Loops 07: Conference report (part 1)
Lucien Hardy talked on the causaloid formalism for quantum gravity. It was actually a foundations of quantum mechaincs talk, based on a "operationalist" philosophy: data are recorded, and physics tries to predict probability correlations among data. These probabilities behave different if data are from "causally connected regions" or not; this allows a definition of what is meant by causal connection in background-independent theories. I found the talk interesting but think that concrete progress in quantum gravity is unlikely to come from such an extremely "top-down" approach. As a matter of philosophical principle, I am suspicious of theories motivated by philosophical principles.
Rafael Sorkin on "anhomomorphic logic". Another foundations of QM talk. Sorkin favours a quantum logic interpretation, in which propositions describing unobserved microevents (e.g. "the particle passed through the lower slit") are assigned truth values that behave according axiomes different from classical logic. Besides what I said above on Hardy, I was especially suspicious of this approach because it "adds sturcture" that is not present on the bare quantum mechanics formalism, for reasons that I find unmotivated.
John Donoghue talked next on Effective Field Theory of General Relativity. This was a much-expected talk, and it was also referenced by many of the following speakers. It was an introduction to effective field theory and the way it provides a consistent perturbative theory
of quantum gravity, for sub-Planckian energy scales. Donoghue emphazised that scattering amplitudes and physical results such as the first quantum correction to the Newtonian potential can be calculated unambiguously and independently of the high-energy completition of the theory, and that any theory that pretends to provide this completition (such as LQG) must recover these corrections as well as the classical "zeroth-order" theory. According to Donoghue, the Problem with capital P is not "reconciliating GR and QM" but finding the fundamental high energy theory that completes quantum GR at the Planck scale. I think, however, that when most people in what is loosely called the "LQG community" talk about reconciliating GR and QM, they understand it as implying much more than what is provided by effective field theory. What is wanted is a quantum theory in which spacetime is fully dynamical, and the EFT results (while important, and truly a nontrivial check for any proposed theory) are still very far from this, as they are based on the perturbative framework of QFT.
My own talk "The transition rate of an Unruh detector in a general spacetime" was scheduled for one of the Monday afternoon sessions. It went quite well, with only a brief question by Jerzy Lewandowski during the presentation, and no questions afterwards (though a couple of persons came to talk to me expressing interest later). I suspect many people couldn't understand much, between my ilegible handwriting in the transparencies (I promise to use software next time!), the bad quality of the projector, and the high speed of my speaking due to nerves. I was feeling uncommonly nervous, both before and after the talk, and I didn't take many notes on other talks that afternoon. I have some notes on Rodolfo Gambini's talk, about how quantum mechanics is modified when instead of an abstract time variable we use a physical clock, subjected to decoherence, in the Schroedinger equation; of course, "unitarity" in this time variable is lost. Then he argued that there are fundamental limitations to any clock a the Planck scale, and therefore quantum mechanics would need modifications there. I think that a "timeless" formalism of QM (as Rovelli, Oeckl and others have tried to build) is needed before one can assess these arguments. Guillermo Mena-Marugan and Iñaki Garay talked about quantizations of restricted classical solutions of GR, the Gowdy model and Einstein-Rosen waves respectively; Iñaki had some nice plots of quantum solutions exhibiting both classical and non-classical behaviour. Garrett Lisi then talked on his ambitious "theory of everything" that attempts to describe the whole Standard Model, gravity included, with a single Lie group, E8. I thought when hearing it that it was just a formal game and was surprised to see Lee Smolin ask interested questions, and even more when I saw that John Baez had wrote a whole TWF column on this theory.
This was "the big LQG day", with talks by heavyweights Thiemann, Ashtekar and Rovelli. There was also a talk by Jan Ambjorn about the discrete sum over histories approach, but I missed it.
Thomas Thiemann gave a summary of things known and unknown in Loop Quantum Gravity. For me it added little to to what he had covered in the more complete series of lectures in Zakopane. "Secured land" includes the kinematical framework, the LOST theorem, the area operator spectrum, and kinematical coherent states. "Uncharted territory" includes his more recent Master Constraint Operator (M) to define physical states and the checking of its good semiclassical behaviour. "Open problems" are whether 0 is in the spectrum of M or whether there are anomalies; the resolution of quantization ambiguities in the definition of M; a systematical calculational framework for physical states; a connection with quantum field theory in curved space, with perturbative theory, and a definition of gravitons and Feynman graphs; and conceptual issues related to the problem of time and relational observables. In response to a question by the audience, he admitted that little or none work had been done to connect LQG with the effective field theory results. I think that everyone came out of the conference with the agreement that this is an extremely important thing to do.
Abhay Ashtekar gave a summary of results in symmetry reduced models: loop quantum cosmology and "loop quantum black holes". He started arguing that while results in symmetric models do not prove generic validity, they cannot be dismissed a priori either; witness the example of the hydrogen atom spectrum predicted correctly from symmetric model, against the complexity of solving full QED. He next summarised the by now familiar results of LQC: the Big Bang singularity is replaced by a bounce, both in the zero and positive curvature cases. An important feature is that the correct semiclassical limit heavily constrains how ambiguities in the Hamiltonian are resolved. Similar bounces avoid the singularity in black hole spacetimes, showing that there is no information loss and that evolution is deterministic throughout the quantum regime into a new classical region. It is also known that these bounces are stable against small perturbations.
Carlo Rovelli asked a question at the end of Ashtekar's talk, one that has worried me for a long time, that I discussed briefly here about a year ago, and that has recently been discussed at Cosmic Variance (see previous post here for the link; I can't access CV now). In our universe, the Big Bang was a state of uncommonly low entropy; this ensures the existence of an arrow of time because entropy has naturally grown since then. If there was a collapsing phase and a bounce before the Big Bang, what was happening to entropy in it? Symmetry seems to demand it to decrease –but "naturally" a gravitational collapse increases entropy to a maximum, as in a black hole. The collapsing universe would need to be extremely fine-tuned for entropy to decrease in it.
I couldn't follow Ashtekar's answer to Rovelli, but later I found an oportunity to pose the question again to him in a coffee break. He said that while matter entropy is very difficult to analyze in the simple models that have been studied so far, gravitational entropy –the "likeliness" of the gravitational state- does indeed seem to behave symmetrically in the bounce models. The quantum regime near the singularity is a very special, intrinsically low-entropy state. I have been convinced by Frank (fh) in the discussion here a year ago that if this is so, the most natural description of the situation is not "a previously collapsing universe with decreasing entropy followed by an expanding universe with increasing entropy" but "a low entropy state that expands, increasing entropy, in both two time directions". In other words, it seems more natuural to define "positive time direction" at each of the two stages by the increase of entropy, even if this gives two different results and time is no more a "line" but a "double arrow". Surely, if there were observers in the (from our point of view) "collapsing"phase, they would take themselves to live in an expanding universe, if as it seems almost certain the psychological arrow of time is tied to the thermodynamical one. Ashetekar however, didn't seem to think much of this point of view (probably dismissing it as too philosophical). For him the scalar field that serves as "internal time" in these quantum cosmology models is the true "clock", and it is monotonically increasing.
I am still puzzled, however, about what happens with entropy in the closed universe model (postive curvature without dark energy). This one becomes under quantization cyclical, expanding and contracting again at regular rate. What happens when the apex of the expansion is reached? does entropy reverse itself suddenly, as in Gold's old cosmology? but how can this be, if the moment of maximum expansion is completely classical and localized systems should follow ordinary mechanical and thermodynamical laws without knowing about the cosmological turnaround? I find this very perplexing. A possible way out is that the existence of dark energy with its actual value, which accelerates the expansion and ensures that the universe is not cyclical, is somehow not an accidental but a necessary feature of the universe, so that the cyclical model will ultimately be shown to be inconsistent. But this is only a personal hope. See also my old review of Price's book on the arrow of time for more discussions of these questions.
Going on with the conference: Carlo Rovelli talked next about the new spinfoam vertex, an improved model that pretends to replace the Barrett-Crane one. He discussed at length the graviton propagator calculation he and his collaborators did a couple of years ago, explaining that since then the nondiagonal terms of the propagator had been computed and found to be wrong –but only because the Barrett-Crane model was used! Using the new model the problem is solved. The key difference is that second class simplicity constraints are imposed weakly rather than strongly. In the improved model the bondary states of spin foams match exactly the spin network states of canonical LQG, and intertwiner degrees of freedom remain free. (There were some technicalities about all these that I couldn't follow, but if you are interested download the slides and audio; it was a very clearly delivered talk.) The conclusion was optimistic: Carlo believes that this model may be the key for reconciliating the "canonical" LQG approach and the "covariant" spin foam one.
The talks I attended to this afternoon were mostly about highly technical aspects of LQG and spin foams, and I don't want to bore neither me nor you by writing much about them. I will comment only on two of them which were of special importance, to me at least. Kristina Giesel talked of the work she did with Thiemann on Algebraic Quantum Gravity, a new version of LQG which is defined in a purely "combinatorial" way; spin networks are abstract graphs and not embedded in any pre-existing manifold. Semiclassical analysis, however, can be done by specifying a 3-manifold and a classical phase space point in it, and constructing coherent states peaked on that geometry. The zeroth-order and first-order in hbar of the expectation value of the master constraint in these states come out correct; what is unknown is whether there are anomalies in M or whether 0 is in its spectrum. The second talk I want to remark upon was Eugenio Bianchi, on work related to the graviton propagator calculations. He showed computations of large scale area correlations in spin foam models, for boundary states peaked on a classical geometry, and showed that they agree exactly with those computed in perturbative Regge calculus. The point is that correlations calculated in a semiclassical state of the full, nonperturbative theory are here compared with correlations in the vacuum state of the perturbative theory around a corresponding classical solution. Finding agreement is a nontrivial check for the spin foam model. In this case the model was Barrett-Crane, but Eugenio thinks the results still hold in the "improved" model Rovelli had talked about.
And this is enough for today. The rest of the conference will be covered in one, or perhaps two, following post(s). As usual, stay tuned!