<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\nHi,\nHow does one explain that every particle associated with a force\n(\'force-carrier\') must have integer spin?\n\nI have read the following in "Feynman Lectures on Gravitation." (for the\nspecial case of a graviton):\n\n"In order to produce a _static_ force and not just scattering, the\nemission or absorption of a single graviton by either particle must\nleave both particles in the same internal state. This rules out the\npossibility that the graviton carries half-integer spin (for example,\nrelated to the fact that it takes a rotation of 720 degrees to return a\nspin-1/2 wavefunction back to itself). Therefore the graviton must\nhave integer spin." ...\n\n1) Why must the internal state of both particles feeling the force be left\nunchanged?\n(sounds reasonable, but is there any good arguments?)\n\n2) I can see that a half integer spin \'force-carrier\' would change the spin\nof both the internal states by _half_ an integer, but\nwouldn\'t also an integer spin \'force-carrier\' change the spin of the\nparticles \'feeling the force\' (now with a _full_ integer instead)?\n\n\n/Michael\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>Hi,
How does one explain that every particle associated with a force
('force-carrier') must have integer spin?
I have read the following in "Feynman Lectures on Gravitation." (for the
special case of a graviton):
"In order to produce a _static_ force and not just scattering, the
emission or absorption of a single graviton by either particle must
leave both particles in the same internal state. This rules out the
possibility that the graviton carries half-integer spin (for example,
related to the fact that it takes a rotation of 720 degrees to return a
spin-1/2 wavefunction back to itself). Therefore the graviton must
have integer spin." ...
1) Why must the internal state of both particles feeling the force be left
unchanged?
(sounds reasonable, but is there any good arguments?)
2) I can see that a half integer spin 'force-carrier' would change the spin
of both the internal states by _half_ an integer, but
wouldn't also an integer spin 'force-carrier' change the spin of the
particles 'feeling the force' (now with a _full_ integer instead)?
/Michael
Rahul Jain
Jul20-04, 04:25 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"Snebula" <x@x.x> writes:\n\n> Hi,\n> How does one explain that every particle associated with a force\n> (\'force-carrier\') must have integer spin?\n\nAs a further question, I was reading the rebuttal by Carlip of TvF\'s\nspeed of gravity claim and started wondering what a spin-3 field would\nbe like.\n\nAlso, I read somewhere else (possibly this NG) that a spin-1 field\ncauses like charges to repel and unlike charges to attract. (The fact\nthat gravity is spin-2 is related to the fact that it causes like\ncharges to attract.) However, the strong force causes _all_ color charge\nto attract, as far as I can tell. Is that wrong?\n\n--\nRahul Jain\nrjain@nyct.net\nProfessional Software Developer, Amateur Quantum Mechanicist\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>"Snebula" <x@x.x> writes:
> Hi,
> How does one explain that every particle associated with a force
> ('force-carrier') must have integer spin?
As a further question, I was reading the rebuttal by Carlip of TvF's
speed of gravity claim and started wondering what a spin-3 field would
be like.
Also, I read somewhere else (possibly this NG) that a spin-1 field
causes like charges to repel and unlike charges to attract. (The fact
that gravity is spin-2 is related to the fact that it causes like
charges to attract.) However, the strong force causes _all_ color charge
to attract, as far as I can tell. Is that wrong?
--
Rahul Jain
rjain@nyct.net
Professional Software Developer, Amateur Quantum Mechanicist
Kefka G
Jul20-04, 04:25 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>\nFrom: "Snebula" x@x.x\n>\n>Hi,\n>How does one explain that every particle associated with a force\n>(\'force-carrier\') must have integer spin?\n>\n>I have read the following in "Feynman Lectures on Gravitation." (for the\n>special case of a graviton):\n>\n>"In order to produce a _static_ force and not just scattering, the\n>emission or absorption of a single graviton by either particle must\n>leave both particles in the same internal state. This rules out the\n>possibility that the graviton carries half-integer spin (for example,\n>related to the fact that it takes a rotation of 720 degrees to return a\n>spin-1/2 wavefunction back to itself). Therefore the graviton must\n>have integer spin." ...\n>\n>1) Why must the internal state of both particles feeling the force be left\n>unchanged?\n> (sounds reasonable, but is there any good arguments?)\n>\n\nIf the internal state of the particle were changed, then you\'d really be\ndealing with some sort of complicated scattering process, not a simple static\nforce. But I don\'t have a really good answer to this, so maybe someone else\ncan answer that. (Actually, don\'t we get a distance-dependent force from\nvirtual electron exchange in atoms? I understand that this will necessarily be\nmore complicated a process than for instance Coulomb interaction - perhaps\nFeynman has a particular definition of "static force" in mind that doesn\'t\ninclude this case)\n\n>2) I can see that a half integer spin \'force-carrier\' would change the spin\n>of both the internal states by _half_ an integer, but\n>wouldn\'t also an integer spin \'force-carrier\' change the spin of the\n>particles \'feeling the force\' (now with a _full_ integer instead)?\n>\n\nDon\'t forget, though, when you\'re adding two particles with spin together, you\ncan\'t just add the absolute values of the spins together and come up with a new\nspin. This doesn\'t even work classically - you have to consider what axes the\nangular momenta are about. Of course, quantum mechanically, the rules are a\nbit more complicated, as you probably know (go to any quantum mechanics\ntextbook if you don\'t, although I doubt if you\'d be reading Feynman\'s gravity\nbook in that case). Consider the projection of the spin on the z-axis - for a\nhalf integer spin particle, this can only be +1/2 or -1/2, but for a spin 1\nparticle, it can be +1, -1, or 0. Hence there\'s always the possibility that if\nyou exchange a spin 1 particle, there will be no change in the z component of\nangular momentum, whereas with spin 1/2, there has to be a change no matter\nwhat. You can look at the total angular momentum squared, too, and find a\nsimilar result - fermion exchange always alters the total, boson exchange can\neither change it or leave it alone. We\'re concerned with the latter\npossibility.\n\nAlso, I\'d suggest putting down the Feynman book once he gets to the usual\nEinstein equation and finding a normal GR text - I\'d suggest Wald, but everyone\nhas their own preference. I also liked Misner, Thorne and Wheeler, but it\'s\nrather heavy (by which I mean it weighs way too much, of course, although some\nof the material is pretty dense, too).\n\n-Eric\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>From: "Snebula" x@x.x
>
>Hi,
>How does one explain that every particle associated with a force
>('force-carrier') must have integer spin?
>
>I have read the following in "Feynman Lectures on Gravitation." (for the
>special case of a graviton):
>
>"In order to produce a _static_ force and not just scattering, the
>emission or absorption of a single graviton by either particle must
>leave both particles in the same internal state. This rules out the
>possibility that the graviton carries half-integer spin (for example,
>related to the fact that it takes a rotation of 720 degrees to return a
>spin-1/2 wavefunction back to itself). Therefore the graviton must
>have integer spin." ...
>
>1) Why must the internal state of both particles feeling the force be left
>unchanged?
> (sounds reasonable, but is there any good arguments?)
>
If the internal state of the particle were changed, then you'd really be
dealing with some sort of complicated scattering process, not a simple static
force. But I don't have a really good answer to this, so maybe someone else
can answer that. (Actually, don't we get a distance-dependent force from
virtual electron exchange in atoms? I understand that this will necessarily be
more complicated a process than for instance Coulomb interaction - perhaps
Feynman has a particular definition of "static force" in mind that doesn't
include this case)
>2) I can see that a half integer spin 'force-carrier' would change the spin
>of both the internal states by _half_ an integer, but
>wouldn't also an integer spin 'force-carrier' change the spin of the
>particles 'feeling the force' (now with a _full_ integer instead)?
>
Don't forget, though, when you're adding two particles with spin together, you
can't just add the absolute values of the spins together and come up with a new
spin. This doesn't even work classically - you have to consider what axes the
angular momenta are about. Of course, quantum mechanically, the rules are a
bit more complicated, as you probably know (go to any quantum mechanics
textbook if you don't, although I doubt if you'd be reading Feynman's gravity
book in that case). Consider the projection of the spin on the z-axis - for a
half integer spin particle, this can only be +1/2 or -1/2, but for a spin 1
particle, it can be +1, -1, or . Hence there's always the possibility that if
you exchange a spin 1 particle, there will be no change in the z component of
angular momentum, whereas with spin 1/2, there has to be a change no matter
what. You can look at the total angular momentum squared, too, and find a
similar result - fermion exchange always alters the total, boson exchange can
either change it or leave it alone. We're concerned with the latter
possibility.
Also, I'd suggest putting down the Feynman book once he gets to the usual
Einstein equation and finding a normal GR text - I'd suggest Wald, but everyone
has their own preference. I also liked Misner, Thorne and Wheeler, but it's
rather heavy (by which I mean it weighs way too much, of course, although some
of the material is pretty dense, too).
-Eric
Torbj?rn Larsson
Jul22-04, 02:28 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>\nkefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...\n> From: "Snebula" x@x.x\n> >\n> >Hi,\n> >How does one explain that every particle associated with a force\n> >(\'force-carrier\') must have integer spin?\n\nThis question has interested me quite some time, since no readily\npresented answer seem to be available, and this would be a good time\nto learn more.\n\n> >\n> >I have read the following in "Feynman Lectures on Gravitation." (for the\n> >special case of a graviton):\n> >\n> >"In order to produce a _static_ force and not just scattering, the\n> >emission or absorption of a single graviton by either particle must\n> >leave both particles in the same internal state. This rules out the\n> >possibility that the graviton carries half-integer spin (for example,\n> >related to the fact that it takes a rotation of 720 degrees to return a\n> >spin-1/2 wavefunction back to itself). Therefore the graviton must\n> >have integer spin." ...\n....\n>\n> >2) I can see that a half integer spin \'force-carrier\' would change the spin\n> >of both the internal states by _half_ an integer, but\n> >wouldn\'t also an integer spin \'force-carrier\' change the spin of the\n> >particles \'feeling the force\' (now with a _full_ integer instead)?\n> >\n>\n> Don\'t forget, though, when you\'re adding two particles with spin together, you\n> can\'t just add the absolute values of the spins together and come up with a new\n> spin. This doesn\'t even work classically - you have to consider what axes the\n> angular momenta are about. Of course, quantum mechanically, the rules are a\n> bit more complicated, as you probably know (go to any quantum mechanics\n> textbook if you don\'t, although I doubt if you\'d be reading Feynman\'s gravity\n> book in that case). Consider the projection of the spin on the z-axis - for a\n> half integer spin particle, this can only be +1/2 or -1/2, but for a spin 1\n> particle, it can be +1, -1, or 0. Hence there\'s always the possibility that if\n> you exchange a spin 1 particle, there will be no change in the z component of\n> angular momentum, whereas with spin 1/2, there has to be a change no matter\n> what. You can look at the total angular momentum squared, too, and find a\n> similar result - fermion exchange always alters the total, boson exchange can\n> either change it or leave it alone. We\'re concerned with the latter\n> possibility.\n....\n>\n> -Eric\n\nIs the explanation selfconsistent though? For example, in a uniform\nfield the degeneracy in the momenta should not be removed, so all\nexchanges should be equally possible and some would lead to scattering\nas per Eric argument. Could it be that Feyman is handwaving here?\n\nI would also like to know if there are a stronger argument without\ninvolving the fields interaction with matter. Can\'t find anything in\nthe FAQs, but Wikipedia says "Because bosons do not obey the Pauli\nexclusion principle, it is much harder to form stable structures with\nbosons than with fermions. This difference accounts for the difference\nbetween what we think of as matter and things that are not matter such\nas light."\n\nIf I had a stab at it myself (not up to QFT yet; any year now, though)\nI would have guessed that anti-symmetric wave functions (exclusion)\nwould prohibit (linear) superposition of fields at all times; which at\nleast EM and NG possess visavi the sources (q,m) as far as I know.\n(Darn, I had to involve interactions too.) Hmm, Wikipedias argument\nseems more general. Can such a simple argument do?\n\n/Torbjörn Larsson\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>kefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...
> From: "Snebula" x@x.x
> >
> >Hi,
> >How does one explain that every particle associated with a force
> >('force-carrier') must have integer spin?
This question has interested me quite some time, since no readily
presented answer seem to be available, and this would be a good time
to learn more.
> >
> >I have read the following in "Feynman Lectures on Gravitation." (for the
> >special case of a graviton):
> >
> >"In order to produce a _static_ force and not just scattering, the
> >emission or absorption of a single graviton by either particle must
> >leave both particles in the same internal state. This rules out the
> >possibility that the graviton carries half-integer spin (for example,
> >related to the fact that it takes a rotation of 720 degrees to return a
> >spin-1/2 wavefunction back to itself). Therefore the graviton must
> >have integer spin." ...
....
>
> >2) I can see that a half integer spin 'force-carrier' would change the spin
> >of both the internal states by _half_ an integer, but
> >wouldn't also an integer spin 'force-carrier' change the spin of the
> >particles 'feeling the force' (now with a _full_ integer instead)?
> >
>
> Don't forget, though, when you're adding two particles with spin together, you
> can't just add the absolute values of the spins together and come up with a new
> spin. This doesn't even work classically - you have to consider what axes the
> angular momenta are about. Of course, quantum mechanically, the rules are a
> bit more complicated, as you probably know (go to any quantum mechanics
> textbook if you don't, although I doubt if you'd be reading Feynman's gravity
> book in that case). Consider the projection of the spin on the z-axis - for a
> half integer spin particle, this can only be +1/2 or -1/2, but for a spin 1
> particle, it can be +1, -1, or . Hence there's always the possibility that if
> you exchange a spin 1 particle, there will be no change in the z component of
> angular momentum, whereas with spin 1/2, there has to be a change no matter
> what. You can look at the total angular momentum squared, too, and find a
> similar result - fermion exchange always alters the total, boson exchange can
> either change it or leave it alone. We're concerned with the latter
> possibility.
....
>
> -Eric
Is the explanation selfconsistent though? For example, in a uniform
field the degeneracy in the momenta should not be removed, so all
exchanges should be equally possible and some would lead to scattering
as per Eric argument. Could it be that Feyman is handwaving here?
I would also like to know if there are a stronger argument without
involving the fields interaction with matter. Can't find anything in
the FAQs, but Wikipedia says "Because bosons do not obey the Pauli
exclusion principle, it is much harder to form stable structures with
bosons than with fermions. This difference accounts for the difference
between what we think of as matter and things that are not matter such
as light."
If I had a stab at it myself (not up to QFT yet; any year now, though)
I would have guessed that anti-symmetric wave functions (exclusion)
would prohibit (linear) superposition of fields at all times; which at
least EM and NG possess visavi the sources (q,m) as far as I know.
(Darn, I had to involve interactions too.) Hmm, Wikipedias argument
seems more general. Can such a simple argument do?
/Torbjörn Larsson
alistair
Jul23-04, 06:35 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\nkefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...\n> From: "Snebula" x@x.x\n> >\n> >Hi,\n> >How does one explain that every particle associated with a force\n> >(\'force-carrier\') must have integer spin?\n\nAlistair writes:\n\nThis is how I think about it:\n\nSuppose a force -carrier had spin 1/2 like a fermion.\nFermions can have one of two spin orientations in magnetic fields\nwhich correspond to different energies in the field.\nIf a force-carrier was spin 1/2 for the attraction between\nelectric charges, then the electric force would\ndepend on the magnetic field strength which isn\'t observed\nexperimentally.\nAlso spin 1/2 particles obey Fermi-Dirac statistics and so\nforce-carriers with\nspin 1/2 would scatter off one another a great deal compared to spin 1\ncarriers\nand this would make the electric force different for large\naggregations of particles than is observed.\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>kefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...
> From: "Snebula" x@x.x
> >
> >Hi,
> >How does one explain that every particle associated with a force
> >('force-carrier') must have integer spin?
Alistair writes:
This is how I think about it:
Suppose a force -carrier had spin 1/2 like a fermion.
Fermions can have one of two spin orientations in magnetic fields
which correspond to different energies in the field.
If a force-carrier was spin 1/2 for the attraction between
electric charges, then the electric force would
depend on the magnetic field strength which isn't observed
experimentally.
Also spin 1/2 particles obey Fermi-Dirac statistics and so
force-carriers with
spin 1/2 would scatter off one another a great deal compared to spin 1
carriers
and this would make the electric force different for large
aggregations of particles than is observed.
Torbj?rn Larsson
Jul23-04, 11:29 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>\nalistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407221137.1b7992e1@posting.google.com>...\n> kefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...\n> > From: "Snebula" x@x.x\n> > >\n> > >Hi,\n> > >How does one explain that every particle associated with a force\n> > >(\'force-carrier\') must have integer spin?\n>\n> Alistair writes:\n>\n> This is how I think about it:\n>\n> Suppose a force -carrier had spin 1/2 like a fermion.\n> Fermions can have one of two spin orientations in magnetic fields\n> which correspond to different energies in the field.\n> If a force-carrier was spin 1/2 for the attraction between\n> electric charges, then the electric force would\n> depend on the magnetic field strength which isn\'t observed\n> experimentally.\n\nThis should be the fourth independent explanation; thank you alistair!\nIt should be useful for vector field theories like EM and NG since\nthey have a magnetic field component (Panofsky-Phillips Classical\nElectricity and Magnetism, treatment of Lagrangian for vector fields,\npp 451-452) as far as I understand it.\n\n> Also spin 1/2 particles obey Fermi-Dirac statistics and so\n> force-carriers with\n> spin 1/2 would scatter off one another a great deal compared to spin 1\n> carriers\n> and this would make the electric force different for large\n> aggregations of particles than is observed.\n\nThis seems to be close to my own argument but stated by a more\nstraightthinking mind. However I don\'t see here how the connection is\nmade between large aggregations of particles (large field strengths\nand/or close to sources, presumably) and observations.\n\nAlso these arguments come back to my feeling that Feynman was\nhandwaving (and not consistent) and the only general argument so far\nseems to be that matter can build complex structures in lieu of the\nexclusion principle because of fermion components; thus forces must\nhave bosons only?! (Ducking from replies thrown around arguing that\nforce theories like LQG does have complexities. :-)\n\n/Torbjörn Larsson\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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0407221137.1b7992e1@posting.google.com>...
> kefkag@aol.com (Kefka G) wrote in message news:<20040719142011.29796.00001594@mb-m18.aol.com>...
> > From: "Snebula" x@x.x
> > >
> > >Hi,
> > >How does one explain that every particle associated with a force
> > >('force-carrier') must have integer spin?
>
> Alistair writes:
>
> This is how I think about it:
>
> Suppose a force -carrier had spin 1/2 like a fermion.
> Fermions can have one of two spin orientations in magnetic fields
> which correspond to different energies in the field.
> If a force-carrier was spin 1/2 for the attraction between
> electric charges, then the electric force would
> depend on the magnetic field strength which isn't observed
> experimentally.
This should be the fourth independent explanation; thank you alistair!
It should be useful for vector field theories like EM and NG since
they have a magnetic field component (Panofsky-Phillips Classical
Electricity and Magnetism, treatment of Lagrangian for vector fields,
pp 451-452) as far as I understand it.
> Also spin 1/2 particles obey Fermi-Dirac statistics and so
> force-carriers with
> spin 1/2 would scatter off one another a great deal compared to spin 1
> carriers
> and this would make the electric force different for large
> aggregations of particles than is observed.
This seems to be close to my own argument but stated by a more
straightthinking mind. However I don't see here how the connection is
made between large aggregations of particles (large field strengths
and/or close to sources, presumably) and observations.
Also these arguments come back to my feeling that Feynman was
handwaving (and not consistent) and the only general argument so far
seems to be that matter can build complex structures in lieu of the
exclusion principle because of fermion components; thus forces must
have bosons only?! (Ducking from replies thrown around arguing that
force theories like LQG does have complexities. :-)
/Torbjörn Larsson
Thomas Dent
Jul26-04, 11:32 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>\n\n\n"Snebula" <x@x.x> wrote\n\n> Hi,\n> How does one explain that every particle associated with a force\n> (\'force-carrier\') must have integer spin?\n>\n> I have read the following in "Feynman Lectures on Gravitation." (for the\n> special case of a graviton):\n>\n> "In order to produce a _static_ force and not just scattering, the\n> emission or absorption of a single graviton by either particle must\n> leave both particles in the same internal state. This rules out the\n> possibility that the graviton carries half-integer spin (for example,\n> related to the fact that it takes a rotation of 720 degrees to return a\n> spin-1/2 wavefunction back to itself). Therefore the graviton must\n> have integer spin." ...\n>\n> 1) Why must the internal state of both particles feeling the force be left\n> unchanged?\n> (sounds reasonable, but is there any good arguments?)\n\nI don\'t entirely understand what "internal state" means here, but it\nis probably something to do with the *static* nature of the force.\nWhat we observe when particles are acted on by a static force (grav.\nfield, electric field, etc.) is that they *don\'t* change internal\nstate, and certainly don\'t change from fermion to boson and vice\nversa. Hence, in order to have a chance of describing what is\nobserved, we need a \'messenger\' particle which can interact without\nchanging the matter particle into something different.\n\n> 2) I can see that a half integer spin \'force-carrier\' would change the spin\n> of both the internal states by _half_ an integer, but\n> wouldn\'t also an integer spin \'force-carrier\' change the spin of the\n> particles \'feeling the force\' (now with a _full_ integer instead)?\n\nTo be a bit more technical here, a vector (spin 1) force-carrier\ncouples to a vector current, a tensor (spin 2) force-carrier couples\nto the energy-momentum tensor, etc. The question is (for example) if\nthe incoming particle and the outgoing particle are in the same spin\nstate (s_o-s_i=0), how can a vector couple to them? There are two\nthings one could say here: first, that a massive vector (or tensor)\nalso has spin zero component. But, for a massless messenger particle,\nthere are only spin-1 (vector) or spin-2 (tensor) components, so that\nis out.\n\nI think the real answer is that the messenger couples to the spacetime\n*derivative* of one or more matter fields. The derivative operator is\nspin-1, so you can use derivatives to build a spin-1 or -2 current.\nNow, this means that, roughly, the vector or tensor only couples to\nthe *change* in energy-momentum of the particle between incoming and\noutgoing. That is, precisely the impulse, the integral of the force!\nNow, this impulse or change in energy-momentum is a vector, even\nthough the particle spins themselves do not change. Or one can also\nbuild a tensor quantity out of it.\n\nOf course, if the particle is in *exactly* the same state incoming and\noutgoing, nothing has happened at all and there is no force. It kind\nof makes sense that a vector or tensor force-carrier couples to a\nparticle if and only if its energy-momentum is changing.\n\nIn equations: L ~ A_mu J^mu where J^mu is the vector current:\n\nJ^mu ~ psi-bar d^mu psi - here is the derivative d^mu, which gives the\nmomentum operator p^mu acting on momentum eigenstates. When you put\nthis into the matrix element it enforces that the difference between\nthe incoming and outgoing fermion momenta should be P^mu, the momentum\ntransfer.\n\nGravity is a bit more complicated, though...\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>"Snebula" <x@x.x> wrote
> Hi,
> How does one explain that every particle associated with a force
> ('force-carrier') must have integer spin?
>
> I have read the following in "Feynman Lectures on Gravitation." (for the
> special case of a graviton):
>
> "In order to produce a _static_ force and not just scattering, the
> emission or absorption of a single graviton by either particle must
> leave both particles in the same internal state. This rules out the
> possibility that the graviton carries half-integer spin (for example,
> related to the fact that it takes a rotation of 720 degrees to return a
> spin-1/2 wavefunction back to itself). Therefore the graviton must
> have integer spin." ...
>
> 1) Why must the internal state of both particles feeling the force be left
> unchanged?
> (sounds reasonable, but is there any good arguments?)
I don't entirely understand what "internal state" means here, but it
is probably something to do with the *static* nature of the force.
What we observe when particles are acted on by a static force (grav.
field, electric field, etc.) is that they *don't* change internal
state, and certainly don't change from fermion to boson and vice
versa. Hence, in order to have a chance of describing what is
observed, we need a 'messenger' particle which can interact without
changing the matter particle into something different.
> 2) I can see that a half integer spin 'force-carrier' would change the spin
> of both the internal states by _half_ an integer, but
> wouldn't also an integer spin 'force-carrier' change the spin of the
> particles 'feeling the force' (now with a _full_ integer instead)?
To be a bit more technical here, a vector (spin 1) force-carrier
couples to a vector current, a tensor (spin 2) force-carrier couples
to the energy-momentum tensor, etc. The question is (for example) if
the incoming particle and the outgoing particle are in the same spin
state (s_o-s_i=0), how can a vector couple to them? There are two
things one could say here: first, that a massive vector (or tensor)
also has spin zero component. But, for a massless messenger particle,
there are only spin-1 (vector) or spin-2 (tensor) components, so that
is out.
I think the real answer is that the messenger couples to the spacetime
*derivative* of one or more matter fields. The derivative operator is
spin-1, so you can use derivatives to build a spin-1 or -2 current.
Now, this means that, roughly, the vector or tensor only couples to
the *change* in energy-momentum of the particle between incoming and
outgoing. That is, precisely the impulse, the integral of the force!
Now, this impulse or change in energy-momentum is a vector, even
though the particle spins themselves do not change. Or one can also
build a tensor quantity out of it.
Of course, if the particle is in *exactly* the same state incoming and
outgoing, nothing has happened at all and there is no force. It kind
of makes sense that a vector or tensor force-carrier couples to a
particle if and only if its energy-momentum is changing.
In equations: L ~ A_{mu} J^\mu where J^\mu is the vector current:
J^\mu ~ \psi-bar d^\mu \psi - here is the derivative d^\mu, which gives the
momentum operator p^\mu acting on momentum eigenstates. When you put
this into the matrix element it enforces that the difference between
the incoming and outgoing fermion momenta should be P^\mu, the momentum
transfer.
Gravity is a bit more complicated, though...
Kefka G
Jul27-04, 08:52 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>\n\n>From alistair:\n>kefkag@aol.com (Kefka G) wrote in message\n>news:<20040719142011.29796.00001594@mb-m18.aol.com>...\n>> From: "Snebula" x@x.x\n>> >\n>> >Hi,\n>> >How does one explain that every particle associated with a force\n>> >(\'force-carrier\') must have integer spin?\n>\n> Alistair writes:\n>\n>This is how I think about it:\n>\n>Suppose a force -carrier had spin 1/2 like a fermion.\n>Fermions can have one of two spin orientations in magnetic fields\n>which correspond to different energies in the field.\n>If a force-carrier was spin 1/2 for the attraction between\n>electric charges, then the electric force would\n>depend on the magnetic field strength which isn\'t observed\n>experimentally.\n>Also spin 1/2 particles obey Fermi-Dirac statistics and so\n>force-carriers with\n>spin 1/2 would scatter off one another a great deal compared to spin 1\n>carriers\n>and this would make the electric force different for large\n>aggregations of particles than is observed.\n\nOk, I agree that they would scatter more often due to an antisymmetrization\nforce, but I don\'t think spin 1/2 necessarily implies that the particle has two\ndifferent energies in a magnetic field - that would assume that all spin 1/2\nparticles have a magnetic dipole moment. If you applied the same logic to spin\n1, you\'d say "if the force carrier was spin 1, there would be three energetic\npossibilities in a magnetic field, thus the electric force would depend on the\nmagnetic field, etc..." which clearly isn\'t true. I\'m also not positive that\nFermi-Dirac statistics alone would entirely preclude the possibility of a\n"static force" in the sense of Feynman (which we haven\'t really defined yet, by\nthe way) - covalent bonds work exactly through exchange of electrons, so I\nguess if we settle on a definition, it would have to be such as to eliminate\nthat case (perhaps since the "particles" there are actually atoms, with many\nparts, that is enough to eliminate it). In the case of the covalent bond, the\nforce is ENTIRELY due to the Fermi-Dirac statistics, so I don\'t think we can\nsay much based on that alone.\n\n-Eric\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>>From alistair:
>kefkag@aol.com (Kefka G) wrote in message
>news:<20040719142011.29796.00001594@mb-m18.aol.com>...
>> From: "Snebula" x@x.x
>> >
>> >Hi,
>> >How does one explain that every particle associated with a force
>> >('force-carrier') must have integer spin?
>
> Alistair writes:
>
>This is how I think about it:
>
>Suppose a force -carrier had spin 1/2 like a fermion.
>Fermions can have one of two spin orientations in magnetic fields
>which correspond to different energies in the field.
>If a force-carrier was spin 1/2 for the attraction between
>electric charges, then the electric force would
>depend on the magnetic field strength which isn't observed
>experimentally.
>Also spin 1/2 particles obey Fermi-Dirac statistics and so
>force-carriers with
>spin 1/2 would scatter off one another a great deal compared to spin 1
>carriers
>and this would make the electric force different for large
>aggregations of particles than is observed.
Ok, I agree that they would scatter more often due to an antisymmetrization
force, but I don't think spin 1/2 necessarily implies that the particle has two
different energies in a magnetic field - that would assume that all spin 1/2
particles have a magnetic dipole moment. If you applied the same logic to spin
1, you'd say "if the force carrier was spin 1, there would be three energetic
possibilities in a magnetic field, thus the electric force would depend on the
magnetic field, etc..." which clearly isn't true. I'm also not positive that
Fermi-Dirac statistics alone would entirely preclude the possibility of a
"static force" in the sense of Feynman (which we haven't really defined yet, by
the way) - covalent bonds work exactly through exchange of electrons, so I
guess if we settle on a definition, it would have to be such as to eliminate
that case (perhaps since the "particles" there are actually atoms, with many
parts, that is enough to eliminate it). In the case of the covalent bond, the
force is ENTIRELY due to the Fermi-Dirac statistics, so I don't think we can
say much based on that alone.