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andrew.stewart@anu.edu.au
Sep24-04, 08:14 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>A physical electron has a radial electric field E due to is electric\ncharge e and a dipole magnetic field B due to the magnetic moment\n(e*hbar/2*m*c) associated with its spin. The vector cross product of\nthe two fields, the Poynting vector S = E x B/(4*pi*c), circulates\nazimuthally around the spin axis. The density j of angular momentum\nof the electromagnetic field is j = r x S. When this is integrated\nover all space to give the angular momentum of the electromagnetic\nfield it is found that it has a component along the spin axis and\ndiverges as the inverse of the lower radial limit of integration a.\n\nIf this lower limit of radial integration is taken to be the Compton\nwavelength a = hbar/(m*c) the angular momentum of this part of the\nelectromagnetic field comes to alpha/3, in units of hbar, where alpha\nis the fine structure constant (approximately 1/137).\n\nMy question is this: is the angular momentum of this part of the\nelectromagnetic field produced by the electron (and also the part\nassociated with a radius less than the Compton wavelength, whatever\nthat is) part of the angular momentum hbar/2 of the electron given by\nDirac theory or in addition to it?\n\nAndrew Stewart\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>A physical electron has a radial electric field E due to is electric
charge e and a dipole magnetic field B due to the magnetic moment
(e*\hbar/2*m*c) associated with its spin. The vector cross product of
the two fields, the Poynting vector S = E x B/(4*\pi*c), circulates
azimuthally around the spin axis. The density j of angular momentum
of the electromagnetic field is j = r x S. When this is integrated
over all space to give the angular momentum of the electromagnetic
field it is found that it has a component along the spin axis and
diverges as the inverse of the lower radial limit of integration a.

If this lower limit of radial integration is taken to be the Compton
wavelength a = \hbar/(m*c) the angular momentum of this part of the
electromagnetic field comes to \alpha/3, in units of \hbar, where \alpha
is the fine structure constant (approximately 1/137).

My question is this: is the angular momentum of this part of the
electromagnetic field produced by the electron (and also the part
associated with a radius less than the Compton wavelength, whatever
that is) part of the angular momentum \hbar/2 of the electron given by
Dirac theory or in addition to it?

Andrew Stewart

Jack Tremarco
Sep27-04, 03:31 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>\nYour description is in classical terms. However, the origin of the\nmagntic dipole moment you mention is the spin which is a quantum\neffect. You are therefore mixing classical and quantum physics, which\nis likely the origin of your confusion.\n\nIn Dirac theory the spin and hence the magnetic moment emerge\nnaturally up to quantum corrections. Dirac theory ultimately makes\nsense only if it is second-quantized. It\'s predictive power as a\nclassical equation of motion seems rather accidental. So you really\nneed a quantum theory to get it right. In a purely classical theory\nthe origin of the spin would necessarily remain a mystery.\n\nAll the best, Jack\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Your description is in classical terms. However, the origin of the
magntic dipole moment you mention is the spin which is a quantum
effect. You are therefore mixing classical and quantum physics, which
is likely the origin of your confusion.

In Dirac theory the spin and hence the magnetic moment emerge
naturally up to quantum corrections. Dirac theory ultimately makes
sense only if it is second-quantized. It's predictive power as a
classical equation of motion seems rather accidental. So you really
need a quantum theory to get it right. In a purely classical theory
the origin of the spin would necessarily remain a mystery.

All the best, Jack