Reality Conditions

Friday, September 21, 2007

Quantum Gravity Colloquium: the discussion. (QM vs. QG: the Grudge Match!)

This is a continuation of the previous post. The discussion session on “Are the foundations of Quantum Mechanics relevant for Quantum Gravity”, informally chaired by Anna Gustavsson, was the ending of the colloquium and one of its high points.

The two main opposing positions (basically “No” and “Yes”) were championed by Frank Hellmann and Jamie Vicary respectively. I took what started as a compromising position and was driven later to stand on Frank’s side when Jamie became more and more iconoclastic. Anna sided with Jamie, but I think few of the rest did, though I can’t really remember any other of the specific opinions voiced.

Frank outlined the “conservative” position: Quantum mechanics works extremely well and has convincingly passed experimental tests in a very large range of scales. Granted, we don’t fully understand its ontological consequences, and thinking about them is a legitimate issue; but there is no reason not to be confident in applying the formalism to the problem of quantum gravity. There are specific technical problems that arise in this application of quantum principles that do not arise in others (e.g. the problem of time and the “partial observables” formalism Frank himself has worked in) but in his opinion, these problems can be examined “orthogonally”, so to say, to the philosophical/interpretational problems.

I am much less convinced that both kinds of problems can always be neatly separated. At first glance, making sense of the quantum formalism in a “timeless” context would seem to require re-examining the notions of measurement and “collapse” in the usual formalism, which are strongly time-asymmetric. The opinion I voiced in the discussion was that, perhaps you don’t need to solve the problem of the foundations of QM to do QG, but at least you will have to worry about it. In the context of normal applications of QM, we have proof that the various “interpretations” (naïve Copenhaguen, Everett, Bohmian…) are not distinguishable in practice and only differ philosophically; for example, decoherence ensures that even if the wavefunction never really “collapses”, it would appear as if having collapsed after a measurement. In the context of QG, we lack a proof that all interpretations give the same answer to questions, or that questions about observables can be framed in a way that is neutral between interpretations. This is simply because we do not know what QG is! So when building up your theory of quantum gravity, you should think about which interpretation you are endorsing, and what do “states”, “measurements” and other thorny terms mean in your theory.

Frank sort of agreed with me on this, but said that his paper with Rovelli, Perez and Mondragon proved that the meaning of these terms in generally covariant quantum theory is as “interpretation-independent”, from a practical point of view, as in ordinary quantum theory. So the worry I raised was legitimate, but has been addressed and solved already. I am unconvinced. The paper considers a particular way of defining the quantum observables in the background-independent case. It applies to quantum theories which are canonical quantizations of a classical theory and where the quantities parametrizing the classical configuration space are promoted to kinematical quantum observables. The problem of what happens with the collapse for several measurements “at different times” is considered, and the answer is given (as far as I understand) that one needs to consider the measuring apparatus of the first measurements as quantum as well, and only apply the formalism to calculate the probability for an outcome in the “final” measurement, where the system and the apparatuses that measured it previously are observed simultaneously. This is clever, but I don’t think it solves the problem as conclusively as Frank implied. Can we be certain that the correct theory of quantum gravity will have the form described above? Can’t the correspondence between classical and quantum observables be more complicated and subtle that in this kind of theory? Just to pick an example, does the formalism outlined apply to a theory of quantum gravity that is defined, as string theorists claim it can be done, by an holographic correspondence between the spacetime and a very different theory on its boundary? How are the observables of such a formalism to be understood? I think it is quite rash to claim, at the present level of ignorance, that we know for certain that quantum gravity can be developed without worrying any more about the philosophical interpretation.

Anyway, this disagreement with Frank played a very short part in the discussion, compared to the more basic argument between both of us and Jamie. Apparently relishing the role of contrarian, Jamie made some strong “radical” claims against the “conservative” position. He said that not only we do not understand the meaning of our present quantum theory; its basic assumptions go also largely unquestioned and are moreover very likely to be false in the realm of quantum gravity; therefore we ought not to try to keep its basic structure, but get rid of it and devise new kinds of theories to attack the problem of QG. When asked what were the “unquestioned basic assumptions” he mentioned a smooth, continuum spacetime, the use of complex numbers, the basic concept of “probability” as a positive real number, and perhaps some other I have forgotten. The rest of us pointed out that the quantum formalism by itself does not require a smooth spacetime and that in many QG approaches spacetime is discrete while the standard rules of QM are preserved; but Jamie seemed to think there is some inconsistency in this. For example, he said that probabilities would not be real numbers unless there was a real physical continuum –but as Frank said, discrete systems such as a qubit can be in an arbitrary superposition state parametrized by real numbers, and besides even if the actual probabilities existent in nature were all combinatorial and measured by rational numbers that would hardly a fundamental difference to the standard situation meriting a whole different formalism. Jamie (and I think someone else as well, but I can't remember whom) also talked about the standard idea of probability as presupposing the possibility of repeating the exact same experiments, which is not possible if spacetime is dynamical. It was answered that, by that reasoning, quantum electrodynamics would require the assumption of a constant background electromagnetic field, which is not true; and that spacetime being dynamical does not preclude the possibility of setting local regions of spacetime in a desired local state –e.g., to do repeatable graviton scattering experiments, if it was technically possible (as black hole production is in large extra dimension models). Another possible answer, which didn’t come to my mind during the discussion, is that probability does not need to be defined by frequencies in repeated experiments; it can be defined by degree of belief as in Bayesianism or by physical “propensities” inherent in particular systems. (A philosopher who specialized in these subjects told me once that the frequentist interpretation of probability is completely discredited and nobody endorses it anymore. This may be an exaggeration, but physicists tend to take too much by granted that probabilities just "mean” frequencies in repeated experiments.)

Anna sided with Jamie, arguing that QM has worked well for the other three forces but not for gravity, which would indicate that something different is needed in this case. Jamie was firm on the idea that different mathematical frameworks need to be explored, and are more likely to work than the old quantum one. Frank and I answered that on the contrary, the most reasonable way to do research in absence of experimental information is to pay maximum respect to ideas that have worked exceptionally well in tested areas, and that Jamie’s method would lead to completely arbitrary new theories, most likely with no relation to reality. Historically, new paradigms are developed replacing old ones when empirical evidence makes it clear that the old ones will not work and gives pointers to new possibilities; trying to develop them in vacuo, in a purely philosophical way, does not lead to anything. (Einstein’s development of GR is perhaps an exception, but it is a unique case. The 200 years of unsuccessful efforts to replace Newton’s action at distance by some kind of mechanical model of gravity is a more likely comparison to what Jamie was proposing, at least in my opinion.)

I think it was Anna who suggested at some point that “quantizing general relativity” was perhaps the wrong track for research; perhaps what we would call “quantum gravity”, in the sense of being the microscopic structure of spacetime, has nothing to do with a quantization of Einstein’s GR. I agreed on this but I thought that this is independent of whether the QM formalism needs modification; string theory would seem to satisfy Anna’s description while being “orthodox” with respect to quantum foundations, as far as I understand it.

This is all I remember of the discussion. It is very likely that my memories are partial, incomplete and downright inaccurate. I beg the participants to join in the comments to give their own account, correct my misrepresentations, add things I forgot, and of course… continue the discussion! People who where not present at the moment are also invited to this last thing, of course.



  • I think Steven, too agreed with Jamie on at least some of the radical critique.

    The excellent argument of the EM background and the meaning of repeat measurements was due to Eugenio.

    On my own work, I hope I did formulate it more weakly, if not I certainly should have:

    "[the issue] has been addressed and solved already."

    should be:

    "[the issue] is being addressed and there seems to be good evidence that it can be solved."

    The work on this is far from finished, and the question about dualities which you point out is a very good one indeed. It's similar to the current dispute between the Thiemann and Rovelli camps.

    By Blogger Frank, at 11:00 AM, September 21, 2007  

  • I may be wrong, but I think that I found an original way to "explain" the foundations of QM (article submitted to Foundations of Physics). The idea is roughly that QM axioms can be seen as a consequence of a selection we make among all physical processes to pick what we call "measurements".

    Here is a simple illustration. The collapse of the wave function is the source of much discussion. But the fact that measurements have to give the same results for the same input is a choice pretty much everybody agrees with. However, if two or more distinct measurement results were allowed for the same input, we would be unable to deduce that the wave-function "collapsed" after the first one (it would be a superposition of the remaining possibilities).

    So my idea is: choice of measurement apparatus => stable measurement values => Collapse of the wave function. This line of reasoning has testable implications, like non-instantaneous collapse, and so on.

    But the reasoning can be elaborated as I did in the article. And that leads me to take a contrarian view, that changing the foundations of QM is necessary for QG.

    By Blogger Christophe de Dinechin, at 11:26 AM, September 24, 2007  

  • QM results from waves. For example, the fact that one can not simultaneously determine the momentum and position of a wave is the Uncertainty Principle, a quintessential tenet of QM. The waves follow from wave equations. The wave equations follow from the curvature scalar in six dimensions (See The curvature scalar is the Lagrangian for GR. Therefore QM is the result of GR.

    By Blogger Peter Gillan, at 2:59 PM, September 24, 2007  

  • Quite effective info, thanks so much for the post.

    By Anonymous, at 9:28 PM, November 27, 2011  

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