Don Marolf, Syracuse University
The appropriate starting point for this review is Carlo Rovelli's plenary talk `quantum spacetime.' Rovelli took upon himself the unenviable task of commenting on the vast variety of approaches to and aspects of the subject of quantum gravity. In the first part of his talk, we found Carlo wearing an unfamiliar hat -- that of an experimental sociologist -- as he presented an inventory of the preprints that appeared on hep-th and gr-qc during the first 10 months of 1997. With a total flux over 400 papers per month, roughly 1 in 4 addressed quantum gravity or related issues. Breaking these up by topic, he found 69 string papers per month, 26 loop gravity papers per month, 8 on QFT in curved spacetime, 7 on lattice Quantum Gravity, and perhaps 29 per month for all other aspects combined (with a given such approach averaging no more than 5 papers per month). In GR15, there were four plenary talks (by Gibbons, Rovelli, Kozameh, and Zeilinger) with quantum themes, as well as a large number of parallel sessions: one afternoon of superstrings and supersymmetry, one afternoon of quantum cosmology and conceptual issues, one afternoon of quantum fields in curved spacetime and semiclassical issues, and two afternoons of `quantum general relativity.'
Since Gary Gibbons gave a talk about M-theory (the theory formerly known as `strings'), Rovelli spent most of his time discussing the loop approach, though he did comment on QFT in curved spacetime, dynamical triangulations, Regge Calculus, and other ideas. I will follow the results of his xxx experiment and address first string issues, then loop issues, and finally other issues in quantum gravity. Unfortunately, it will not be possible to discuss here more than a few talks from the 5 afternoons of parallel sessions on quantum issues.
The plenary lecture by Gary Gibbons gave a brief overview of what has become known as M-theory; the lecture was quite well received. Briefly, M-theory is a project arising out of string theory which is supposed to be a more fundamental and, when complete, nonperturbative formulation of quantum gravity. Gibbons made an analogy between M-theory and a Northern European Medieval cathedral whose many parts, created by individual artisans, are works of art on their own, but whose real beauty and structure are apparent only when the cathedral is completed -- perhaps long after the deaths of the earliest contributors. M-theory is to be viewed as such a cathedral under construction. Some pieces are in place, and there are many architects who share a common vision for what the cathedral will become. However, the building process is far from complete, and Gibbons reminds us that many cathedrals were completely redesigned as they were being built so that, in the end, they bore little resemblance to the original conception. Indeed, some designs were simply impossible to build.
Nevertheless, Gibbons emphasized the solidity of the of the foundation of M-theory (which rests on all of the successes of string theory, understandings of string duality, and the impressive calculations of black hole entropy by Strominger, Vafa, etc.) as well as the sweeping vision of the architects. He also described the ``landscape and architecture of the partially completed cathedral and of the surrounding countryside.'' His talk focused on the relationship of M-theory with supergravity, and with various BPS (aka supersymmetric) objects. [The most commonly discussed supersymmetric objects are extremal black holes.] Readers interested in an introduction to this subject will surely enjoy the version of his talk to be published in the conference proceedings.
The other major contribution to GR15 in the string/M-theory vein was a review talk ``Strings and Semiclassical properties of black holes'' given by Gautam Mandal in the parallel session on superstring theory and supergravity. His review was necessarily short and condensed, but fairly thorough. The 1996 work on reproducing black hole thermodynamics from string calculations was also nicely summarized in a talk given by A. Dasgupta, who reported some new results on fermionic Hawking radiation in effective string models of black holes. In addition, some observations about superstring inspired cosmological models and the graceful exit problem for inflation were made by S. Bose.
Let us now return to Rovelli's discussion of loop quantum gravity. He stressed the fact that this approach is essentially non-perturbative so that it could, in principle, provide a complete definition of the theory. However, this also means that it is difficult to compute the kind of perturbative scattering results that are common in, for example, string theory. As major results, Rovelli described the predicted quantization of areas and volumes, the recent calculations of black-hole entropy by Ashtekar et. al., and the fact that a set of constraints has been proposed which, if correct, could provide a complete non-perturbative definition of Quantum Gravity.
On the other hand, Rovelli also mentioned two difficulties: one was the lack of a general algorithm for computing physical results (such as scattering phenomena) and the other was a concern over whether the proposed constraints do indeed describe gravity or whether they need to be modified or replaced in some way. This concern was largely based on the results of Lewandowski and Marolf showing that the algebra of the proposed constraints does not seem to match the classical hypersurface deformation algebra (instead, it gives for the commutator of two Hamiltonian constraints) and the corresponding work by Lewandowski, Marolf, Gambini, and Pullin. This issue was a matter of some discussion both in the parallel session on quantum general relativity and in informal discussion. An overview of the results was presented by J. Lewandowski, and comments were made in the talks by T. Thiemann and J. Pullin. As the subject is still under consideration (and since I am a participant in this discussion), I will summarize the comments only very briefly without drawing particular conclusions: Thiemann and Pullin each suggested a possible way to modify the loop approach in order to improve the situation, while other comments were made that, since the constraints themselves are not directly physical observables, it is unclear exactly what physical problems the above algebra would cause. Discussion continues, and should remain interesting.
A few words are now in order regarding other quantum aspects of the conference. Kozameh's plenary talk on the null surface formulation of GR was mostly classical, but described some recent results concerning linearized quantum theory in this framework, in which the coordinates of certain events become quantum operators. He also expressed a hope that this formulation will help to untangle deeper mysteries of quantum gravity.
Without going into details, let me say that a high point of the conference was the plenary talk by A. Zeilinger on precision experiments using quantum correlations. These ranged from classic EPR tests to `quantum teleportation' -- all effects predicted by standard quantum mechanics and verified in his laboratory. A hope was expressed that, in the near future, experimental techniques would be refined to the extent that they could directly test Roger Penrose's ideas about the effects of gravity on quantum decoherence. I would strongly recommend a visit to Zeilinger's web site at
Finally, a number of extremely interesting (non-string, non-loop) papers were presented in the parallel sessions. Unfortunately, there is only space to mention a few of them here. The talks by L. Ford, E. Flanagan, and S. Carlip seemed to be the most popular. Very Briefly, Ford reviewed the latest results on providing inequalities that restrict the negative energy that states of a quantum field may have in static spacetimes. Flanagan discussed the (quantum) stability of Cauchy horizons in 1+1 dimensions and described a necessary condition for the horizon to be classically stable but quantum mechanically unstable. Carlip discussed his recent paper in which he argues that, if a sum over topologies is to be performed, the partition function for 3+1 gravity with negative cosmological constant cannot converge, and that it is formally analogous to a system with negative specific heat. He also noted that the formal role of the cosmological constant is similar to the temperature of such a system, and this observation led him to speculate that it might provide a mechanism for setting . The idea is that, somehow, due to the negative `specific heat,' processes that would normally increase would instead drive it to zero.