nonlocalized electron's EM field [Archive]

Blake Winter

Sep21-04, 03:30 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\nRecently I heard that there was an experiment done in which an\nelectron was placed in a two dimsionional "ring" of sorts, in such a\nmanner that its wavefunction spread throughout the ring but was\nessentially still localized in the perpendicular dimension. Then the\nelectric field resulting was measured and was found to behave as\nthough there was a charge distribution proportional to the probability\ndensity from the wave function with a total charge equal to that of an\nelectron.\nUnfortunately the person who told me about this couldn\'t remember who\nhad done this experiment or where to find anything more about it,\nexcept that it was probably in "Schrodinger\'s Kittens". Can anyone\npoint me to more information about it? Maybe even the original paper?\nAlso, has it had any profound influence on our understanding of\nquantum theory?\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>Recently I heard that there was an experiment done in which an
electron was placed in a two dimsionional "ring" of sorts, in such a
manner that its wavefunction spread throughout the ring but was
essentially still localized in the perpendicular dimension. Then the
electric field resulting was measured and was found to behave as
though there was a charge distribution proportional to the probability
density from the wave function with a total charge equal to that of an
electron.
Unfortunately the person who told me about this couldn't remember who
had done this experiment or where to find anything more about it,
except that it was probably in "Schrodinger's Kittens". Can anyone
point me to more information about it? Maybe even the original paper?
Also, has it had any profound influence on our understanding of
quantum theory?

Arnold Neumaier

Sep22-04, 03:45 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\nBlake Winter wrote:\n\n> Recently I heard that there was an experiment done in which an\n> electron was placed in a two dimsionional "ring" of sorts, in such a\n> manner that its wavefunction spread throughout the ring but was\n> essentially still localized in the perpendicular dimension. Then the\n> electric field resulting was measured and was found to behave as\n> though there was a charge distribution proportional to the probability\n> density from the wave function with a total charge equal to that of an\n> electron.\n\nI don\'t know about the experiment, but the outcome is exactly how it\nshould be, from a QFT point of view. Indeed, the charge density of an\narbitrary Fock state is the expectation\ne(x) = <Psi_0(x)^* e Psi_0(x)>,\nwhere Psi_0(x) is the time component of the Fermion field. For a\nsingle electron in the pure state psi we simply get e(x)=e|psi(x)|^2.\nThis is also the chemists\' point of view; see the section\n\'How real is the wave function?\' in my theoretical physics FAQ at\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\n\n\n> Unfortunately the person who told me about this couldn\'t remember who\n> had done this experiment or where to find anything more about it,\n> except that it was probably in "Schrodinger\'s Kittens". Can anyone\n> point me to more information about it? Maybe even the original paper?\n\nI\'d be interested in the details, too.\n\n\n> Also, has it had any profound influence on our understanding of\n> quantum theory?\n\nMaybe it will lead to more attention for the fact that what we can really\nmeasure are all sorts of expectations, and not just eigenvalues\n(which are simply expectations in an eigenstate). Cf. my paper\nquant-ph/0303047 = Int. J. Mod. Phys. B 17 (2003), 2937-2980.\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>Blake Winter wrote:

> Recently I heard that there was an experiment done in which an
> electron was placed in a two dimsionional "ring" of sorts, in such a
> manner that its wavefunction spread throughout the ring but was
> essentially still localized in the perpendicular dimension. Then the
> electric field resulting was measured and was found to behave as
> though there was a charge distribution proportional to the probability
> density from the wave function with a total charge equal to that of an
> electron.

I don't know about the experiment, but the outcome is exactly how it
should be, from a QFT point of view. Indeed, the charge density of an
arbitrary Fock state is the expectation
e(x) = <\Psi_0(x)^* e \Psi_0(x)>,
where \Psi_0(x) is the time component of the Fermion field. For a
single electron in the pure state \psi we simply get e(x)=e|\psi(x)|^2.
This is also the chemists' point of view; see the section
'How real is the wave function?' in my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt

> Unfortunately the person who told me about this couldn't remember who
> had done this experiment or where to find anything more about it,
> except that it was probably in "Schrodinger's Kittens". Can anyone
> point me to more information about it? Maybe even the original paper?

I'd be interested in the details, too.

> Also, has it had any profound influence on our understanding of
> quantum theory?

Maybe it will lead to more attention for the fact that what we can really
measure are all sorts of expectations, and not just eigenvalues
(which are simply expectations in an eigenstate). Cf. my paper
http://www.arxiv.org/abs/quant-ph/0303047 = \Int. J. Mod. Phys. B 17 (2003), 2937-2980.

Arnold Neumaier

Blake Winter

Sep23-04, 04:46 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> Maybe it will lead to more attention for the fact that what we can really\n> measure are all sorts of expectations, and not just eigenvalues\n> (which are simply expectations in an eigenstate). Cf. my paper\n> quant-ph/0303047 = Int. J. Mod. Phys. B 17 (2003), 2937-2980.\n>\n>\n> Arnold Neumaier\n\nEspecially it seems to signal to me that the wavefunction cannot only\nbe looked upon as a probability density, but something more than that.\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>Maybe it will lead to more attention for the fact that what we can really
> measure are all sorts of expectations, and not just eigenvalues
> (which are simply expectations in an eigenstate). Cf. my paper
> http://www.arxiv.org/abs/quant-ph/0303047 = \Int. J. Mod. Phys. B 17 (2003), 2937-2980.
>
>
> Arnold Neumaier

Especially it seems to signal to me that the wavefunction cannot only
be looked upon as a probability density, but something more than that.

alistair

Sep23-04, 04:46 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\nblake.winter@houghton.edu (Blake Winter) wrote in message news:<87423d2a.0409201632.14bd753d@posting.google. com>...\n> Recently I heard that there was an experiment done in which an\n> electron was placed in a two dimsionional "ring" of sorts, in such a\n> manner that its wavefunction spread throughout the ring but was\n> essentially still localized in the perpendicular dimension. Then the\n> electric field resulting was measured and was found to behave as\n> though there was a charge distribution proportional to the probability\n> density from the wave function with a total charge equal to that of an\n> electron.\n\nblake.winter@houghton.edu (Blake Winter) wrote in message news:<87423d2a.0409201632.14bd753d@posting.google. com>...\n> Recently I heard that there was an experiment done in which an\n> electron was placed in a two dimsionional "ring" of sorts, in such a\n> manner that its wavefunction spread throughout the ring but was\n> essentially still localized in the perpendicular dimension. Then the\n> electric field resulting was measured and was found to behave as\n> though there was a charge distribution proportional to the probability\n> density from the wave function with a total charge equal to that of an\n> electron.\n\n\nThis does not prove that the charge of a single electron is spread out\naround the ring.The single electron can affect other charges around\nthe ring when its electric field displaces non-conducting electrons\nnear to it, which in turn displace non-conducting electrons near to\nthem (electrons whose charge is normally completely cancelled by\nproton charges - as seen from a long distance -would no longer have\ntheir charges completely cancelled.The original electron\nwould get feedback from the displacements it causes and so a\nnon-uniform electric field can arise around the ring.\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>blake.winter@houghton.edu (Blake Winter) wrote in message news:<87423d2a.0409201632.14bd753d@posting.google.com>...
> Recently I heard that there was an experiment done in which an
> electron was placed in a two dimsionional "ring" of sorts, in such a
> manner that its wavefunction spread throughout the ring but was
> essentially still localized in the perpendicular dimension. Then the
> electric field resulting was measured and was found to behave as
> though there was a charge distribution proportional to the probability
> density from the wave function with a total charge equal to that of an
> electron.

blake.winter@houghton.edu (Blake Winter) wrote in message news:<87423d2a.0409201632.14bd753d@posting.google.com>...
> Recently I heard that there was an experiment done in which an
> electron was placed in a two dimsionional "ring" of sorts, in such a
> manner that its wavefunction spread throughout the ring but was
> essentially still localized in the perpendicular dimension. Then the
> electric field resulting was measured and was found to behave as
> though there was a charge distribution proportional to the probability
> density from the wave function with a total charge equal to that of an
> electron.

This does not prove that the charge of a single electron is spread out
around the ring.The single electron can affect other charges around
the ring when its electric field displaces non-conducting electrons
near to it, which in turn displace non-conducting electrons near to
them (electrons whose charge is normally completely cancelled by
proton charges - as seen from a long distance -would no longer have
their charges completely cancelled.The original electron
would get feedback from the displacements it causes and so a
non-uniform electric field can arise around the ring.