d24$1@lfa222122.richmond.edu>...
>
>
>>Virtual photons mediating the Coulomb repulsion between electrons
>>have spacelike momenta and hence would proceed faster than light
>>if there were any reality to them. But there cannot be; you'd need
>>infinitely many of them, and infinitely many virtual electron-positron
>>pairs (and then superpositions of any numbers of these) to match exactly
>>a real, dressed object or interaction.
>
>
> I am not sure of iy. If you are meaning that you need to sum the
> full perturbative series, then you should explain how the divergence
> problem is avoided.
You need to sum all ladder diagrams - and then solve an approximate
Bethe-Salpeter equation to get the result. These are nonperturbative
techniques. The computations are still done at few loops only,
which means that questions of convergence never enter.
> Also I don't get what a "dressed interaction" is.
The dressed object is the renormalized, physical object,
described perturbatively as the bare object 'clothed' by the
cloud of virtual particles. The dressed interaction is the 'screened'
physical interaction between these dress objects.
To draw an analogy in nonrelativistic QM
think of nuclei as bare atoms, electrons as virtual particles,
atoms as dressed nuclei and the residual interaction between atoms,
computed in the Born-Oppenheimer approximation, as the dressed
interaction. Thus, for Argon atoms, the dressed interaction is
something close to a Lennard-Jones potential, while the bare
interaction is Coulomb repulsion. This is the situation physicists
had in mind when they invented the notions of bare and dressed
particles.
Arnold Neumaier
Patrick Van Esch
Apr24-04, 12:18 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>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<4084D08B.5070605@info.unicaen.fr>...\n> Patrick Van Esch wrote:\n>\n>\n> I have the impression that most people here - and PVE in particular, when\n> fighting "against virtual particles" fight against mythology. One CAN\n> take those entities seriously without committing any sin against common\n> sense. It is not a question of seeing virtual photons, mesons, etc. as\n> billard balls. Properly educated people know that REAL particles are\n> neither !\n\nI suppose you are right. This must come from an unfortunate\nexperience I had when I was a PhD student. I still remember lots of\nvery weird discussions based on the in my interpretation "virtual\nbilliard ball" paradigm in diffractive deep inelastic scattering. To\nme, these explanations of observed effects in the data didn\'t make any\nsense, but gave rise to heated (and to me totally uncomprehensive)\ndiscussions within working groups of experimentalists (young and old).\nIt really went like "this pomeron kicks that gluon out of the\n(dressed up) photon" and then people went calculating the angle as if\nwe were throwing out billiard balls, and compared it to - in my\nopinion - sometimes dubiously preselected data. It might very well be\nthat those people had a very strong intuition and that it was me who\ndidn\'t understand a yota of what they were talking about. But I had\nthe impression it was total gibberish.\n\n\n>\n> > Moreover, we\'re working here with Fourier transforms, so this process\n> > is timeless. In fact, working out what it means, you find back the\n> > standard Coulomb interaction. So you can picture a "virtual photon"\n> > as "one classical coulomb interaction". Nobody associates a billiard\n> > ball to "coulomb interaction" but rather a continuous pulling or\n> > pushing. Nevertheless, this is what is mathematically represented by\n> > one virtual photon in this case.\n>\n>\n> Now, there are curious methodological sins above. Saying "we are working\n> in Fourier space, so the process is timeless" is - with my full respect -\n> an absurdity. If you analyse the spectrum of musical instruments, and you\n> pass to the frequency domain, you will do the same. Will you claim that\n> "music is a timeless process"??\n>\n\nYou are right that I was very sloppy in what I wrote down, I tried to\nconcentrate too much stuff in too little words. Concerning the\ntimelessness, I often have the impression that people think that in a\ntree diagram, at a specific moment, you send out a virtual particle,\nthe trajectory of the emitting particle then suddenly has a kink, and\nafter some travelling time (distance over the speed of the virtual\nparticle) it hits the other one and there\'s a kick in the other\ntrajectory. With "timelessness", I wanted to point out that the whole\nsmooth potential 1/r is described by that tree diagram and that there\nis no specific moment where this interchange is worked out.\n\n\n> It is well known that we have to go to\n> the infra-red limit; the classical force will result from an infinite number\n> of wee photons, with infinite wavelength... So, first of all, one should\n> refrain from imagining a classical, macroscopical interaction as the exchange\n> of virtual particles, unless one knows that one has to descend to a delicate\n> coherent limit.\n\nThis is true for bound states (I don\'t know much of that). But how do\nyou explain that the right potential (1/r) comes out of the single\ntree diagram in scattering ? This means that the essence of the\nCoulomb interaction is already present in this single exchange, no ?\n\ncheers,\nPatrick.\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>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<4084D08B.5070605@info.unicaen.fr>...
> Patrick Van Esch wrote:
>
>
> I have the impression that most people here - and PVE in particular, when
> fighting "against virtual particles" fight against mythology. One CAN
> take those entities seriously without committing any sin against common
> sense. It is not a question of seeing virtual photons, mesons, etc. as
> billard balls. Properly educated people know that REAL particles are
> neither !
I suppose you are right. This must come from an unfortunate
experience I had when I was a PhD student. I still remember lots of
very weird discussions based on the in my interpretation "virtual
billiard ball" paradigm in diffractive deep inelastic scattering. To
me, these explanations of observed effects in the data didn't make any
sense, but gave rise to heated (and to me totally uncomprehensive)
discussions within working groups of experimentalists (young and old).
It really went like "this pomeron kicks that gluon out of the
(dressed up) photon" and then people went calculating the angle as if
we were throwing out billiard balls, and compared it to - in my
opinion - sometimes dubiously preselected data. It might very well be
that those people had a very strong intuition and that it was me who
didn't understand a yota of what they were talking about. But I had
the impression it was total gibberish.
>
> > Moreover, we're working here with Fourier transforms, so this process
> > is timeless. In fact, working out what it means, you find back the
> > standard Coulomb interaction. So you can picture a "virtual photon"
> > as "one classical coulomb interaction". Nobody associates a billiard
> > ball to "coulomb interaction" but rather a continuous pulling or
> > pushing. Nevertheless, this is what is mathematically represented by
> > one virtual photon in this case.
>
>
> Now, there are curious methodological sins above. Saying "we are working
> in Fourier space, so the process is timeless" is - with my full respect -
> an absurdity. If you analyse the spectrum of musical instruments, and you
> pass to the frequency domain, you will do the same. Will you claim that
> "music is a timeless process"??
>
You are right that I was very sloppy in what I wrote down, I tried to
concentrate too much stuff in too little words. Concerning the
timelessness, I often have the impression that people think that in a
tree diagram, at a specific moment, you send out a virtual particle,
the trajectory of the emitting particle then suddenly has a kink, and
after some travelling time (distance over the speed of the virtual
particle) it hits the other one and there's a kick in the other
trajectory. With "timelessness", I wanted to point out that the whole
smooth potential 1/r is described by that tree diagram and that there
is no specific moment where this interchange is worked out.
> It is well known that we have to go to
> the infra-red limit; the classical force will result from an infinite number
> of wee photons, with infinite wavelength... So, first of all, one should
> refrain from imagining a classical, macroscopical interaction as the exchange
> of virtual particles, unless one knows that one has to descend to a delicate
> coherent limit.
This is true for bound states (I don't know much of that). But how do
you explain that the right potential (1/r) comes out of the single
tree diagram in scattering ? This means that the essence of the
Coulomb interaction is already present in this single exchange, no ?
cheers,
Patrick.
Charles Francis
Apr24-04, 09:17 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In message <1d8a7d98.0404210822.533f46db@posting.google.com >, Alejandro\n<arivero@posta.unizar.es> writes\n>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message\n>news:<c61502\\$d24\\$1@lfa222122.richmon d.edu>...\n>\n>> Virtual photons mediating the Coulomb repulsion between electrons\n>> have spacelike momenta and hence would proceed faster than light\n>> if there were any reality to them. But there cannot be; you\'d need\n>> infinitely many of them, and infinitely many virtual electron-positron\n>> pairs (and then superpositions of any numbers of these) to match exactly\n>> a real, dressed object or interaction.\n>\n>I am not sure of iy. If you are meaning that you need to sum the\n>full perturbative series, then you should explain how the divergence\n>problem is avoided.\n\nOne assumes that something happens at short range (larger than the\nLandau Pole) and hence that the series becomes inaccurate for higher\norder terms.\n>\n>Also I don\'t get what a "dressed interaction" is.\n>\nA bare interaction is something like a photon being absorbed by an\nelectron. But the electron may emit another photon first and reabsorb it\nafter emitting the photon. The photon may become a matter-antimatter\npair and go back to being a photon before it is absorbed. If you include\nall such interactions, that is a dressed interaction.\n\n--\nCharles Francis\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In message <1d8a7d98.0404210822.533f46db@posting.google.com>, Alejandro
<arivero@posta.unizar.es> writes
>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message
>news:<c61502$d24$1@lfa222122.richmond.edu>...
>
>> Virtual photons mediating the Coulomb repulsion between electrons
>> have spacelike momenta and hence would proceed faster than light
>> if there were any reality to them. But there cannot be; you'd need
>> infinitely many of them, and infinitely many virtual electron-positron
>> pairs (and then superpositions of any numbers of these) to match exactly
>> a real, dressed object or interaction.
>
>I am not sure of iy. If you are meaning that you need to sum the
>full perturbative series, then you should explain how the divergence
>problem is avoided.
One assumes that something happens at short range (larger than the
Landau Pole) and hence that the series becomes inaccurate for higher
order terms.
>
>Also I don't get what a "dressed interaction" is.
>
A bare interaction is something like a photon being absorbed by an
electron. But the electron may emit another photon first and reabsorb it
after emitting the photon. The photon may become a matter-antimatter
pair and go back to being a photon before it is absorbed. If you include
all such interactions, that is a dressed interaction.
--
Charles Francis
arivero
Apr27-04, 02:38 PM
>. In fact, working out what it means, you find back the
> standard Coulomb interaction. So you can picture a "virtual photon"
> as "one classical coulomb interaction".[/color]
This is not quite correct. The Coulomb interaction is a ladder
approximation, and hence corresponds to summing all diagrams with
0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.
Single exchanged photons are completely meaningless.
Arnold Neumaier
I am getting something wrong somewere. Three points:
-ladder sum is only a formal sum, and it should diverge for any
value of the coupling constant, should it?
-coulomb potential is recovered from Fourier transforming the first order
Born approximation, is it?
-The photon propagator is got directly from the EM interaction. Why should
us to need to sum a full series of Ferynman diagrams in order to get back
the EM interaction?
Danny Ross Lunsford
Apr27-04, 02:46 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> To draw an analogy in nonrelativistic QM\n> think of nuclei as bare atoms, electrons as virtual particles,\n> atoms as dressed nuclei and the residual interaction between atoms,\n> computed in the Born-Oppenheimer approximation, as the dressed\n> interaction. Thus, for Argon atoms, the dressed interaction is\n> something close to a Lennard-Jones potential, while the bare\n> interaction is Coulomb repulsion. This is the situation physicists\n> had in mind when they invented the notions of bare and dressed\n> particles.\n\nVery nice analogy, I had not seen this before.\n\n-danny\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:
> To draw an analogy in nonrelativistic QM
> think of nuclei as bare atoms, electrons as virtual particles,
> atoms as dressed nuclei and the residual interaction between atoms,
> computed in the Born-Oppenheimer approximation, as the dressed
> interaction. Thus, for Argon atoms, the dressed interaction is
> something close to a Lennard-Jones potential, while the bare
> interaction is Coulomb repulsion. This is the situation physicists
> had in mind when they invented the notions of bare and dressed
> particles.
Very nice analogy, I had not seen this before.
-danny
Arnold Neumaier
Apr27-04, 02:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Patrick Van Esch wrote:\n\n> But how do\n> you explain that the right potential (1/r) comes out of the single\n> tree diagram in scattering ? This means that the essence of the\n> Coulomb interaction is already present in this single exchange, no ?\n\nThe Coulomb interaction is simply the Fourier transform of the\nphoton propagator 1/q^2, followed by a nonrelativistic approximation.\nIt has nothing at all to do with virtual particle exchanges ---\nexcept if you do perturbation theory. But then there is no surprise\nthat it must occur already at tree level.\n\n\nArnold Neumaier\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Patrick Van Esch wrote:
> But how do
> you explain that the right potential (1/r) comes out of the single
> tree diagram in scattering ? This means that the essence of the
> Coulomb interaction is already present in this single exchange, no ?
The Coulomb interaction is simply the Fourier transform of the
photon propagator 1/q^2, followed by a nonrelativistic approximation.
It has nothing at all to do with virtual particle exchanges ---
except if you do perturbation theory. But then there is no surprise
that it must occur already at tree level.
Arnold Neumaier
Arnold Neumaier
Apr28-04, 04:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nDanny Ross Lunsford wrote:\n> Arnold Neumaier wrote:\n>\n>> To draw an analogy in nonrelativistic QM\n>> think of nuclei as bare atoms, electrons as virtual particles,\n>> atoms as dressed nuclei and the residual interaction between atoms,\n>> computed in the Born-Oppenheimer approximation, as the dressed\n>> interaction. Thus, for Argon atoms, the dressed interaction is\n>> something close to a Lennard-Jones potential, while the bare\n>> interaction is Coulomb repulsion. This is the situation physicists\n>> had in mind when they invented the notions of bare and dressed\n>> particles.\n>\n>\n> Very nice analogy, I had not seen this before.\n\nOf course, it is only an analogy, and should not be taken very seriously.\nIt just explains the intuition about the terminology used.\n\nThe electrons in QM are real, physical electrons that can be isolated.\nThe reason is that they are good eigenstates of the Hamiltonian.\n\nOn the other hand, virtual particles don\'t have this nice attribute since\nthe relativistic Hamiltonian from field theory contains creation and\nannihilation operators which mess things up. The eigenstates of the\nrelativistic Hamiltonian are complicated multibody states consisting\nof a superposition of states with any number of particles and\nantiparticles, just subject to the restriction that the total quantum\nnumbers come out right. These are the dressed particles.\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>Danny Ross Lunsford wrote:
> Arnold Neumaier wrote:
>
>> To draw an analogy in nonrelativistic QM
>> think of nuclei as bare atoms, electrons as virtual particles,
>> atoms as dressed nuclei and the residual interaction between atoms,
>> computed in the Born-Oppenheimer approximation, as the dressed
>> interaction. Thus, for Argon atoms, the dressed interaction is
>> something close to a Lennard-Jones potential, while the bare
>> interaction is Coulomb repulsion. This is the situation physicists
>> had in mind when they invented the notions of bare and dressed
>> particles.
>
>
> Very nice analogy, I had not seen this before.
Of course, it is only an analogy, and should not be taken very seriously.
It just explains the intuition about the terminology used.
The electrons in QM are real, physical electrons that can be isolated.
The reason is that they are good eigenstates of the Hamiltonian.
On the other hand, virtual particles don't have this nice attribute since
the relativistic Hamiltonian from field theory contains creation and
annihilation operators which mess things up. The eigenstates of the
relativistic Hamiltonian are complicated multibody states consisting
of a superposition of states with any number of particles and
antiparticles, just subject to the restriction that the total quantum
numbers come out right. These are the dressed particles.
Arnold Neumaier
Curious
Apr28-04, 02:30 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>Charles Francis <charles@clef.demon.co.uk> wrote in message news:<FhINWQEoDtiAFwYO@clef.demon.co.uk>...\n\n> The photon may become a matter-antimatter\n> pair and go back to being a photon before it is absorbed.\n\n"Matter-antimatter" is due to one photon\'s phase being the reverse of\nthe other other photon, right?\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>Charles Francis <charles@clef.demon.co.uk> wrote in message news:<FhINWQEoDtiAFwYO@clef.demon.co.uk>...
> The photon may become a matter-antimatter
> pair and go back to being a photon before it is absorbed.
"Matter-antimatter" is due to one photon's phase being the reverse of
the other other photon, right?
Arnold Neumaier
Apr28-04, 03:32 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>arivero wrote:\n> Arnold Neumaier Wrote:\n>\n>>>. In fact, working out what it means, you find back the\n>>>standard Coulomb interaction. So you can picture a "virtual\n>>photon"\n>>\n>>>as "one classical coulomb interaction".[/color]\n>>\n>>This is not quite correct. The Coulomb interaction is a ladder\n>>approximation, and hence corresponds to summing all diagrams with\n>>0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.\n>>\n>>Single exchanged photons are completely meaningless.\n>>\n>>Arnold Neumaier\n>\n>\n> I am getting something wrong somewere. Three points:\n>\n> -ladder sum is only a formal sum, and it should diverge for any\n> value of the coupling constant, should it?\n\nAll the formal stuff diverges. Only after enough resummation one\ngets (after additional approximation) integral equations that\ncan be reinterpreted as Lippmann-Schwinger equations for Coulomb\ninteractions.\n\n\n> -coulomb potential is recovered from Fourier transforming the first\n> order\n> Born approximation, is it?\n\nOne gets a 1/r term. Then one identifies it with the Coulomb potential\non the basis that the Born approximation to the latter generates\nthe same contribution to the scattering.\n\n>\n> -The photon propagator is got directly from the EM interaction. Why\n> should\n> us to need to sum a full series of Ferynman diagrams in order to get\n> back\n> the EM interaction?\n\nBecause there is no interaction between electrons in QED.\nTo prove that there is interaction in the effective, photon-free\napproximation, one must derive a dynamical equation, and not\nonly show the coincidence of the Born approximation.\n\nThe photon propagator is not identical with the EM interaction;\nso you don\'t get the latter \'back\'.\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>arivero wrote:
> Arnold Neumaier Wrote:
>
>>>. In fact, working out what it means, you find back the
>>>standard Coulomb interaction. So you can picture a "virtual
>>photon"
>>
>>>as "one classical coulomb interaction".
>>
>>This is not quite correct. The Coulomb interaction is a ladder
>>approximation, and hence corresponds to summing all diagrams with
>>0,1,2,3,...,n,... exchanged photons arranged in form of a ladder.
>>
>>Single exchanged photons are completely meaningless.
>>
>>Arnold Neumaier
>
>
> I am getting something wrong somewere. Three points:
>
> -ladder sum is only a formal sum, and it should diverge for any
> value of the coupling constant, should it?[/color]
All the formal stuff diverges. Only after enough resummation one
gets (after additional approximation) integral equations that
can be reinterpreted as Lippmann-Schwinger equations for Coulomb
interactions.
> -coulomb potential is recovered from Fourier transforming the first
> order
> Born approximation, is it?
One gets a 1/r term. Then one identifies it with the Coulomb potential
on the basis that the Born approximation to the latter generates
the same contribution to the scattering.
>
> -The photon propagator is got directly from the EM interaction. Why
> should
> us to need to sum a full series of Ferynman diagrams in order to get
> back
> the EM interaction?
Because there is no interaction between electrons in QED.
To prove that there is interaction in the effective, photon-free
approximation, one must derive a dynamical equation, and not
only show the coincidence of the Born approximation.
The photon propagator is not identical with the EM interaction;
so you don't get the latter 'back'.
Arnold Neumaier
Charles Francis
Apr30-04, 03:01 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In message <34a4f456.0404271506.52bc08cb@posting.google.com >, Curious\n<curious11112001@yahoo.com> writes\n>Charles Francis <charles@clef.demon.co.uk> wrote in message\n>news:<FhINWQEoDtiAFwYO@clef.demon.co.uk> ...\n>\n>> The photon may become a matter-antimatter\n>> pair and go back to being a photon before it is absorbed.\n>\n>"Matter-antimatter" is due to one photon\'s phase being the reverse of\n>the other other photon, right?\n>\nNo. The photon ceases to be a photon and becomes, e.g. an electron and a\npositron.\n\n\nRegards\n\n--\nCharles Francis\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In message <34a4f456.0404271506.52bc08cb@posting.google.com>, Curious
<curious11112001@yahoo.com> writes
>Charles Francis <charles@clef.demon.co.uk> wrote in message
>news:<FhINWQEoDtiAFwYO@clef.demon.co.uk>...
>
>> The photon may become a matter-antimatter
>> pair and go back to being a photon before it is absorbed.
>
>"Matter-antimatter" is due to one photon's phase being the reverse of
>the other other photon, right?
>
No. The photon ceases to be a photon and becomes, e.g. an electron and a
positron.
Regards
--
Charles Francis
Jerzy Karczmarczuk
Apr30-04, 05:57 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\nCharles Francis wrote:\n> Curious writes\n>\n>>Charles Francis <charles@clef.demon.co.uk> wrote in message\n>>\n>>>The photon may become a matter-antimatter\n>>>pair and go back to being a photon before it is absorbed.\n>>\n>>"Matter-antimatter" is due to one photon\'s phase being the reverse of\n>>the other other photon, right?\n>>\n>\n> No. The photon ceases to be a photon and becomes, e.g. an electron and a\n> positron.\n\nMoreover, when you speak about ONE PHOTON, then *don\'t speak* about its phase.\nIt is a somehow complementary view, no?\n\n\nJerzy Karczmarczuk\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>Charles Francis wrote:
> Curious writes
>
>>Charles Francis <charles@clef.demon.co.uk> wrote in message
>>
>>>The photon may become a matter-antimatter
>>>pair and go back to being a photon before it is absorbed.
>>
>>"Matter-antimatter" is due to one photon's phase being the reverse of
>>the other other photon, right?
>>
>
> No. The photon ceases to be a photon and becomes, e.g. an electron and a
> positron.
Moreover, when you speak about ONE PHOTON, then *don't speak* about its phase.
It is a somehow complementary view, no?
Jerzy Karczmarczuk
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