Arnold Neumaier
Apr15-04, 11:37 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>CCRyder wrote:\n> In article <407BE664.1010808@univie.ac.at>, Arnold Neumaier\n> <Arnold.Neumaier@univie.ac.at> wrote:\n>\n>\n>>CCRyder wrote:\n>>\n>>>In article <407408D7.2010704@somewhere.com>, Rich\n>>><someone@somewhere.com> wrote:\n>>>\n>>>\n>>>\n>>>>In infinite wisdom CCRyder answered:\n>>>>\n>>>>\n>>>>>In article <z1kcc.43\\$Ax1.50086@news.uswest.net>, Michael Varney\n>>>>><varney@colorado_no_spam.edu> wrote:\n>>>>>\n>>>>>\n>>>>>\n>>>>>\n>>>>>>The photons do not occupy the same "space" as each other. The can share\n>>>>>>the\n>>>>>>same quantum state, which is a different thing.\n>>>>>\n>>>>>\n>>>>>Nothing like the air of authority to settle such arguments. Except we\n>>>>>must be sure that it is not really the authority of air. :-). The idea\n>>>>>that bosons cannot be in the same \'space\' is forbidden by what \'law\' in\n>>>>>physics? What experimental data confirms your belief in this matter?\n>>>>>Fermions, for example, cannot occupy the same quantum state but pairs\n>>>>>of electrons, one spin up the other spin down appear to be able to\n>>>>>occupy the same \'space\'.\n>>>>\n>>>>This is curious, I\'m given to understand that electrons have no\n>>>>structure, that every new experiment sets a smaller upper bound\n>>>>on the, err, size of an electron. And then there\'s the small matter\n>>>>of Heisenberg.\n>>>\n>>>\n>>>It is *supposed* that electrons have no structure.\n>>\n>>Physical electros _do_ have structure. it is given by the form factor,\n>>computed to some approximation in most QFT books. Only bare electrons\n>>are structureless; but they are unobservable fictions of the same kind\n>>as virtual photons.\n>>\n>>\n>>Arnold Neumaier\n>\n>\n> What possibly could you mean by the term \'bare electrons\'? Do you\n> envision electrons as singularities? Do you conceive of electrons as\n> unconnected to the rest of the universe?\n\nNeither. A bare electron is the formal entity discussed in textbooks\nwhen they do perturbative quantum electrodynamics. The intuitive\npicture generally given is that a bare electron is surrounded\nby a clud of virtual photons and virtual electron-positron pairs\nto make up a physical, \'dressed\' electron. Only the latter is real\nand observable. The former is a formal caricature of the latter,\nwith paradoxical properties (infinite mass, etc.).\n\nOn a more substantial level, the observable electrons are produced\nfrom the bare electrons by a process called renormalization,\nwhich modifies the propagators by self-energy terms\nand the currents by form factors. As the name says, the latter define\nthe \'form\' of a particle. (In the above picture, it would correspond\nto the shape of the virtual cloud, though it is better to avoid\ngiving the virtual particles too much of meaning.)\n\nThe observable electrons indeed have structure, since their form\nfactors are nontrivial. For example, in his book\nS. Weinberg,\nThe quantum theory of fields, Vol. I,\nCambridge University Press, 1995,\nWeinberg defines and explicitly computes in (11.3.33) the\n\'charge radius\' of a physical electron.\n\n\nArnold Neumaier\n\n\n\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>CCRyder wrote:
> In article <407BE664.1010808@univie.ac.at>, Arnold Neumaier
> <Arnold.Neumaier@univie.ac.at> wrote:
>
>
>>CCRyder wrote:
>>
>>>In article <407408D7.2010704@somewhere.com>, Rich
>>><someone@somewhere.com> wrote:
>>>
>>>
>>>
>>>>In infinite wisdom CCRyder answered:
>>>>
>>>>
>>>>>In article <z1kcc.43$Ax1.50086@news.uswest.net>, Michael Varney
>>>>><varney@colorado_no_spam.edu> wrote:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>The photons do not occupy the same "space" as each other. The can share
>>>>>>the
>>>>>>same quantum state, which is a different thing.
>>>>>
>>>>>
>>>>>Nothing like the air of authority to settle such arguments. Except we
>>>>>must be sure that it is not really the authority of air. :-). The idea
>>>>>that bosons cannot be in the same 'space' is forbidden by what 'law' in
>>>>>physics? What experimental data confirms your belief in this matter?
>>>>>Fermions, for example, cannot occupy the same quantum state but pairs
>>>>>of electrons, one spin up the other spin down appear to be able to
>>>>>occupy the same 'space'.
>>>>
>>>>This is curious, I'm given to understand that electrons have no
>>>>structure, that every new experiment sets a smaller upper bound
>>>>on the, err, size of an electron. And then there's the small matter
>>>>of Heisenberg.
>>>
>>>
>>>It is *supposed* that electrons have no structure.
>>
>>Physical electros _do_ have structure. it is given by the form factor,
>>computed to some approximation in most QFT books. Only bare electrons
>>are structureless; but they are unobservable fictions of the same kind
>>as virtual photons.
>>
>>
>>Arnold Neumaier
>
>
> What possibly could you mean by the term 'bare electrons'? Do you
> envision electrons as singularities? Do you conceive of electrons as
> unconnected to the rest of the universe?
Neither. A bare electron is the formal entity discussed in textbooks
when they do perturbative quantum electrodynamics. The intuitive
picture generally given is that a bare electron is surrounded
by a clud of virtual photons and virtual electron-positron pairs
to make up a physical, 'dressed' electron. Only the latter is real
and observable. The former is a formal caricature of the latter,
with paradoxical properties (infinite mass, etc.).
On a more substantial level, the observable electrons are produced
from the bare electrons by a process called renormalization,
which modifies the propagators by self-energy terms
and the currents by form factors. As the name says, the latter define
the 'form' of a particle. (In the above picture, it would correspond
to the shape of the virtual cloud, though it is better to avoid
giving the virtual particles too much of meaning.)
The observable electrons indeed have structure, since their form
factors are nontrivial. For example, in his book
S. Weinberg,
The quantum theory of fields, Vol. I,
Cambridge University Press, 1995,
Weinberg defines and explicitly computes in (11.3.33) the
'charge radius' of a physical electron.
Arnold Neumaier
> In article <407BE664.1010808@univie.ac.at>, Arnold Neumaier
> <Arnold.Neumaier@univie.ac.at> wrote:
>
>
>>CCRyder wrote:
>>
>>>In article <407408D7.2010704@somewhere.com>, Rich
>>><someone@somewhere.com> wrote:
>>>
>>>
>>>
>>>>In infinite wisdom CCRyder answered:
>>>>
>>>>
>>>>>In article <z1kcc.43$Ax1.50086@news.uswest.net>, Michael Varney
>>>>><varney@colorado_no_spam.edu> wrote:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>The photons do not occupy the same "space" as each other. The can share
>>>>>>the
>>>>>>same quantum state, which is a different thing.
>>>>>
>>>>>
>>>>>Nothing like the air of authority to settle such arguments. Except we
>>>>>must be sure that it is not really the authority of air. :-). The idea
>>>>>that bosons cannot be in the same 'space' is forbidden by what 'law' in
>>>>>physics? What experimental data confirms your belief in this matter?
>>>>>Fermions, for example, cannot occupy the same quantum state but pairs
>>>>>of electrons, one spin up the other spin down appear to be able to
>>>>>occupy the same 'space'.
>>>>
>>>>This is curious, I'm given to understand that electrons have no
>>>>structure, that every new experiment sets a smaller upper bound
>>>>on the, err, size of an electron. And then there's the small matter
>>>>of Heisenberg.
>>>
>>>
>>>It is *supposed* that electrons have no structure.
>>
>>Physical electros _do_ have structure. it is given by the form factor,
>>computed to some approximation in most QFT books. Only bare electrons
>>are structureless; but they are unobservable fictions of the same kind
>>as virtual photons.
>>
>>
>>Arnold Neumaier
>
>
> What possibly could you mean by the term 'bare electrons'? Do you
> envision electrons as singularities? Do you conceive of electrons as
> unconnected to the rest of the universe?
Neither. A bare electron is the formal entity discussed in textbooks
when they do perturbative quantum electrodynamics. The intuitive
picture generally given is that a bare electron is surrounded
by a clud of virtual photons and virtual electron-positron pairs
to make up a physical, 'dressed' electron. Only the latter is real
and observable. The former is a formal caricature of the latter,
with paradoxical properties (infinite mass, etc.).
On a more substantial level, the observable electrons are produced
from the bare electrons by a process called renormalization,
which modifies the propagators by self-energy terms
and the currents by form factors. As the name says, the latter define
the 'form' of a particle. (In the above picture, it would correspond
to the shape of the virtual cloud, though it is better to avoid
giving the virtual particles too much of meaning.)
The observable electrons indeed have structure, since their form
factors are nontrivial. For example, in his book
S. Weinberg,
The quantum theory of fields, Vol. I,
Cambridge University Press, 1995,
Weinberg defines and explicitly computes in (11.3.33) the
'charge radius' of a physical electron.
Arnold Neumaier