Virtual electron-positron pairs question? [Archive]

Vencislav

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>Hello,\n\nif virtual photons are transformed into virtual electron-positron pairs,\nthen what is the "density" of such process.\n\nIn other words, how can I found how many such electron-positron pairs\nare being created every second in 1 cubic meter, for example?\n\nThank you!\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hello,

if virtual photons are transformed into virtual electron-positron pairs,
then what is the "density" of such process.

In other words, how can I found how many such electron-positron pairs
are being created every second in 1 cubic meter, for example?

Thank you!

FrediFizzx

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>\n\n"Vencislav" <vencib@yahoo.com> wrote in message\nnews:a259f310.0405221654.7b9a947c@posting .google.com...\n| Hello,\n|\n| if virtual photons are transformed into virtual electron-positron pairs,\n| then what is the "density" of such process.\n|\n| In other words, how can I found how many such electron-positron pairs\n| are being created every second in 1 cubic meter, for example?\n\nWhat is the conditions? Do you mean in the vacuum far away from any matter?\n\nFrediFizzx\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>"Vencislav" <vencib@yahoo.com> wrote in message
news:a259f310.0405221654.7b9a947c@posting.google.c om...
| Hello,
|
| if virtual photons are transformed into virtual electron-positron pairs,
| then what is the "density" of such process.
|
| In other words, how can I found how many such electron-positron pairs
| are being created every second in 1 cubic meter, for example?

What is the conditions? Do you mean in the vacuum far away from any matter?

FrediFizzx

Vencislav

May24-04, 11:43 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n"FrediFizzx" <fredifizzx@hotmail.com> wrote in message news:<2hc6ifFb88rvU1@uni-berlin.de>...\n> "Vencislav" <vencib@yahoo.com> wrote in message\n> news:a259f310.0405221654.7b9a947c@posting.google.c om...\n> | Hello,\n> |\n> | if virtual photons are transformed into virtual electron-positron pairs,\n> | then what is the "density" of such process.\n> |\n> | In other words, how can I found how many such electron-positron pairs\n> | are being created every second in 1 cubic meter, for example?\n>\n> What is the conditions? Do you mean in the vacuum far away from any matter?\n>\n> FrediFizzx\n\n\nYes, in vacuum and in air... air on ground level of Earth.\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>"FrediFizzx" <fredifizzx@hotmail.com> wrote in message news:<2hc6ifFb88rvU1@uni-berlin.de>...
> "Vencislav" <vencib@yahoo.com> wrote in message
> news:a259f310.0405221654.7b9a947c@posting.google.c om...
> | Hello,
> |
> | if virtual photons are transformed into virtual electron-positron pairs,
> | then what is the "density" of such process.
> |
> | In other words, how can I found how many such electron-positron pairs
> | are being created every second in 1 cubic meter, for example?
>
> What is the conditions? Do you mean in the vacuum far away from any matter?
>
> FrediFizzx

Yes, in vacuum and in air... air on ground level of Earth.

Mike Crowe

May25-04, 01:29 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>"Vencislav" <vencib@yahoo.com> wrote in message\nnews:a259f310.0405221654.7b9a947c@posting .google.com...\n> Hello,\n>\n> if virtual photons are transformed into virtual electron-positron pairs,\n> then what is the "density" of such process.\n>\n> In other words, how can I found how many such electron-positron pairs\n> are being created every second in 1 cubic meter, for example?\n>\n> Thank you!\n>\n\nIts not an easy task, particularly if you are talking about second and third\norders, such as virtual photons creating virtual pairs.\n\nIt is a little simpler to work out the density of first order virtual e+e-\npairs in a cube of radiation at thermal equilibrium though, but still\ntaxing.\n\nFirst take a single photon and work out for how much time it exists as\ne+e-. Do this by knowing its energy, and hence its momentum. Then\ncalculate how far off mass shell the electron positron pair would be.\nThen work out the partial cross section for the process gamma --> e+e-\n--> gamma by using the Breit-Vigner equation. When you have this as a\nfunction of the photon energy then integrate over the black body energy\ndistribution for you cube in thermal equilibrium and you will get the\nanswer you require.\n\nFrom real photons to e+e- pairs, the next order of creation is fourth\norder i think (gamma bridging between the e+e-, which in turn produces\ne+e-, then there are also gammas that leave the electron and come back\nto it pair producing on the way, we now have 4 virtuals (treating e+e-\nas 1) so 4th order) hence this is surpressed by 1/alpha^3 or about\n3.9x10^-7, so makes little difference to your answer. But were you to\nwant to work it out then you would have to write out all the fourth\norder feynman diagrams (i think there are three) and find the partial\ncross section for each of them, then add these three together and add\nthem on to the partial cross section worked out above, then this will\ngive you them to 4th order accuracy.\n\nRepeat ad absurdum.\n\nMike Crowe\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>"Vencislav" <vencib@yahoo.com> wrote in message
news:a259f310.0405221654.7b9a947c@posting.google.c om...
> Hello,
>
> if virtual photons are transformed into virtual electron-positron pairs,
> then what is the "density" of such process.
>
> In other words, how can I found how many such electron-positron pairs
> are being created every second in 1 cubic meter, for example?
>
> Thank you!
>

Its not an easy task, particularly if you are talking about second and third
orders, such as virtual photons creating virtual pairs.

It is a little simpler to work out the density of first order virtual e+e-
pairs in a cube of radiation at thermal equilibrium though, but still
taxing.

First take a single photon and work out for how much time it exists as
e+e-. Do this by knowing its energy, and hence its momentum. Then
calculate how far off mass shell the electron positron pair would be.
Then work out the partial cross section for the process \gamma --> e+e-
--> \gamma by using the Breit-Vigner equation. When you have this as a
function of the photon energy then integrate over the black body energy
distribution for you cube in thermal equilibrium and you will get the
answer you require.

From real photons to e+e- pairs, the next order of creation is fourth
order i think (\gamma bridging between the e+e-, which in turn produces
e+e-, then there are also gammas that leave the electron and come back
to it pair producing on the way, we now have 4 virtuals (treating e+e-
as 1) so 4th order) hence this is surpressed by 1/\alpha^3 or about
3.9x10^-7, so makes little difference to your answer. But were you to
want to work it out then you would have to write out all the fourth
order feynman diagrams (i think there are three) and find the partial
cross section for each of them, then add these three together and add
them on to the partial cross section worked out above, then this will
give you them to 4th order accuracy.

Repeat ad absurdum.

Mike Crowe

John Baez

May25-04, 01:33 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>In article <a259f310.0405240839.73f3bc38@posting.google.com>, \nVencislav <vencib@yahoo.com> wrote:\n\n| In other words, how can I found how many such electron-positron pairs\n| are being created every second in 1 cubic meter, for example?\n\nDifferent ways of "looking" for virtual particles will give you\ncompletely different answers to this question. That\'s why they\'re\ncalled "virtual".\n\nWhen you learn more about virtual particles, your desire to ask\nthis question will go away.\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 <a259f310.0405240839.73f3bc38@posting.google.com>,
Vencislav <vencib@yahoo.com> wrote:

| In other words, how can I found how many such electron-positron pairs
| are being created every second in 1 cubic meter, for example?

Different ways of "looking" for virtual particles will give you
completely different answers to this question. That's why they're
called "virtual".

When you learn more about virtual particles, your desire to ask
this question will go away.

Martin Lohmann

May29-04, 11:52 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>> Its not an easy task, particularly if you are talking about second and third\n> orders, such as virtual photons creating virtual pairs.\n>\n> It is a little simpler to work out the density of first order virtual e+e-\n> pairs in a cube of radiation at thermal equilibrium though, but still\n> taxing.\n>\n> First take a single photon and work out for how much time it exists as\n> e+e-. Do this by knowing its energy, and hence its momentum. Then\n> calculate how far off mass shell the electron positron pair would be.\n> Then work out the partial cross section for the process gamma --> e+e-\n> --> gamma by using the Breit-Vigner equation. When you have this as a\n> function of the photon energy then integrate over the black body energy\n> distribution for you cube in thermal equilibrium and you will get the\n> answer you require.\n>\n> From real photons to e+e- pairs, the next order of creation is fourth\n> order i think (gamma bridging between the e+e-, which in turn produces\n> e+e-, then there are also gammas that leave the electron and come back\n> to it pair producing on the way, we now have 4 virtuals (treating e+e-\n> as 1) so 4th order) hence this is surpressed by 1/alpha^3 or about\n> 3.9x10^-7, so makes little difference to your answer. But were you to\n> want to work it out then you would have to write out all the fourth\n> order feynman diagrams (i think there are three) and find the partial\n> cross section for each of them, then add these three together and add\n> them on to the partial cross section worked out above, then this will\n> give you them to 4th order accuracy.\n>\n> Repeat ad absurdum.\n>\n> Mike Crowe\n\nWhat you would really like to have is some nonpertubative treatment\nwhere you dont have to rely on such pertubative expansions and order\naccuracy. But although the exact formulas for a nonpertubative\ncalculations like this are perfectly known (such as the reduction\nformulas), there is really no way to deal with them without\npertubation theory. SO, in some sense, this question is rather\ninteresting for mathematicians who would like to find a method for a\ndirect calculation of such densities without any approximation by\npertubation theory.\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>> Its not an easy task, particularly if you are talking about second and third
> orders, such as virtual photons creating virtual pairs.
>
> It is a little simpler to work out the density of first order virtual e+e-
> pairs in a cube of radiation at thermal equilibrium though, but still
> taxing.
>
> First take a single photon and work out for how much time it exists as
> e+e-. Do this by knowing its energy, and hence its momentum. Then
> calculate how far off mass shell the electron positron pair would be.
> Then work out the partial cross section for the process \gamma --> e+e-
> --> \gamma by using the Breit-Vigner equation. When you have this as a
> function of the photon energy then integrate over the black body energy
> distribution for you cube in thermal equilibrium and you will get the
> answer you require.
>
> From real photons to e+e- pairs, the next order of creation is fourth
> order i think (\gamma bridging between the e+e-, which in turn produces
> e+e-, then there are also gammas that leave the electron and come back
> to it pair producing on the way, we now have 4 virtuals (treating e+e-
> as 1) so 4th order) hence this is surpressed by 1/\alpha^3 or about
> 3.9x10^-7, so makes little difference to your answer. But were you to
> want to work it out then you would have to write out all the fourth
> order feynman diagrams (i think there are three) and find the partial
> cross section for each of them, then add these three together and add
> them on to the partial cross section worked out above, then this will
> give you them to 4th order accuracy.
>
> Repeat ad absurdum.
>
> Mike Crowe

What you would really like to have is some nonpertubative treatment
where you dont have to rely on such pertubative expansions and order
accuracy. But although the exact formulas for a nonpertubative
calculations like this are perfectly known (such as the reduction
formulas), there is really no way to deal with them without
pertubation theory. SO, in some sense, this question is rather
interesting for mathematicians who would like to find a method for a
direct calculation of such densities without any approximation by
pertubation theory.