Larry Yaffe’s comments about string theory reflect well mainstream opinion in the particle physics community. On matters of fact I think what he has to say is pretty accurate, but I disagree with some of his statements that reflect not facts but scientific judgements. Of his positive comments about string theory, the ones about its impact on mathematics and about AdS/CFT are right on target. For an interesting talk explaining the status of attempts to use AdS/CFT to say something about QCD, see Larry’s colleague Matt Strassler’s talk this month opening a workshop in Santa Barbara (don’t miss the heated exchange at the end of the talk about whether or not this is all just supergravity).
Larry’s comments about “compelling hints” that there is something “deep and meaningful” to string theory and that it has provided “partial insights” into conceptual problems in quantum gravity are hard to to argue with. But while these hints seem to point in the direction of the existence of an interesting 11 dimensional supersymmetric theory, they provide no evidence that it has anything to do with the standard model. Quite the opposite, the evidence of the “landscape” suggests that any attempts to relate such a theory to the real world produce a framework that is completely vacuous, and can never explain anything (or, equivalently, can explain absolutely anything you choose).
The one place where I think I really disagree with Larry is his claim that, indisputably, “string theory is the most promising framework we have for combining quantum mechanics and gravity”. This “most promising framework” locution has been around now for nearly twenty years. It was justifiable when people were just starting to try and understand the implications of superstring theory, but the failure of twenty years of effort by thousands of very talented physicists has to be taken into account. The fact is that despite all this effort, string theorists still don’t have a consistent theory of 4-dimensional quantum gravity and prospects are not promising that this situation is going to change anytime soon.
As part of this “most promising” comment, Larry has critical things to say about loop quantum gravity. I’m no expert on this myself, but, like many theorists, he seems to me to be holding string theory and loop quantum gravity to quite different standards. Lee Smolin recently wrote to me and Larry to respond to Larry’s comments, he allowed me to reproduce his e-mail here:
“Dear Peter and Larry,
Thanks for the comments, most of which I agree with. But in case either of you are interested, Larry’s comments about loop quantum gravity do not reflect the real results.
A side effect of the sociology of string theory seems to be that there is as much ignorance of the genuine results concerning loop quantum gravity and other approaches to quantum gravity as there is overhype in string theory. It is fascinating that, just there are results that are believed to be true in string theory, despite never having been shown, there are results that have been shown, in some cases rigorously, in lqg, about which many people seem not to have heard about, in spite of being published 5-10 years ago on the archive and in the standard journals.
To combat this I wrote a recent review hep-th/0408048 which I would gently suggest reading before making public pronouncements about the status of the field. There are also good reviews on the rigorous side by Ashtekar and Lewandowski and by Thiemann, as well as two textbooks in press from CUP, one from Rovelli and one more rigorous from Thiemann.
Larry says of LQG that it “has not been shown to have anything to do with gravity. Does it have a large-volume limit? Does it have long distance dynamics…”
Can I mention some of the results that show that lqg quite definitely is a quantum theory of gravity, with details and referenceds in the paper? Larry, if you think any of these results are wrong, please tell us on what step of what calculation or proof someone made an error. Otherwise, we invite you to study the results and the methods by which they were gotten. You might surprise yourself by coming to agree with us, after all this is just quantum gauge theory, but in a diffeomorphism invariant setting rather than on a background manifold.
A key result is the LOST uniqueness theorem which shows that for d >=2 the hilbert space LQG is based on is the UNIQUE quantization of a gauge field that carries a unitary rep of the diffeo group, in which both the wilson loop and non-abelian electric flux operator are well defined operators. (see the paper and references for the precise statement).
Given that GR and supergravity are well understood to have configuration spaces defined as configurations of gauge fields mod diffeos, to which the theorem applies, this implies that the hilbert space used is uniquely suited to the quantization of those theories.
It is further shown that the hamiltonian contraint of GR for d=3+1 is rigorously defined on the hilbert space of diffeo constraints, allowing exact solutions to all the quantum constraints to be constructed.
As far as the path integral is concerned, using the method of spin foam models, based on the observation that GR and supergravity in all dimensions are constrained topological field theory, leads to rigorously defined path integral measures corresponding to the quantization of these theories. There are in addition rigorous UV finiteness results. There are also results that establish correspondences with Regge calculus in various limits.
These results all are quite sufficient to establsih that these theories are precisely the quantization of GR or supergravity. Surely this has something to do with gravity.
Regarding the low energy limit, more explicitly, there are several classes of candidate ground states that have the property that 1) measurements of coarse grained geometrical operators agree with classical flat or deSitter spacetime, up to small fluctuations. 2) small excitations of the gravitational degrees of freedom, which satisfy the constraints to linear order in l_Planck/wavelength have two spin two massless degrees of freedom per momentum mode (i.e. the gravitons are recovered for wavelengths long in planck units, again showing this is a quantization of gravity.) 3) after coupling to any standard matter field, excitations of the ground state yield a cutoff version of the quantum matter field theory on the classical background, cutoff at the planck scale because of the finiteness of quantum geometry.
The classes of states these statements characterize are a) coherent states, b) eigenvalues of coarse grained 3-geometry (sometimes called weave states) and c) for non-zero cosmological constant, the Kodama state.
I would think that finding explicit states with these properties proves that at least linearized gravity and effective field theories correspodning to qft on background manifolds is recovered. Certainly this is again something to do with gravity.
In addition, we can mention 1) the black hole results, which give an exact description of the quantum geometry of an horizon, in agreement with all semiclassical results and 2) the loop quantum cosmology results, which again recover all results of semiclassical quantum cosmology and go beyond them in the context of a rigorously defined framework. Again, some things to do with gravity.
See my paper for complete references.
I’m sorry for the tone, but one loses patience after 15 years. We have always been careful to state results precisely with full qualifications and never to overclaim. By now there are sufficient results that I think the many good people who are working hard in this field deserve to have their results much better known.
As always, I and my (rapdily growing number of) colleagues are happy to talk to anyone and go anywhere to explain the results and the methods by which they were gotten. Indeed, the number of invitations for talks at places that previously expressed no interest previously is growing. I’d certainly be glad to recommend good speakers who could educate your department about the state of art in quantum gravity.