Feynman's QED and reflection of a photon [Archive]

Hari Seldon

May23-04, 03:14 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>Hi,\n\nI have a question about Feynman\'s description of reflection of light\nof a mirror as he described in his famous QED lectures. Related\nquestions were asked before on this newsgroup, but I was unable to\nfind the answer to my problems.\n\nFeynman describes the following situation. Suppose we have an incoming\nphoton (emitted from a source S) propagating towards a mirror. We also\nhave a photon detector D and we would like to find the amplitude (or\nits square the probability) that we detect the photon at D. See also\nthe figure below.\n\n|\nS | D\n\n\n-------------P-------------------- Mirror\n\nThe vertical lines describe a wall to make sure the photons cannot go\ndirectly from the source to the detector in a straight line without\ngoing via the mirror.\n\nNow feynman explains that to find the amplitude to detect a photon at\nD that was emitted at S, you must sum over all paths that the photon\ncan take from S to D. This corresponds to the path integral\nformulation of qm (as i understand it).\n\nThis is the way Feynman solved the problem. Now I would like to know\nwhat Feynman meant with his answer in terms of qm/qed. What is a more\nexact way to describe what happens? What parts of the following two\ndifferent descriptions is better and how should one modify them to get\nthe right description? I only give two possible description for the\nfirst half of the exeriment since in my opinion the S -> Mirror part\nis symmetric to the Mirror -> D part.\n\n1) Suppose we assume a photon being emitted at S and absorbed\nsomewhere at a point P at the mirror, then my quess would be that we\nneed to describe this by a QED interaction, where the propagation of\nthe photon to the mirror is in fact described by an internal photon\npropagator (describing a virtual photon) as given by QED. If this is\nso, where does the sum over all paths come in?\nAnd another confusing thing for me is, according to the Feynman rules\nyou sum over all of spacetime for this interaction point, but in fact\nisnt the electron that the photon is interacting with at a specific\nlocalised point in spacetime? So why sum over all of spacetime for the\ninteraction point?\n\n2) Or should we neglect the source and assume an incoming photon which\nat some time t is at a definite position, say X (meaning that the\nmomentum is entirely unknown according the heisenberg). Then calculate\nthe amplitude to go from X to P (by summing over all paths) and do\nthis for all points P of the mirror, then at the point P use a QED\ninteraction feynman diagram? If this is the right way to look at it, I\nam a bit confused cause it seems that you assume the photon is\nregular particle like the electron, which you can describe by quantum\nmechanics, but it is actually entirely a field theory concept. To see\nmore clearly what goes wrong is when we use this picture to describe\nthe incoming photon with a localised momentum and position, which we\nwould quantum mechanically describe by a wave packet. However, I have\nread that you cannot describe a single photon by a wavepacket.\n\nWell as you can see, I have been unable to understand what exactly is\ngoing on in this experiment. Was Feynman giving a correct description\nor was he approximating? I hope that someone can help me to get things\nright.\n\nThanks in advance,\n\nHari Seldon\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>Hi,

I have a question about Feynman's description of reflection of light
of a mirror as he described in his famous QED lectures. Related
questions were asked before on this newsgroup, but I was unable to
find the answer to my problems.

Feynman describes the following situation. Suppose we have an incoming
photon (emitted from a source S) propagating towards a mirror. We also
have a photon detector D and we would like to find the amplitude (or
its square the probability) that we detect the photon at D. See also
the figure below.

|
S | D

-------------P-------------------- Mirror

The vertical lines describe a wall to make sure the photons cannot go
directly from the source to the detector in a straight line without
going via the mirror.

Now feynman explains that to find the amplitude to detect a photon at
D that was emitted at S, you must sum over all paths that the photon
can take from S to D. This corresponds to the path integral
formulation of qm (as i understand it).

This is the way Feynman solved the problem. Now I would like to know
what Feynman meant with his answer in terms of qm/qed. What is a more
exact way to describe what happens? What parts of the following two
different descriptions is better and how should one modify them to get
the right description? I only give two possible description for the
first half of the exeriment since in my opinion the S -> Mirror part
is symmetric to the Mirror -> D part.

1) Suppose we assume a photon being emitted at S and absorbed
somewhere at a point P at the mirror, then my quess would be that we
need to describe this by a QED interaction, where the propagation of
the photon to the mirror is in fact described by an internal photon
propagator (describing a virtual photon) as given by QED. If this is
so, where does the sum over all paths come in?
And another confusing thing for me is, according to the Feynman rules
you sum over all of spacetime for this interaction point, but in fact
isnt the electron that the photon is interacting with at a specific
localised point in spacetime? So why sum over all of spacetime for the
interaction point?

2) Or should we neglect the source and assume an incoming photon which
at some time t is at a definite position, say X (meaning that the
momentum is entirely unknown according the heisenberg). Then calculate
the amplitude to go from X to P (by summing over all paths) and do
this for all points P of the mirror, then at the point P use a QED
interaction feynman diagram? If this is the right way to look at it, I
am a bit confused cause it seems that you assume the photon is
regular particle like the electron, which you can describe by quantum
mechanics, but it is actually entirely a field theory concept. To see
more clearly what goes wrong is when we use this picture to describe
the incoming photon with a localised momentum and position, which we
would quantum mechanically describe by a wave packet. However, I have
read that you cannot describe a single photon by a wavepacket.

Well as you can see, I have been unable to understand what exactly is
going on in this experiment. Was Feynman giving a correct description
or was he approximating? I hope that someone can help me to get things
right.

Thanks in advance,

Hari Seldon

Charles Francis

May24-04, 04:31 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>\nIn message <f507ac4c.0405220615.7c4a5973@posting.google.com >, Hari\nSeldon <waterballon@hotmail.com> writes\n\n>Feynman describes the following situation. Suppose we have an incoming\n>photon (emitted from a source S) propagating towards a mirror. We also\n>have a photon detector D and we would like to find the amplitude (or\n>its square the probability) that we detect the photon at D. See also\n>the figure below.\n>\n> |\n> S | D\n>\n>\n> -------------P-------------------- Mirror\n>\n>The vertical lines describe a wall to make sure the photons cannot go\n>directly from the source to the detector in a straight line without\n>going via the mirror.\n>\n>Now feynman explains that to find the amplitude to detect a photon at\n>D that was emitted at S, you must sum over all paths that the photon\n>can take from S to D. This corresponds to the path integral\n>formulation of qm (as i understand it).\n>\n>This is the way Feynman solved the problem. Now I would like to know\n>what Feynman meant with his answer in terms of qm/qed. What is a more\n>exact way to describe what happens? What parts of the following two\n>different descriptions is better and how should one modify them to get\n>the right description? I only give two possible description for the\n>first half of the exeriment since in my opinion the S -> Mirror part\n>is symmetric to the Mirror -> D part.\n>\n>1) Suppose we assume a photon being emitted at S and absorbed\n>somewhere at a point P at the mirror, then my quess would be that we\n>need to describe this by a QED interaction, where the propagation of\n>the photon to the mirror is in fact described by an internal photon\n>propagator (describing a virtual photon) as given by QED. If this is\n>so, where does the sum over all paths come in?\n>And another confusing thing for me is, according to the Feynman rules\n>you sum over all of spacetime for this interaction point, but in fact\n>isnt the electron that the photon is interacting with at a specific\n>localised point in spacetime?\n\nNo. The electron can be anywhere in the mirror, and we have no way of\nlocalising it, or saying which electron it was. The sum of paths is\neffectively the sum of possible positions for the electron.\n\n>2) Or should we neglect the source and assume an incoming photon which\n>at some time t is at a definite position, say X (meaning that the\n>momentum is entirely unknown according the heisenberg). Then calculate\n>the amplitude to go from X to P (by summing over all paths) and do\n>this for all points P of the mirror, then at the point P use a QED\n>interaction feynman diagram? If this is the right way to look at it, I\n>am a bit confused cause it seems that you assume the photon is\n>regular particle like the electron, which you can describe by quantum\n>mechanics, but it is actually entirely a field theory concept.\n\nFeynman seems to have preferred the idea that a photon is a particle,\nnot a field, as do I.\n\n--\nCharles Francis\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 <f507ac4c.0405220615.7c4a5973@posting.google.com>, Hari
Seldon <waterballon@hotmail.com> writes

>Feynman describes the following situation. Suppose we have an incoming
>photon (emitted from a source S) propagating towards a mirror. We also
>have a photon detector D and we would like to find the amplitude (or
>its square the probability) that we detect the photon at D. See also
>the figure below.
>
> |
> S | D
>
>
> -------------P-------------------- Mirror
>
>The vertical lines describe a wall to make sure the photons cannot go
>directly from the source to the detector in a straight line without
>going via the mirror.
>
>Now feynman explains that to find the amplitude to detect a photon at
>D that was emitted at S, you must sum over all paths that the photon
>can take from S to D. This corresponds to the path integral
>formulation of qm (as i understand it).
>
>This is the way Feynman solved the problem. Now I would like to know
>what Feynman meant with his answer in terms of qm/qed. What is a more
>exact way to describe what happens? What parts of the following two
>different descriptions is better and how should one modify them to get
>the right description? I only give two possible description for the
>first half of the exeriment since in my opinion the S -> Mirror part
>is symmetric to the Mirror -> D part.
>
>1) Suppose we assume a photon being emitted at S and absorbed
>somewhere at a point P at the mirror, then my quess would be that we
>need to describe this by a QED interaction, where the propagation of
>the photon to the mirror is in fact described by an internal photon
>propagator (describing a virtual photon) as given by QED. If this is
>so, where does the sum over all paths come in?
>And another confusing thing for me is, according to the Feynman rules
>you sum over all of spacetime for this interaction point, but in fact
>isnt the electron that the photon is interacting with at a specific
>localised point in spacetime?

No. The electron can be anywhere in the mirror, and we have no way of
localising it, or saying which electron it was. The sum of paths is
effectively the sum of possible positions for the electron.

>2) Or should we neglect the source and assume an incoming photon which
>at some time t is at a definite position, say X (meaning that the
>momentum is entirely unknown according the heisenberg). Then calculate
>the amplitude to go from X to P (by summing over all paths) and do
>this for all points P of the mirror, then at the point P use a QED
>interaction feynman diagram? If this is the right way to look at it, I
>am a bit confused cause it seems that you assume the photon is
>regular particle like the electron, which you can describe by quantum
>mechanics, but it is actually entirely a field theory concept.

Feynman seems to have preferred the idea that a photon is a particle,
not a field, as do I.

--
Charles Francis

Bob The Tough

Mar3-05, 04:25 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>Hmm - good post. I have just started reading Feynman\'s QED, and would\nlike some clarification on this experiment (Chapter 2, pages 42-48 , in\nmy book anyway).\n\nThe following is my understanding as of this moment:\n\nIt seems to me that somehow the photon knows all the possible paths\nthat it can take. It does fundamentally interact at a specific place\non the mirror, but this location can not be predicted before hand.\nWhen feynman sums all the little arrows it seems to me that he is\ncalculating how the probability waves interact with each other.\nSuppose that instead of breaking the mirror down into 10 pieces, we\nbreak it just into two halves. Then the photon can either bounce of the\nfirst half, or the second. There is a probability wave corresponding to\neach path, oscillating at some frequency (guess: the same as the\nfrequency of light?).\nWhen the two probability waves are in phase at the location of the\ndetector (the arrows point the same way) the probability of finding the\nlight at the detector is increased. In contrast, when two probability\nwaves are out of phase by pi radians (the arrows point in opposite\ndirections) the probability of detecting light is zero.\n\nIn the situation where we consider the mirror split into many small\nparts, we need to calculate the interaction of many probability waves.\nAs Feynman explains, the greatest contribution to probability of\ndetection is due to the parts of the mirror near the middle point.\nHowever, as he explains when he goes on to talk about diffraction\ngratings, one can NOT ignore the contributions from the edge parts of\nthe mirror.\n\nHmm - hope this is sort of correct, but would be nice if someone who\nreally understood this stuff posted and cleared this issue up.\n\nLater,\nBob\n\n------------------------------------------------------------------------\nThis post submitted through the LaTeX-enabled physicsforums.com\nTo view this post with LaTeX images:\nhttp://www.physicsforums.com/showthread.php?t=27141#post469895\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>Hmm - good post. I have just started reading Feynman's QED, and would
like some clarification on this experiment (Chapter 2, pages 42-48 , in
my book anyway).

The following is my understanding as of this moment:

It seems to me that somehow the photon knows all the possible paths
that it can take. It does fundamentally interact at a specific place
on the mirror, but this location can not be predicted before hand.
When feynman sums all the little arrows it seems to me that he is
calculating how the probability waves interact with each other.
Suppose that instead of breaking the mirror down into 10 pieces, we
break it just into two halves. Then the photon can either bounce of the
first half, or the second. There is a probability wave corresponding to
each path, oscillating at some frequency (guess: the same as the
frequency of light?).
When the two probability waves are in phase at the location of the
detector (the arrows point the same way) the probability of finding the
light at the detector is increased. In contrast, when two probability
waves are out of phase by \pi radians (the arrows point in opposite
directions) the probability of detecting light is zero.

In the situation where we consider the mirror split into many small
parts, we need to calculate the interaction of many probability waves.
As Feynman explains, the greatest contribution to probability of
detection is due to the parts of the mirror near the middle point.
However, as he explains when he goes on to talk about diffraction
gratings, one can NOT ignore the contributions from the edge parts of
the mirror.

Hmm - hope this is sort of correct, but would be nice if someone who
really understood this stuff posted and cleared this issue up.

Later,
Bob

------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=27141#post469895