Freethought & Rationalism Archive

Friar Bellows · 01-31-2003, 09:03 PM

Below is a brief description of each of these lines of research, stolen from "Notes for a brief history of quantum gravity" by Carlo Rovelli (2001) gr-qc/0006061. Which of these approaches do you think will win?

Covariant:

Quote:

The covariant line of research is the attempt to build the theory as a quantum field theory of the fluctuations of the metric over a flat Minkowski space, or some other background metric space. The program was started by Rosenfeld, Fierz and Pauli in the thirties. The Feynman rules of general relativity (GR, from now on) were laboriously found by DeWitt and Feynman in the sixties. t'Hooft and Veltman, Deser and Van Nieuwenhuizen, and others, found firm evidence of non-renormalizability at the beginning of the seventies. Then, a search for an extension of GR giving a renormalizable or finite perturbation expansion started. Through high derivative theory and supergravity, the search converged successfully to string theory in the late eighties.

Canonical:

Quote:

The canonical line of research is the attempt to construct a quantum theory in which the Hilbert space carries a representation of the operators corresponding to the full metric, or some functions of the metric, without a background metric to be fixed. The program was set by Bergmann and Dirac in the fifties. Unraveling the canonical structure of GR turned out to be laborious. Bergmann and his group, Dirac, Peres, Arnowit Deser and Misner completed the task in the late fifties and early sixties. The formal equations of the quantum theory were then written down by Wheeler and DeWitt in the middle sixties, but turned out to be too ill-defined. A well defined version of the same equations was successfully found only in the late eighties, with loop quantum gravity.

Sum over histories:

Quote:

The sum over histories line of research is the attempt to use some version of Feynman's functional integral quantization to define the theory. Hawking's Euclidean quantum gravity, introduced in the seventies, most of the the discrete (lattice-like, posets . . . ) approaches and the spin foam models, recently introduced, belong to this line.

Others:

Quote:

There are of course other ideas that have been explored:

Twistor theory has been more fruitful on the mathematical side than on the strictly physical side, but it is still actively developing.
Noncommutative geometry has been proposed as a key mathematical tool for describing Planck scale geometry, and has recently obtained very surprising results, particularly with the work of Connes and collaborators.
Finkelstein, Sorkin, and others, pursue courageous and intriguing independent paths (e.g. causal sets).
Penrose idea of a gravity induced quantum state reduction have recently found new life with the perspective of a possible experimental test.
. . .

So far, however, none of these alternatives has been developed into a large scale research program.

fando · 02-01-2003, 02:03 PM

I'm a fan of loop quantum gravity. It makes more intuitive sense to me than the string theory stuff. My background is mostly GR and basic QM (no QFT).

Friar Bellows · 02-02-2003, 06:29 PM

Quote:

Originally posted by fando
I'm a fan of loop quantum gravity. It makes more intuitive sense to me than the string theory stuff. My background is mostly GR and basic QM (no QFT).

Me too, fando. The string theorist's view of gravity as excitations of a string on a background spacetime bothers me, mostly because I take the lessons of general relativity very (maybe too) seriously, i.e. that there is no such background over which physics happens (except when we do approximations). On the other hand, string theory is a very elegant theory, and it seeks to unify all known fundamental physics. So maybe if the string theorists create a background-free formulation of their theory, as well as provide us with a better understanding of the non-perturbative regime, then I'll change sides.

P.S. I wish I could understand the math behind Loop Quantum Gravity . . . but you'd almost have to be a Fields medallist to do so! :banghead:

Answerer · 02-02-2003, 06:53 PM

My choice two as well, probably because I have more faith in Einstein and his theory of relativity over QM and its predecessors. Besides, the string theory equation are enormously complicated, therefore I don't think anyone will able to solve it in the near future.

Friar Bellows · 02-04-2003, 05:40 AM

Our poll suffers from small-number statistics, but string theory is winning. These stringy types want to relegate our beloved general relativity to the role of a mere effective theory, like Navier-Stokes fluid dynamics. We loopy types are not amused.

In another paper, Rovelli did a rough statistical analysis of quantum gravity papers submitted to the arxiv.org e-Print archive in 1998, and he found the following breakdown of papers in each field per month:

String theory: 69
Loop quantum gravity: 25
QFT in curved spaces: 8
Lattice approaches: 7
Euclidean quantum gravity: 3
Non-commutative geometry: 3
Quantum cosmology: 1
Twistors: 1
Others: 6

String theory wins again.

Hey, wouldn't it be interesting if both string theory and loop quantum gravity both eventually succeeded and were found to be equivalent, at least within their shared domain? Sort of like the equivalence of the Heisenberg and Schr�dinger approaches to (non-relativistic) quantum mechanics.

View Poll Results: Which line of research will produce a successful theory of quantum gravity?
Covariant (e.g. string theory)	10	50.00%
Canonical (e.g. loop quantum gravity)	5	25.00%
Sum over histories (e.g. lattice theories)	0	0%
Others (e.g. twistors, causal sets)	3	15.00%
None (i.e. we'll never find such a theory)	2	10.00%
Voters: 20. You may not vote on this poll

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02-01-2003, 02:03 PM	#2
fando Veteran Member Join Date: Sep 2001 Location: Los Angeles Area Posts: 1,372	I'm a fan of loop quantum gravity. It makes more intuitive sense to me than the string theory stuff. My background is mostly GR and basic QM (no QFT).

02-02-2003, 06:53 PM	#4
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	My choice two as well, probably because I have more faith in Einstein and his theory of relativity over QM and its predecessors. Besides, the string theory equation are enormously complicated, therefore I don't think anyone will able to solve it in the near future.

02-04-2003, 05:40 AM	#5
Friar Bellows Veteran Member Join Date: Apr 2001 Location: arse-end of the world Posts: 2,305	Our poll suffers from small-number statistics, but string theory is winning. These stringy types want to relegate our beloved general relativity to the role of a mere effective theory, like Navier-Stokes fluid dynamics. We loopy types are not amused. In another paper, Rovelli did a rough statistical analysis of quantum gravity papers submitted to the arxiv.org e-Print archive in 1998, and he found the following breakdown of papers in each field per month: String theory: 69 Loop quantum gravity: 25 QFT in curved spaces: 8 Lattice approaches: 7 Euclidean quantum gravity: 3 Non-commutative geometry: 3 Quantum cosmology: 1 Twistors: 1 Others: 6 String theory wins again. Hey, wouldn't it be interesting if both string theory and loop quantum gravity both eventually succeeded and were found to be equivalent, at least within their shared domain? Sort of like the equivalence of the Heisenberg and Schr�dinger approaches to (non-relativistic) quantum mechanics.

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