Reviewing Quantum Gravity
Abhay Ashtekar: Gravity, Geometry and the Quantum
Lee Smolin: Generic predictions of quantum theories of gravity
Marcus has asked me to make a comment on the second of them, but I will include also the first because it will enable me to sneak in a question that has puzzled me for a while about the results in singularity resolution within Loop Quantum Cosmology. I should start by saying that I am no expert in LQG, not even in the measure a graduate student working directly in it would be; I work in quantum field theory in curved spacetime, not quantum gravity proper. True, I am a member of a research group with an important LQG component, and I have a great interest in the developments made in the theory; but I have not studied it “seriously” (which means: beyond reading several review articles and Rovelli’s Quantum Gravity textbook without following the more technical parts of the math, and assisting to several seminars and to the Loops 05 conference). So my comment on these papers can’t be an “informed critical comment”; it will be more like a “summary plus personal subjective impressions and questions”. I’m not sure if that is what Marcus wanted, but it’s the best I can make. I hope that people with more knowledge than me will jump in and correct any mistakes.
OK, no more disclaimers. Smolin’s paper is focused on generic predictions from background independent quantum theories of spacetime. It starts listing four assumptions these theories are based on: quantum mechanics, background independence (partial, because some structures like dimension and topology may be fixed), discreteness and causality. And here comes my first question: I thought one of the main selling points of LQG was that the discreteness of spacetime is not an assumption of the theory but a natural consequence of a background independent quantization of grvity. In fact, when Smolin lists the theories he has in mind he includes causal sets, dynamical triangulations and consistent discretization models, but not canonical loop quantum gravity proper. The formal description of the theories made later, however, seems appropiate only for the latter, describing Wilson loops, spin networks, and so on. If these feature in causal sets or CDT models, I was not aware of it.
Likewise, the “well studied generic consequences” discussed in Section 3 are three results classically associated with canonical LQG: ultraviolet finiteness due to discreteness, elimination of spacetime singularities (these are discussed at much more length in Ashtekar’s paper) and horizon entropy. I am surprised that Smolin seems to regard the last of these as a settled matter, with the “correct” way of doing the calculation already known as being the one that gives the same Immirizi parameter implied by classical quasinormal modes. That is not the impression I obtained from a seminar we had a couple of months ago. A fourth generic consequence, of which I was not aware of previously, seems to be a natural role for the cosmological constant in the theory; the description of this is intriguing but too sketchy for me to follow, so I guess I’ll have to llok at the 59-pages long referenced paper.
Section 4 mentions briefly the results in recovering a classical spacetime for long distances: Rovelli’s “gravitons from LQG” calculation, Freidel and Levine’s result of DSR as flat limit of 2+1 QG, Loll et al.’s results on the large distance limit of CDTs with 3+1 emergent dimensions, and work using noiseless subsystems techniques. Section 5 is on “Possible new generic consequences”, which are more speculative than those in previous sections. The first is DSR (doubly or deformed special relativity) as classical limit of QG in 3+1 dimensions. Smolin mentions possible experimantal tests of this idea, but downplays a bit what are (in my impression) large technical and conceptual problems to understand fully what DSR means, let alone what it predicts. Next come Smolin’s pet speculation on matter as emergent from geometry (ridiculed by Lubos here; I as a rule take with suspicion anything Lubos says outside from technical areas of string theory, but in this case it does seem to me that, at the least, Smolin’s idea needs quite a lot of more hard working on until we can say that matter as we know it can arise from geometry). Follows a discussion on disordered locality, which excites Smolin becase he hopes it may explain puzzles like dark matter (via some MOND-like model) and the Pioneer anomaly, as he explained in a Loops 05 talk. This seems very optimistic to me; intuitively I would expect non-local effects, if they persist at low energies, to mess up the theory and perhaps make it inconsistent with our present well tested low-energy local physics, instead of magically creating exactly the kind of effect that accounts for the few anomalies we presently cannot explain. Surely, a lot of more work needs to be done here. Finally there is a simple calculation attempting to relate disordered locality to the cosmological power spectrum.
In general, the impression I have is that all the “generic predictions” Smolin discusses in section 5 are at this stage more speculations than predictions, even tentative ones. The strongest generic results of the LQG program seem to me the discretization of spacetime giving finitenesss to the theory and the resolution of singularities. This last issue brings us to Ashetekar’s paper.
This paper starts with a brief revision fo the formal structure of LQG, and then applies it to homogeneous and isotropical cosmology. In Loop Quantum Cosmology, the spacetime is first assumed to have the usual symmetries so there is effectively only one degree of freedom (the scale factor) and then this variable is quantized following an analogous procedure as the degrees of freedom in the compelte theory. One might of course question whether the operations of quantizing and imposing symmetry “commute”, so the results found this way would be preserved for cosmology in the full theory; but leaving that aside, the results found in LQC are indeed impressive. Starting with a semiclassical state approaching a Friedmann clasical solution at late times, with a scalar field added as a non-geometrical degree of freedom, and evolve it backwards towards the Big Bang. What you find is that the matter density increases until reaching approximately 2.5 times the Plack density, and then it bounces and starts to decrease again, approaching another classical (collapsing) universe in the distant past. The singularity is avoided by the effect, at Planckian distances, of what Ashtekar calls an effective repulsive gravitational force arising from the quantisation of the geometry, akin to the effective repulsion between fermions arising from the Pauli principle.
This result is without a doubt important and exciting, especially because similar effects may resolve black hole singularities as well. However, the idea that a bounce from the collapse of a previous classical universe is a realistic scenario for “what happened before the Big Bang” is one that creates a host of problems in my opinion. First, our universe is known to be in an accelerated expansion that will not recollapse to a Big Crunch, quite the opposite; then why did the previous universe collapse? To postulate as "cosmic initial condition" a large classical universe collapsing seems even stranger than a singularity to me. Leaving aside this quasi-metaphysical worry, I see a serious potential problem in the second law of thermodynamics. A realistic collapsing universe would almost certainly be increasing its entropy to a maximum, ending in a very "messy" state with lots of black holes; not the kind of smooth, low entropy state we have at the beginning of our universe. Of course the calculations Ashtekar presents can't address these problems because they restrict to a case with imposed homogeneity. I would be surprised if the apparent mirror symmetry between the collapsing and the expanding phase persists when anisotropy is allowed, as this would seem to be against the Second Law. (You would be right in presuming that my worries about time asymmetry and the low-entropy beginning of the universe were spawned by reading Penrose; see this Physics Musings recent post). A similar question arises if black hole singularities are resolved with a similar bounce: does the black hole transform into a white hole after passing through the Planckian regime? But don't white holes violate the Second Law?
In summary, the elimination of singularities thanks to the loop quantization seems compelling, but the bouncing mechanism puzzles me because in a realistic scenario I don't see how to reconciliate it with the Second Law. Any ideas?