pair annihilation [Archive]

alistair

Nov3-04, 10:04 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>When a positron and electron become close together a massless photon\nforms. Why doesn\'t a massless particle form when particles of the same\nelectric charge move together? And why doesn\'t a massless particle form\nwhen particles of different rest masses interact? Is it possible that\nparticles of the same electric charge form a massless photon which\nbecomes the original particles again in a very short space of time? And\nin a black hole,where quarks are very close together and gravity strong,\ncould some up and down quarks, form a photon that does not change back\ninto quarks because gravity will not allow them to separate in space?\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>When a positron and electron become close together a massless photon
forms. Why doesn't a massless particle form when particles of the same
electric charge move together? And why doesn't a massless particle form
when particles of different rest masses interact? Is it possible that
particles of the same electric charge form a massless photon which
becomes the original particles again in a very short space of time? And
in a black hole,where quarks are very close together and gravity strong,
could some up and down quarks, form a photon that does not change back
into quarks because gravity will not allow them to separate in space?

Hendrik van Hees

Nov4-04, 03:42 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>alistair wrote:\n\n> When a positron and electron become close together a massless photon\n> forms. Why doesn\'t a massless particle form when particles of the same\n> electric charge move together? And why doesn\'t a massless particle\n> form when particles of different rest masses interact? Is it possible\n> that particles of the same electric charge form a massless photon\n> which becomes the original particles again in a very short space of\n> time? And in a black hole,where quarks are very close together and\n> gravity strong, could some up and down quarks, form a photon that does\n> not change back into quarks because gravity will not allow them to\n> separate in space?\n\nWho told you this? The process\n\ne^+ + e^- ->\\gamma\n\nis kinematically impossible, because all particles have to be on shell\nand energy-momentum conservation must hold (for asymptotic states).\n\nDenote with p and q the four momenta of positron and electron in the\ninitial state respectively and with k the four momentum of the photon.\nThen we must have\n\np+q=k, p^2=q^2=m^2, k^2=0\n\nThis means\n\nk^2=0=(p+q)^2=2m^2+2 p q\n\nOn the other hand\n\np=(sqrt(m^2+P^2),\\vec{p}), P=|\\vec{p}|\nq=(sqrt(m^2+Q^2),\\vec{q}), Q=|\\vec{q}|\n\nThus we should have\n\np q=-m^2=sqrt[(m^2+P^2)(m^2+Q^2)]-\\vec{p} \\vec{q}<0 (because m^2>0)\n\nThis is a contradiction, because\n\nsqrt[(m^2+P^2)(m^2+Q^2)]>=P Q>=\\vec{p} \\vec{q} (Cauchy-Schwarz\ninequality).\n\nThus the process is impossible.\n\nOf course, you can have pair annihilation to two photons. This is a\nprocess, crossing symmetric to Compton scattering. You may look at\nPeskin Schroeder or any other reasonable textbook about QED for the\ntree-level calculations!\n\n--\nHendrik van Hees Cyclotron Institute\nPhone: +1 979/845-1411 Texas A&M University\nFax: +1 979/845-1899 Cyclotron Institute, MS-3366\nhttp://theory.gsi.de/~vanhees/ College Station, TX 77843-3366\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>alistair wrote:

> When a positron and electron become close together a massless photon
> forms. Why doesn't a massless particle form when particles of the same
> electric charge move together? And why doesn't a massless particle
> form when particles of different rest masses interact? Is it possible
> that particles of the same electric charge form a massless photon
> which becomes the original particles again in a very short space of
> time? And in a black hole,where quarks are very close together and
> gravity strong, could some up and down quarks, form a photon that does
> not change back into quarks because gravity will not allow them to
> separate in space?

Who told you this? The process

e^+ + e^- ->\gamma

is kinematically impossible, because all particles have to be on shell
and energy-momentum conservation must hold (for asymptotic states).

Denote with p and q the four momenta of positron and electron in the
initial state respectively and with k the four momentum of the photon.
Then we must have

p+q=k, p^2=q^2=m^2, k^2=0

This means

k^2=0=(p+q)^2=2m^2+2 p q

On the other hand

p=(\sqrt(m^2+P^2),\vec{p}), P=|\vec{p}|q=(\sqrt(m^2+Q^2),\vec{q}), Q=|\vec{q}|

Thus we should have

p q=-m^2=\sqrt[(m^2+P^2)(m^2+Q^2)]-\vec{p} \vec{q}<0[/itex] (because m^2>0)

This is a contradiction, because

\sqrt[(m^2+P^2)(m^2+Q^2)]>=P Q>=\vec{p} \vec{q} (Cauchy-Schwarz
inequality).

Thus the process is impossible.

Of course, you can have pair annihilation to two photons. This is a
process, crossing symmetric to Compton scattering. You may look at
Peskin Schroeder or any other reasonable textbook about QED for the
tree-level calculations!

--
Hendrik van Hees Cyclotron Institute
Phone: +1 979/845-1411 Texas A&M University
Fax: +1 979/845-1899 Cyclotron Institute, MS-3366
http://theory.gsi.de/~vanhees/ College Station, [itex]TX 77843-3366

Jack Tremarco

Nov5-04, 06:11 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>Hendrik explained to you why the process you thought was possible\nactually isn\'t. The other processes you ask about (two particles of\nlike charge to photons) are forbidden because this would violate\ncharge conservation. Couldn\'t be more obvious.\n\nAll the best, Jack\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>Hendrik explained to you why the process you thought was possible
actually isn't. The other processes you ask about (two particles of
like charge to photons) are forbidden because this would violate
charge conservation. Couldn't be more obvious.

All the best, Jack

Igor Khavkine

Nov5-04, 08:20 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>\nOn Wed, 03 Nov 2004 16:04:24 +0000, alistair wrote:\n\n> When a positron and electron become close together a massless photon\n> forms. Why doesn\'t a massless particle form when particles of the same\n> electric charge move together?\n\nMasslessness has nothing to do with whether this kind of interaction is\nallowed. You have to check that charge and fermion number are conserved.\nYou might also check for some discrete symmetries like parity, etc.\n\n> And why doesn\'t a massless particle form\n> when particles of different rest masses interact? Is it possible that\n> particles of the same electric charge form a massless photon which becomes\n> the original particles again in a very short space of time?\n\nPhoton has zero charge, two particles of the same non-zero charge cannot\nmake a photon.\n\n> And in a black\n> hole,where quarks are very close together and gravity strong, could some\n> up and down quarks, form a photon that does not change back into quarks\n> because gravity will not allow them to separate in space?\n\nThe premise of your question has an unwarranted assumption about quarks\nand black holes which makes your deductions meaningless. An up and down\nquark cannot make a photon, but they can can form a charged Z boson,\ngranted that one of them is an anti-particle so that fermion number is\nconserved. The Z boson may do as it wishes but it has a high probability\nof decaying into other particles. Whether this is inside a black hole or\nnot does not really apply since local curvature may still be small. If\nspacetime curvature is very large then the Standard Model is not known to\napply.\n\nIgor\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 03 Nov 2004 16:04:24 +0000, alistair wrote:

> When a positron and electron become close together a massless photon
> forms. Why doesn't a massless particle form when particles of the same
> electric charge move together?

Masslessness has nothing to do with whether this kind of interaction is
allowed. You have to check that charge and fermion number are conserved.
You might also check for some discrete symmetries like parity, etc.

> And why doesn't a massless particle form
> when particles of different rest masses interact? Is it possible that
> particles of the same electric charge form a massless photon which becomes
> the original particles again in a very short space of time?

Photon has zero charge, two particles of the same non-zero charge cannot
make a photon.

> And in a black
> hole,where quarks are very close together and gravity strong, could some
> up and down quarks, form a photon that does not change back into quarks
> because gravity will not allow them to separate in space?

The premise of your question has an unwarranted assumption about quarks
and black holes which makes your deductions meaningless. An up and down
quark cannot make a photon, but they can can form a charged Z boson,
granted that one of them is an anti-particle so that fermion number is
conserved. The Z boson may do as it wishes but it has a high probability
of decaying into other particles. Whether this is inside a black hole or
not does not really apply since local curvature may still be small. If
spacetime curvature is very large then the Standard Model is not known to
apply.

Igor

Arnold Neumaier

Nov5-04, 08:20 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\nalistair wrote:\n> When a positron and electron become close together a massless photon\n> forms. Why doesn\'t a massless particle form when particles of the same\n> electric charge move together?\n\nIt would have to be a massless charged particle. No such particles\nwere observed.\n\n> And why doesn\'t a massless particle form\n> when particles of different rest masses interact? Is it possible that\n> particles of the same electric charge form a massless photon which\n> becomes the original particles again in a very short space of time?\n\nNo, since charge is conserved even in virtual reactions.\n\n\nArnold Neumaier\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>alistair wrote:
> When a positron and electron become close together a massless photon
> forms. Why doesn't a massless particle form when particles of the same
> electric charge move together?

It would have to be a massless charged particle. No such particles
were observed.

> And why doesn't a massless particle form
> when particles of different rest masses interact? Is it possible that
> particles of the same electric charge form a massless photon which
> becomes the original particles again in a very short space of time?

No, since charge is conserved even in virtual reactions.

Arnold Neumaier

John T Lowry

Nov5-04, 08:20 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\n"alistair" <alistair@goforit64.fsnet.co.uk> wrote in message\nnews:861c1b21.0410310930.68872f19@posting .google.com...\n> When a positron and electron become close together a massless photon\n> forms. Why doesn\'t a massless particle form when particles of the same\n> electric charge move together? And why doesn\'t a massless particle\n> form\n> when particles of different rest masses interact? Is it possible that\n> particles of the same electric charge form a massless photon which\n> becomes the original particles again in a very short space of time?\n> And\n> in a black hole,where quarks are very close together and gravity\n> strong,\n> could some up and down quarks, form a photon that does not change back\n> into quarks because gravity will not allow them to separate in space?\n\nReasonable questions, but to understand the answers you\'re first going\nto have to learn quite a bit of quantum mechanics. In fact positronium\ndecays into two (or more!) photons. And photons are "particles" in only\na very loose sense of that word. Photons do form when particles of\ndifferent rest mass interact: atoms put out photons when they decay from\nan excited state to a less excited one. Do it! (Learn quantum\nmechanics.) It\'s a great adventure. Even better than flying airplanes.\n\nJohn Lowry\nFlight Physics\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"alistair" <alistair@goforit64.fsnet.co.uk> wrote in message
news:861c1b21.0410310930.68872f19@posting.google.c om...
> When a positron and electron become close together a massless photon
> forms. Why doesn't a massless particle form when particles of the same
> electric charge move together? And why doesn't a massless particle
> form
> when particles of different rest masses interact? Is it possible that
> particles of the same electric charge form a massless photon which
> becomes the original particles again in a very short space of time?
> And
> in a black hole,where quarks are very close together and gravity
> strong,
> could some up and down quarks, form a photon that does not change back
> into quarks because gravity will not allow them to separate in space?

Reasonable questions, but to understand the answers you're first going
to have to learn quite a bit of quantum mechanics. In fact positronium
decays into two (or more!) photons. And photons are "particles" in only
a very loose sense of that word. Photons do form when particles of
different rest mass interact: atoms put out photons when they decay from
an excited state to a less excited one. Do it! (Learn quantum
mechanics.) It's a great adventure. Even better than flying airplanes.

John Lowry
Flight Physics