Equivalence principle and spin [Archive]

Andres Berenguer

Mar11-05, 02:32 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>Thank you for your clever answers, but that is the main point. Why\npseudo-Riemannian manifolds are -strictly speaking- unable to manage\nwith non-zero spins? Is it because of they do not have any "torsion"\nidea or due to the fact that rotations are not well-defined in curved\nmanifolds? If the latter reason is right, what about rotating systems\nof reference like our very planet Earth?\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>Thank you for your clever answers, but that is the main point. Why
pseudo-Riemannian manifolds are -strictly speaking- unable to manage
with non-zero spins? Is it because of they do not have any "torsion"
idea or due to the fact that rotations are not well-defined in curved
manifolds? If the latter reason is right, what about rotating systems
of reference like our very planet Earth?

Cl.Massé

Mar11-05, 02:32 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>"Uncle Al" <UncleAl0@hate.spam.net> a écrit dans le message de\nnews:422CEEC1.32BD6458@hate.spam.net...\n\n> 1) Name an elementary particle with a spin greater than (+/-1)\n> other than the postulated graviton. How does one get two or three\n> quarks to sum their spins to greater than (+/-1)?\n\nPerhaps in a Delta resonance?\n\n--\n~~~~ clmasse on free F-country\nLiberty, Equality, Profitability.\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>"Uncle Al" <UncleAl0@hate.spam.net> a écrit dans le message de
news:422CEEC1.32BD6458@hate.spam.net...

> 1) Name an elementary particle with a spin greater than (+/-1)
> other than the postulated graviton. How does one get two or three
> quarks to sum their spins to greater than (+/-1)?

Perhaps in a \Delta resonance?

--
~~~~ clmasse on free F-country
Liberty, Equality, Profitability.

Franz Heymann

Mar12-05, 08:07 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>"Cl.Massé" <info@optinbig.com> wrote in message\nnews:42309331\\$0\\$29906\\$626a14ce@news .free.fr...\n> "Uncle Al" <UncleAl0@hate.spam.net> a écrit dans le message de\n> news:422CEEC1.32BD6458@hate.spam.net...\n>\n> > 1) Name an elementary particle with a spin greater than (+/-1)\n> > other than the postulated graviton. How does one get two or three\n> > quarks to sum their spins to greater than (+/-1)?\n>\n> Perhaps in a Delta resonance?\n\nThey incolve orbital angular momnenta as well as spin.\n\n--\nFranz\n"A first-rate laboratory is one in which mediocre scientists can\nproduce outstanding work"\nP.M.S. Blackett\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>"Cl.Massé" <info@optinbig.com> wrote in message
news:42309331$0$29906$626a14ce@news.free.fr...
> "Uncle Al" <UncleAl0@hate.spam.net> a écrit dans le message de
> news:422CEEC1.32BD6458@hate.spam.net...
>
> > 1) Name an elementary particle with a spin greater than (+/-1)
> > other than the postulated graviton. How does one get two or three
> > quarks to sum their spins to greater than (+/-1)?
>
> Perhaps in a \Delta resonance?

They incolve orbital angular momnenta as well as spin.

--
Franz
"A first-rate laboratory is one in which mediocre scientists can
produce outstanding work"
P.M.S. Blackett

Uncle Al

Mar15-05, 12:17 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>\nAndres Berenguer wrote:\n>\n> Thank you for your clever answers, but that is the main point. Why\n> pseudo-Riemannian manifolds are -strictly speaking- unable to manage\n> with non-zero spins? Is it because of they do not have any "torsion"\n> idea or due to the fact that rotations are not well-defined in curved\n> manifolds? If the latter reason is right, what about rotating systems\n> of reference like our very planet Earth?\n\nThe Earth rotates but it is not chiral, it only has helicity. View\nfrom the north pole and view from the south pole. The sense of\nrotation reverses. Is the problem with rotation per se or with\nchirality (non-superposable mirror reflection along one coordinate\naxis) or parity (non-superposable mirror reflection along all\ncoordinate axes)?\n\nWhat happens when there is no coordinate background? Chirality, only\nrequiring a causal and orientable spacetime manifold, arises from\ncoordinate-free Hodge duality equivalent to a pseudoscalar field\n(Levi-Civita tensor). True chiral systems exist in two distinct\nenantiomorphic states interconverted by space inversion but not by\ntime reversal combined with any proper spatial rotation,\n\nJ. Mol. Phys. 43, 1395 (1981)\n\nEquating spin with rotation is very dangerous.\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/\n(Toxic URL! Unsafe for children and most mammals)\nhttp://www.mazepath.com/uncleal/qz.pdf\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>Andres Berenguer wrote:
>
> Thank you for your clever answers, but that is the main point. Why
> pseudo-Riemannian manifolds are -strictly speaking- unable to manage
> with non-zero spins? Is it because of they do not have any "torsion"
> idea or due to the fact that rotations are not well-defined in curved
> manifolds? If the latter reason is right, what about rotating systems
> of reference like our very planet Earth?

The Earth rotates but it is not chiral, it only has helicity. View
from the north pole and view from the south pole. The sense of
rotation reverses. Is the problem with rotation per se or with
chirality (non-superposable mirror reflection along one coordinate
axis) or parity (non-superposable mirror reflection along all
coordinate axes)?

What happens when there is no coordinate background? Chirality, only
requiring a causal and orientable spacetime manifold, arises from
coordinate-free Hodge duality equivalent to a pseudoscalar field
(Levi-Civita tensor). True chiral systems exist in two distinct
enantiomorphic states interconverted by space inversion but not by
time reversal combined with any proper spatial rotation,

J. Mol. Phys. 43, 1395 (1981)

Equating spin with rotation is very dangerous.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

whopkins@csd.uwm.edu

Mar16-05, 02:06 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>Andres Berenguer wrote:\n> Thank you for your clever answers, but that is the main point. Why\n> pseudo-Riemannian manifolds are -strictly speaking- unable to manage\n> with non-zero spins? Is it because of they do not have any "torsion"\n> idea or due to the fact that rotations are not well-defined in curved\n> manifolds? If the latter reason is right, what about rotating systems\n> of reference like our very planet Earth?\n\nBecause there\'s insufficient structure within the framework of\nRiemannian geometry (manifold + differentiability + metric +\nconnection) to handle the job. Spinors are representations of SL(2,C)\n(Dirac spinors of ISL(2,C)=Poincare), so you need a SL(2,C) gauge field\n-- the spin bundle and, more generally, a Poincare gauge field -- a\nspin bundle + frame field. So, spinors require the structure\n(manifold + differentiability + metric + connection + frame field +\nspin bundle).\n\nSince the metric and connection can be defined from the frame field and\nthe spin bundle, the structure in fact reduces to:\n(manifold + differentiability + frame field + spin bundle).\n\nIn effect, this is just Poincare\' gauge theory and is equivalent to\nteleparallel gravity with a non-zero curvature.\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>Andres Berenguer wrote:
> Thank you for your clever answers, but that is the main point. Why
> pseudo-Riemannian manifolds are -strictly speaking- unable to manage
> with non-zero spins? Is it because of they do not have any "torsion"
> idea or due to the fact that rotations are not well-defined in curved
> manifolds? If the latter reason is right, what about rotating systems
> of reference like our very planet Earth?

Because there's insufficient structure within the framework of
Riemannian geometry (manifold + differentiability + metric +
connection) to handle the job. Spinors are representations of SL(2,C)
(Dirac spinors of ISL(2,C)=Poincare), so you need a SL(2,C) gauge field
-- the spin bundle and, more generally, a Poincare gauge field -- a
spin bundle + frame field. So, spinors require the structure
(manifold + differentiability + metric + connection + frame field +
spin bundle).

Since the metric and connection can be defined from the frame field and
the spin bundle, the structure in fact reduces to:
(manifold + differentiability + frame field + spin bundle).

In effect, this is just Poincare' gauge theory and is equivalent to
teleparallel gravity with a non-zero curvature.