View Full Version : Why gravity is incompatible with quantum theory?
Todd Pellman
Jul15-04, 02:23 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\nEverybody knows there are problems formulating a quantum theory of\ngravity, but what are those problems? Could someone please recommend\na text or article that discusses them in detail?\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>Everybody knows there are problems formulating a quantum theory of
gravity, but what are those problems? Could someone please recommend
a text or article that discusses them in detail?
mathman
Jul16-04, 08:20 AM
Brian Greene's latest book discusses this problem in some detail. The essential point is that in regimes where you need to consider both (black holes or the universe at the time of the big bang), the analytical results are nonsensical.
Uncle Al
Jul16-04, 08:20 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\nTodd Pellman wrote:\n>\n> Everybody knows there are problems formulating a quantum theory of\n> gravity, but what are those problems? Could someone please recommend\n> a text or article that discusses them in detail?\n\nLet\'s paint with a broad brush. It is straightforward\nincompatiblity:\n\nGeneral Relativity\'s physical systems are always spatially\nseparable into independent components. Systems of three or more\nparticles require cluster separability (macroscopic locality).\nWhen the system is separated into subsystems, the overall\nmathematical description must reduce to descriptions of the\nsubsystems. This is vital in scattering problems with two or more\nfragments.\n\nQuantum mechanics allows entangled states (superpositions of\nproduct states) that require a fundamental irresolvable\nconnection within readily demonstrated physical systems (two-slit\ndiffraction, the Einstein-Podolsky-Rosen paradox). Macroscopic\nlocality is violated: Measuring the state of one slit in a double\nslit experiment alters the observed diffraction pattern to single\nslit patterns (quantum eraser experiments). Relativistic and\nquantum views are in conflict.\n\nRelativity models continuous spacetime, going beyond conformal\nsymmetry (scale independence) to symmetry under all smooth\ncoordinate transformations - general covariance (the\nstress-energy tensor embodying local energy and momentum) -\nresisting quantization. General Relativity is invariant under\ntransformations of the diffeomorphism group. General Relativity\npredicts evolution of an initial system state with arbitrary\ncertainty.\n\nQuantum mechanics\' observables display discrete states.\nHeisenberg\'s Uncertainty Principle limits knowledge about\nconjugate variables in a system state, disallowing exact\nprediction of its evolution. Covariance with respect to\nreflection in space and time is not required by the Poincare\ngroup of Special Relativity or the Einstein group of General\nRelativity.\n\nLoop quantum theory, brane/string/M-theory, and Lorentzian\nlattice quantum gravity all fail at being testable by prediction\nvs. observation. They are formulated to be parity-even, (x,y,z)\nand(-x,-y,-z) giving identical answers. If the were an empirical\ngravitational parity anomaly, of the three only a small piece of\nM-theory would survive. That alone is powerful incentive to\nperform the parity Eotvos experiment.\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>Todd Pellman wrote:
>
> Everybody knows there are problems formulating a quantum theory of
> gravity, but what are those problems? Could someone please recommend
> a text or article that discusses them in detail?
Let's paint with a broad brush. It is straightforward
incompatiblity:
General Relativity's physical systems are always spatially
separable into independent components. Systems of three or more
particles require cluster separability (macroscopic locality).
When the system is separated into subsystems, the overall
mathematical description must reduce to descriptions of the
subsystems. This is vital in scattering problems with two or more
fragments.
Quantum mechanics allows entangled states (superpositions of
product states) that require a fundamental irresolvable
connection within readily demonstrated physical systems (two-slit
diffraction, the Einstein-Podolsky-Rosen paradox). Macroscopic
locality is violated: Measuring the state of one slit in a double
slit experiment alters the observed diffraction pattern to single
slit patterns (quantum eraser experiments). Relativistic and
quantum views are in conflict.
Relativity models continuous spacetime, going beyond conformal
symmetry (scale independence) to symmetry under all smooth
coordinate transformations - general covariance (the
stress-energy tensor embodying local energy and momentum) -
resisting quantization. General Relativity is invariant under
transformations of the diffeomorphism group. General Relativity
predicts evolution of an initial system state with arbitrary
certainty.
Quantum mechanics' observables display discrete states.
Heisenberg's Uncertainty Principle limits knowledge about
conjugate variables in a system state, disallowing exact
prediction of its evolution. Covariance with respect to
reflection in space and time is not required by the Poincare
group of Special Relativity or the Einstein group of General
Relativity.
Loop quantum theory, brane/string/M-theory, and Lorentzian
lattice quantum gravity all fail at being testable by prediction
vs. observation. They are formulated to be parity-even, (x,y,z)
and(-x,-y,-z) giving identical answers. If the were an empirical
gravitational parity anomaly, of the three only a small piece of
M-theory would survive. That alone is powerful incentive to
perform the parity Eotvos experiment.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Peter Shor
Jul16-04, 11:17 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>\nt_pellman@hotmail.com (Todd Pellman) wrote in message news:<3aea8311.0407150746.69bb25e7@posting.google. com>...\n> Everybody knows there are problems formulating a quantum theory of\n> gravity, but what are those problems? Could someone please recommend\n> a text or article that discusses them in detail?\n\nI went to a talk by t\'Hooft that addressed this question. This isn\'t\nmy area, so I may get things wrong, but I haven\'t seen what he said\nmentioned anywhere else so I\'ll mention it here anyway.\n\nIn order to get around all the inconsistencies that plague the\nperturbation expansions of quantum field theories, it\'s good to\nuse quantum field theories that are renormalizable (especially\nsince all the predictions come from perturbation expansions, and\nif you have a non-renormalizable quantum field theory, there\'s no\nway of getting reasonable perturbation expansions from it).\nUnfortunately, people can show that there are no renormalizable\n3+1 dimensional quantum field theories containing a spin-2 graviton,\nwhich is the elementary particle you need to carry the force of\ngravity. Now, t\'Hooft decided to look at perturbation expansions\nanyway, and discovered that in the first order perturbation expansion\nfor quantum gravity, there\'s only one free constant. And for low\norder expansions, there are only a small number of extra free\nconstants. Of course, for the full theory, you still have an\ninfinite number of free constants rather than the finite number you\nfind in renormalizable quantum field theories, which is somewhat\ndisturbing; but he seemed to think this might be a useful approach\nnonetheless.\n\nI\'d be happy if somebody who really knows what they\'re talking\nabout elaborates on this.\n\nAnother fundamental difficulty of unifying quantum mechanics and gravity\nis that quantum mechanics has as one of its most fundamental assumptions\nthat the universe is unitary, so no information is ever fundamentally lost.\nGeneral relativity seems to say that when you toss something in a black\nhole, the only information about that something that survives is its\nmass, its charge, and its angular momentum (and of course, any classical\nrecords that mention it). And it says this pretty convincingly, so,\nbarring Hawking\'s lecture next week, nobody has come up with a convincing\nmechanism for getting information out of a black hole, a necessary\nprerequisite for reconciling GR with QM.\n\nString theorists are absolutely convinced that the universe is unitary,\nbut none of them has been able to convince me that it\'s impossible for\nthe universe to be non-unitary at the Planck scale and still look very,\nvery close to unitary at experimental scales. A couple of them have\ntried to, but these attempts generally involve a lot of waving of hands\nand words like "in the generic case," and arguments along the same lines\nwould seem to imply that quantum error correction is impossible, and\nthat\'s something I know is wrong.\n\nI\'ll be very interested to hear reports of Hawking\'s lecture next week.\n\n\nPeter Shor\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>t_{pellman}@hotmail.com (Todd Pellman) wrote in message news:<3aea8311.0407150746.69bb25e7@posting.google.com>...
> Everybody knows there are problems formulating a quantum theory of
> gravity, but what are those problems? Could someone please recommend
> a text or article that discusses them in detail?
I went to a talk by t'Hooft that addressed this question. This isn't
my area, so I may get things wrong, but I haven't seen what he said
mentioned anywhere else so I'll mention it here anyway.
In order to get around all the inconsistencies that plague the
perturbation expansions of quantum field theories, it's good to
use quantum field theories that are renormalizable (especially
since all the predictions come from perturbation expansions, and
if you have a non-renormalizable quantum field theory, there's no
way of getting reasonable perturbation expansions from it).
Unfortunately, people can show that there are no renormalizable
3+1 dimensional quantum field theories containing a spin-2 graviton,
which is the elementary particle you need to carry the force of
gravity. Now, t'Hooft decided to look at perturbation expansions
anyway, and discovered that in the first order perturbation expansion
for quantum gravity, there's only one free constant. And for low
order expansions, there are only a small number of extra free
constants. Of course, for the full theory, you still have an
infinite number of free constants rather than the finite number you
find in renormalizable quantum field theories, which is somewhat
disturbing; but he seemed to think this might be a useful approach
nonetheless.
I'd be happy if somebody who really knows what they're talking
about elaborates on this.
Another fundamental difficulty of unifying quantum mechanics and gravity
is that quantum mechanics has as one of its most fundamental assumptions
that the universe is unitary, so no information is ever fundamentally lost.
General relativity seems to say that when you toss something in a black
hole, the only information about that something that survives is its
mass, its charge, and its angular momentum (and of course, any classical
records that mention it). And it says this pretty convincingly, so,
barring Hawking's lecture next week, nobody has come up with a convincing
mechanism for getting information out of a black hole, a necessary
prerequisite for reconciling GR with QM.
String theorists are absolutely convinced that the universe is unitary,
but none of them has been able to convince me that it's impossible for
the universe to be non-unitary at the Planck scale and still look very,
very close to unitary at experimental scales. A couple of them have
tried to, but these attempts generally involve a lot of waving of hands
and words like "in the generic case," and arguments along the same lines
would seem to imply that quantum error correction is impossible, and
that's something I know is wrong.
I'll be very interested to hear reports of Hawking's lecture next week.
Peter Shor
FrediFizzx
Jul19-04, 03:18 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"Todd Pellman" <t_pellman@hotmail.com> wrote in message\nnews:3aea8311.0407150746.69bb25e7@posting .google.com...\n|\n|\n| Everybody knows there are problems formulating a quantum theory of\n| gravity, but what are those problems? Could someone please recommend\n| a text or article that discusses them in detail?\n\nHere is a fun one by Carlo Rovelli.\n\nhttp://www.arxiv.org/abs/hep-th/0310077\n\nSearch arXiv for more Rovelli. Fascinating stuff!\n\nFrediFizzx\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>"Todd Pellman" <t_{pellman}@hotmail.com> wrote in message
news:3aea8311.0407150746.69bb25e7@posting.google.c om...
|
|
| Everybody knows there are problems formulating a quantum theory of
| gravity, but what are those problems? Could someone please recommend
| a text or article that discusses them in detail?
Here is a fun one by Carlo Rovelli.
http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0310077
Search arXiv for more Rovelli. Fascinating stuff!
FrediFizzx
arivero
Jul20-04, 03:51 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>\nHi Todd,\n\nA point of incompatibility is that in quantum theory, an attractive\nforce such as gravity needs of a spin 2 particle, so you need an action\nprinciple containing it. The standard one, Einstein-Hilbert action,\ndoes not work because it is non renormalizable; it drives to\nuncontrolled infinities.\n\nAlso it can be said, more simplistic way, that the coupling constant of\ngravity is not a number without dimensions, so one expects it to be an\neffective theory, just an approximation to a less problematic one, as\nit happened with the other known coupling constant having this problem,\nthe electroweak Fermi constant.\n\n\n\nUniv Zaragoza, PhD Science------------------------------------------------------------------------\nThis post submitted through the LaTeX-enabled physicsforums.com\nTo view this post with LaTeX images:\nhttp://www.physicsforums.com/showthread.php?t=35220#post258229\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 Todd,
A point of incompatibility is that in quantum theory, an attractive
force such as gravity needs of a spin 2 particle, so you need an action
principle containing it. The standard one, Einstein-Hilbert action,
does not work because it is non renormalizable; it drives to
uncontrolled infinities.
Also it can be said, more simplistic way, that the coupling constant of
gravity is not a number without dimensions, so one expects it to be an
effective theory, just an approximation to a less problematic one, as
it happened with the other known coupling constant having this problem,
the electroweak Fermi constant.
Univ Zaragoza, PhD Science------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
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kurious
Jul20-04, 03:51 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>\nPaul Dirac didn\'t think that electricity had been quantized properly (he\nsaid so in an interview in the 1970s after quantum field theory had\nbecome generally accepted).\nHe pointed the finger at infinities and said that although they had\nbeen removed,\nhe did not believe the correct theory that quantizes electricity would\nhave given rise to infinities in the first place.The difficulty\nquantizing gravity may stem from Dirac being right about this, although\nqft has been experimentally verified to 11 decimal places.Rather than\nqft being wrong, perhaps it just needs to be reinterpreted in a subtle\nway that can also enable the quantization of gravity.\n\n------------------------------------------------------------------------\nThis post submitted through the LaTeX-enabled physicsforums.com\nTo view this post with LaTeX images:\nhttp://www.physicsforums.com/showthread.php?t=35220#post258643\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>Paul Dirac didn't think that electricity had been quantized properly (he
said so in an interview in the 1970s after quantum field theory had
become generally accepted).
He pointed the finger at infinities and said that although they had
been removed,
he did not believe the correct theory that quantizes electricity would
have given rise to infinities in the first place.The difficulty
quantizing gravity may stem from Dirac being right about this, although
qft has been experimentally verified to 11 decimal places.Rather than
qft being wrong, perhaps it just needs to be reinterpreted in a subtle
way that can also enable the quantization of gravity.
------------------------------------------------------------------------
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Todd Pellman
Jul22-04, 12:07 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\nThanks all. So far there two published works have been referenced:\nBrian Greene\'s book and the Carlo Rovelli article. If anyone can\nsuggest a work with more mathematical detail, I would appreciate it.\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>Thanks all. So far there two published works have been referenced:
Brian Greene's book and the Carlo Rovelli article. If anyone can
suggest a work with more mathematical detail, I would appreciate it.
Everybody knows there are problems formulating a quantum theory of
gravity, but what are those problems? Could someone please recommend
a text or article that discusses them in detail?
Thanks all. So far there two published works have been referenced:
Brian Greene's book and the Carlo Rovelli article. If anyone can
suggest a work with more mathematical detail, I would appreciate it.
Rovelli's book "Quantum Gravity" is 350 pages and predominantly mathematical. It is being published by Cambridge this Fall, but an earlier draft (which may serve your purpose) is available free for download at Rovelli's website.
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
Rovelli examines in considerable technical detail the difficulties which have been experienced over more than half a century in attempts to quantize gravity.
He has a massive bibliography. Each time some approach was proven not to work he tells you who and why and cites the paper where they proved it.
"Quantum Gravity" also has non-mathematical sections, and a historical appendix, and chapters where a non-technical overview is provided. So you can probably get the level of detail you want from it.
I see someone gave a link here to some humorous writing of Rovelli--his "Dialog on Quantum Gravity" which is an imagined conversation. The person who gave the link mentioned that it's "fun". You are complaining beause "Dialog" lacks mathematical detail. Indeed it does! It is not particularly representative of Rovelli's writing, or mathematical, but it is fun.
Rovelli has a minor specialty in Science History as well as his main field of Quantum Gravity----I cant think of anyone with a clearer perspective on the long struggle to quantize gravity and the obstacles along the way.
Danny Ross Lunsford
Jul29-04, 04:59 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\nUncle Al <UncleAl0@hate.spam.net> wrote in message news:<40F6DFFD.A2049C12@hate.spam.net>...\n> Todd Pellman wrote:\n> >\n> > Everybody knows there are problems formulating a quantum theory of\n> > gravity, but what are those problems? Could someone please recommend\n> > a text or article that discusses them in detail?\n>\n> Let\'s paint with a broad brush. It is straightforward\n> incompatiblity:\n>\n> General Relativity\'s physical systems are always spatially\n> separable into independent components. Systems of three or more\n> particles require cluster separability (macroscopic locality).\n> When the system is separated into subsystems, the overall\n> mathematical description must reduce to descriptions of the\n> subsystems. This is vital in scattering problems with two or more\n> fragments.\n\nInteresting. I was going to say *the exact opposite* :) - namely\nquantum theory has good, local conservation laws, while gravity does\nnot (no tensor for the gravitational energy). So in QM you can make a\nsane equation with conserved sources on the right, but in gravity you\ncannot. The non-locality of energy guarantees a missing gauge symmetry\n(it\'s fixed by tacitly normalizing gmn).\n\nTo get to quantum gravity, this problem has to be fixed. The "quantum"\npart is incidental to the "locality" part. If gravitation had a sane\nconserved current it would most likely be easy to quantize. I have an\nexample if anyone wants to have at it.\n\n-drl\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> wrote in message news:<40F6DFFD.A2049C12@hate.spam.net>...
> Todd Pellman wrote:
> >
> > Everybody knows there are problems formulating a quantum theory of
> > gravity, but what are those problems? Could someone please recommend
> > a text or article that discusses them in detail?
>
> Let's paint with a broad brush. It is straightforward
> incompatiblity:
>
> General Relativity's physical systems are always spatially
> separable into independent components. Systems of three or more
> particles require cluster separability (macroscopic locality).
> When the system is separated into subsystems, the overall
> mathematical description must reduce to descriptions of the
> subsystems. This is vital in scattering problems with two or more
> fragments.
Interesting. I was going to say *the exact opposite* :) - namely
quantum theory has good, local conservation laws, while gravity does
not (no tensor for the gravitational energy). So in QM you can make a
sane equation with conserved sources on the right, but in gravity you
cannot. The non-locality of energy guarantees a missing gauge symmetry
(it's fixed by tacitly normalizing gmn).
To get to quantum gravity, this problem has to be fixed. The "quantum"
part is incidental to the "locality" part. If gravitation had a sane
conserved current it would most likely be easy to quantize. I have an
example if anyone wants to have at it.
-drl
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