Re: Reconciling quantum theory & relativity [Archive]

Arnold Neumaier

Aug16-04, 01:01 PM

<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> In essence, that means all the electrons in the universe is actually\n> the same electron at different places at the same time. All the\n> photons is the same photon at different places at the same time.\n> They have no more identity as individual objects than waves on an\n> ocean do.\n\nI find this a misleading way of picturing indistinguishability.\n\nIt is nore like having a bumpy but materially uniform surface,\nwhere one cannot label the local maxima in a \'distinguishable\' way\nexcept by their relative position, and where new maxima may appear\nor old ones disappear). Exactly the same happens for electrons and\npositrons, which are in QFT just excitations of the electron field.\nThe analogue to the quantum field is the scalar field defining the\nheight of the surface at each point.\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>In essence, that means all the electrons in the universe is actually
> the same electron at different places at the same time. All the
> photons is the same photon at different places at the same time.
> They have no more identity as individual objects than waves on an
> ocean do.

I find this a misleading way of picturing indistinguishability.

It is nore like having a bumpy but materially uniform surface,
where one cannot label the local maxima in a 'distinguishable' way
except by their relative position, and where new maxima may appear
or old ones disappear). Exactly the same happens for electrons and
positrons, which are in QFT just excitations of the electron field.
The analogue to the quantum field is the scalar field defining the
height of the surface at each point.

Arnold Neumaier

Bjoern Feuerbacher

Aug19-04, 07:24 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\nVery cryptic wrote:\n\n[snip]\n\n> I\'m not sure what the theorem actually states, but I do know there IS\n> a covariant canonical QM model of a single relativistic particle.\n> [x^mu,x^nu]=[p_mu,p_nu]=0\n> [x^mu,p_nu]=i hbar delta^mu_nu\n>\n> has an irreducible rep. The trick is to impose the constraint\n> [(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with\n> "physical" operators which commute with [(p-qA)^2-m^2].\n\nExcuse me, but what is x^0? A time operator? What are its eigenvalues\nand eigenstates?\n\n\nBye,\nBjoern\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>Very cryptic wrote:

[snip]

> I'm not sure what the theorem actually states, but I do know there IS
> a covariant canonical QM model of a single relativistic particle.
> [x^\mu,x^\nu]=[p_{mu},p_{nu}]=0
> [x^\mu,p_{nu}]=i \hbar \delta^\mu_nu
>
> has an irreducible rep. The trick is to impose the constraint
> [(p-qA)^2-m^2]|\psi>=0 for the physical states |\psi> and only work with
> "physical" operators which commute with [(p-qA)^2-m^2].

Excuse me, but what is x^0? A time operator? What are its eigenvalues
and eigenstates?

Bye,
Bjoern

very_cryptic@hotmail.com

Aug20-04, 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>\nArnold Neumaier wrote:\n\n> >>More generally, it\'s not possible to represent particle worldlines\n> >>in a relativistic setting in a way compatible with quantum theory\n> >>without violating causality. This is a fairly well-known result\n> >>explained, for instance, in Ticciati (Quantum Field Theory For\n> >>Mathematicians; section 1.6 The Position Operator [and it\'s\n> >>impossibility]).\n\n> The theorem says that any multiparticle theory with well-defined\n> world-lines satisfying certain natural conditions necessarily\ndescribes\n> noninteracting particles only (a tenso product of what you\ndescribed).\n> This is not intrinsically QM, but also valid in classical\nrelativistic\n> mechanics.\n\nIsn\'t the feynmann-Wheeler model of electrodynamics where they\neliminated the electromagnetic field in favor of direct interactions\nalong light cones a counterexample?\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>Arnold Neumaier wrote:

> >>More generally, it's not possible to represent particle worldlines
> >>in a relativistic setting in a way compatible with quantum theory
> >>without violating causality. This is a fairly well-known result
> >>explained, for instance, in Ticciati (Quantum Field Theory For
> >>Mathematicians; section 1.6 The Position Operator [and it's
> >>impossibility]).

> The theorem says that any multiparticle theory with well-defined
> world-lines satisfying certain natural conditions necessarily
describes
> noninteracting particles only (a tenso product of what you
described).
> This is not intrinsically QM, but also valid in classical
relativistic
> mechanics.

Isn't the feynmann-Wheeler model of electrodynamics where they
eliminated the electromagnetic field in favor of direct interactions
along light cones a counterexample?

Arnold Neumaier

Aug24-04, 04:52 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>very_cryptic@hotmail.com wrote:\n> Arnold Neumaier wrote:\n>\n>>>>More generally, it\'s not possible to represent particle worldlines\n>>>>in a relativistic setting in a way compatible with quantum theory\n>>>>without violating causality. This is a fairly well-known result\n>>>>explained, for instance, in Ticciati (Quantum Field Theory For\n>>>>Mathematicians; section 1.6 The Position Operator [and it\'s\n>>>>impossibility]).\n>\n>>The theorem says that any multiparticle theory with well-defined\n>>world-lines satisfying certain natural conditions necessarily describes\n>>noninteracting particles only (a tenso product of what you described).\n>>This is not intrinsically QM, but also valid in classical relativistic\n>>mechanics.\n>\n\n> Isn\'t the feynmann-Wheeler model of electrodynamics where they\n> eliminated the electromagnetic field in favor of direct interactions\n> along light cones a counterexample?\n\nThis is a classical model, and it fails to satisfy the assumptions\nof the no-go theorem. In fact Wheeler-Feynman is quite nonlocal in\ntime - dynamics depends not only on the past but also on the future!\n\nAs is well-known from von Neumann\'s nogo theorem for hidden variables,\nevery nogo theorem can be circumvented by violating its assumptions.\nSo if you are interested in this kind of modles you need to study such\ntheorems and their proof - they tell you what you need to avoid in an\nattempt to proceed further. Usually it means that you need to accept\nat least one weird feature, and work out the consequences of that...\n\n\nArnold Neumaier\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>very_cryptic@hotmail.com wrote:
> Arnold Neumaier wrote:
>
>>>>More generally, it's not possible to represent particle worldlines
>>>>in a relativistic setting in a way compatible with quantum theory
>>>>without violating causality. This is a fairly well-known result
>>>>explained, for instance, in Ticciati (Quantum Field Theory For
>>>>Mathematicians; section 1.6 The Position Operator [and it's
>>>>impossibility]).
>
>>The theorem says that any multiparticle theory with well-defined
>>world-lines satisfying certain natural conditions necessarily describes
>>noninteracting particles only (a tenso product of what you described).
>>This is not intrinsically QM, but also valid in classical relativistic
>>mechanics.
>

> Isn't the feynmann-Wheeler model of electrodynamics where they
> eliminated the electromagnetic field in favor of direct interactions
> along light cones a counterexample?

This is a classical model, and it fails to satisfy the assumptions
of the no-go theorem. In fact Wheeler-Feynman is quite nonlocal in
time - dynamics depends not only on the past but also on the future!

As is well-known from von Neumann's nogo theorem for hidden variables,
every nogo theorem can be circumvented by violating its assumptions.
So if you are interested in this kind of modles you need to study such
theorems and their proof - they tell you what you need to avoid in an
attempt to proceed further. Usually it means that you need to accept
at least one weird feature, and work out the consequences of that...

Arnold Neumaier

Danny Ross Lunsford

Aug24-04, 04:57 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>very_cryptic@hotmail.com wrote in message news:<cg3br4\\$b34@odah37.prod.google.com>...\n> Arnold Neumaier wrote:\n>\n> > >>More generally, it\'s not possible to represent particle worldlines\n> > >>in a relativistic setting in a way compatible with quantum theory\n> > >>without violating causality. This is a fairly well-known result\n> > >>explained, for instance, in Ticciati (Quantum Field Theory For\n> > >>Mathematicians; section 1.6 The Position Operator [and it\'s\n> > >>impossibility]).\n>\n> > The theorem says that any multiparticle theory with well-defined\n> > world-lines satisfying certain natural conditions necessarily\n> describes\n> > noninteracting particles only (a tenso product of what you\n> described).\n> > This is not intrinsically QM, but also valid in classical\n> relativistic\n> > mechanics.\n>\n> Isn\'t the feynmann-Wheeler model of electrodynamics where they\n> eliminated the electromagnetic field in favor of direct interactions\n> along light cones a counterexample?\n\nThe "natural conditions" probably don\'t involve using advanced\npotentials, as in W-F.\n\n-drl\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>very_cryptic@hotmail.com wrote in message news:<cg3br4$b34@odah37.prod.google.com>...
> Arnold Neumaier wrote:
>
> > >>More generally, it's not possible to represent particle worldlines
> > >>in a relativistic setting in a way compatible with quantum theory
> > >>without violating causality. This is a fairly well-known result
> > >>explained, for instance, in Ticciati (Quantum Field Theory For
> > >>Mathematicians; section 1.6 The Position Operator [and it's
> > >>impossibility]).
>
> > The theorem says that any multiparticle theory with well-defined
> > world-lines satisfying certain natural conditions necessarily
> describes
> > noninteracting particles only (a tenso product of what you
> described).
> > This is not intrinsically QM, but also valid in classical
> relativistic
> > mechanics.
>
> Isn't the feynmann-Wheeler model of electrodynamics where they
> eliminated the electromagnetic field in favor of direct interactions
> along light cones a counterexample?

The "natural conditions" probably don't involve using advanced
potentials, as in W-F.

-drl

whopkins@csd.uwm.edu

Dec9-04, 11:33 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>\n\n\n\nIt\'s the only way to picture indistinguishability, and\neverything has it as a corollary. NOT making the\nconflation is misleading. You\'re always free to call\nthings the same when they only count once.\n\nThere is only 1 way to put two of the same particles\nin 2 boxes, one in each box. Therefore, you\'re perfectly\nfree to say they\'re the same. Literally. The relevant\nconcept "genidentity" can be taken anywhere you\nplease, as long as the prerequisite holds, of identity in\nthe sense of counting. There is no prior notion of\ngenidentity, so we\'re free to define it anyway we want\nand call any two things the same -- as long as they\nonly "count once".\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>It's the only way to picture indistinguishability, and
everything has it as a corollary. NOT making the
conflation is misleading. You're always free to call
things the same when they only count once.

There is only 1 way to put two of the same particles
in 2 boxes, one in each box. Therefore, you're perfectly
free to say they're the same. Literally. The relevant
concept "genidentity" can be taken anywhere you
please, as long as the prerequisite holds, of identity in
the sense of counting. There is no prior notion of
genidentity, so we're free to define it anyway we want
and call any two things the same -- as long as they
only "count once".