Arnold Neumaier
Jul29-04, 11:08 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>\nPeter Shor wrote:\n> t_pellman@hotmail.com (Todd Pellman) wrote in message news:<3aea8311.0407150746.69bb25e7@posting.google. com>...\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>\n> I went to a talk by t\'Hooft that addressed this question. This isn\'t\n> my area, so I may get things wrong, but I haven\'t seen what he said\n> mentioned anywhere else so I\'ll mention it here anyway.\n>\n> In order to get around all the inconsistencies that plague the\n> perturbation expansions of quantum field theories, it\'s good to\n> use quantum field theories that are renormalizable (especially\n> since all the predictions come from perturbation expansions, and\n> if you have a non-renormalizable quantum field theory, there\'s no\n> way of getting reasonable perturbation expansions from it).\n> Unfortunately, people can show that there are no renormalizable\n> 3+1 dimensional quantum field theories containing a spin-2 graviton,\n> which is the elementary particle you need to carry the force of\n> gravity. Now, t\'Hooft decided to look at perturbation expansions\n> anyway, and discovered that in the first order perturbation expansion\n> for quantum gravity, there\'s only one free constant. And for low\n> order expansions, there are only a small number of extra free\n> constants. Of course, for the full theory, you still have an\n> infinite number of free constants rather than the finite number you\n> find in renormalizable quantum field theories, which is somewhat\n> disturbing; but he seemed to think this might be a useful approach\n> nonetheless.\n>\n> I\'d be happy if somebody who really knows what they\'re talking\n> about elaborates on this.\n\nSee, e.g., the remark after (2.8) in hep-ph/0309049.\nThe difference between renormalizable and unrenormalizable theories is\nthat the former are specified by a (small) finite number of parameters\nwhile the latter are specified by an infinite number of parameters.\nIn both cases, it is possible to extract approximate results from\ncomputations, and the parameters can be tuned to fit the experimental\nresults. This gives a consistent procedure for predictions. Indeed,\nmany nonrenormalizable theories are in use as effective field theories.\n\nPeople who dislike nonrenormalizable theories do this on the basis of\na claim that their predictive value is nil because of the infinitely\nmany constants. But this is as unfounded as saying that thermodynamics\nin not predictive because it depends on a function (the expression for\nthe free energy, say) that require an infinite number of degrees of\nfreedom for their complete specification. Clearly, in the latter case,\nthe widespread use of finitely parameterized imperfect free energies\ndoes not hamper the usefulness of thermodynamics. The same can be\nsaid about nonrenormalizable field theories. It only implies that to\nextract arbitrarily precise predictions one needs correspondingly\nmuch information as input. We know that this is the case already for\nthe simpler phenomena in physics.\n\nA different matter is the dream of a fundamental theory without any\nfree parameters, which of course conflicts with a theory in which\ninfinitely parameters are needed for its complete specification.\nBut there is no theorem that says that nature is governed by unique\nprinciples, and it is quite likely that the designer of the universe\nhad some choices besides the constraints imposed by logical consistency.\nThus I think this dream (which also fuels string theory), is misguided,\nand the correct quantum version of general relativity is standard,\nnonrenormalizable canonical quantum gravity.\n\nThis means that, quite likely, gravity is not at all incompatible\nwith quantum theory.\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>Peter Shor wrote:
> 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.
See, e.g., the remark after (2.8) in http://www.arxiv.org/abs/hep-ph/0309049.
The difference between renormalizable and unrenormalizable theories is
that the former are specified by a (small) finite number of parameters
while the latter are specified by an infinite number of parameters.
In both cases, it is possible to extract approximate results from
computations, and the parameters can be tuned to fit the experimental
results. This gives a consistent procedure for predictions. Indeed,
many nonrenormalizable theories are in use as effective field theories.
People who dislike nonrenormalizable theories do this on the basis of
a claim that their predictive value is nil because of the infinitely
many constants. But this is as unfounded as saying that thermodynamics
in not predictive because it depends on a function (the expression for
the free energy, say) that require an infinite number of degrees of
freedom for their complete specification. Clearly, in the latter case,
the widespread use of finitely parameterized imperfect free energies
does not hamper the usefulness of thermodynamics. The same can be
said about nonrenormalizable field theories. It only implies that to
extract arbitrarily precise predictions one needs correspondingly
much information as input. We know that this is the case already for
the simpler phenomena in physics.
A different matter is the dream of a fundamental theory without any
free parameters, which of course conflicts with a theory in which
infinitely parameters are needed for its complete specification.
But there is no theorem that says that nature is governed by unique
principles, and it is quite likely that the designer of the universe
had some choices besides the constraints imposed by logical consistency.
Thus I think this dream (which also fuels string theory), is misguided,
and the correct quantum version of general relativity is standard,
nonrenormalizable canonical quantum gravity.
This means that, quite likely, gravity is not at all incompatible
with quantum theory.
Arnold Neumaier
> 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.
See, e.g., the remark after (2.8) in http://www.arxiv.org/abs/hep-ph/0309049.
The difference between renormalizable and unrenormalizable theories is
that the former are specified by a (small) finite number of parameters
while the latter are specified by an infinite number of parameters.
In both cases, it is possible to extract approximate results from
computations, and the parameters can be tuned to fit the experimental
results. This gives a consistent procedure for predictions. Indeed,
many nonrenormalizable theories are in use as effective field theories.
People who dislike nonrenormalizable theories do this on the basis of
a claim that their predictive value is nil because of the infinitely
many constants. But this is as unfounded as saying that thermodynamics
in not predictive because it depends on a function (the expression for
the free energy, say) that require an infinite number of degrees of
freedom for their complete specification. Clearly, in the latter case,
the widespread use of finitely parameterized imperfect free energies
does not hamper the usefulness of thermodynamics. The same can be
said about nonrenormalizable field theories. It only implies that to
extract arbitrarily precise predictions one needs correspondingly
much information as input. We know that this is the case already for
the simpler phenomena in physics.
A different matter is the dream of a fundamental theory without any
free parameters, which of course conflicts with a theory in which
infinitely parameters are needed for its complete specification.
But there is no theorem that says that nature is governed by unique
principles, and it is quite likely that the designer of the universe
had some choices besides the constraints imposed by logical consistency.
Thus I think this dream (which also fuels string theory), is misguided,
and the correct quantum version of general relativity is standard,
nonrenormalizable canonical quantum gravity.
This means that, quite likely, gravity is not at all incompatible
with quantum theory.
Arnold Neumaier