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.


Monday, September 17, 2007

Quantum Gravity Colloquium: the talks

Last Friday I went to London for a quantum gravity student colloquium at the Imperial College. The idea was to meet up with postgraduates working in quantum gravity in UK and other European countries, and have some give talks explaining their research, with ample time for questions and discussion, in a very informal setting. Keeping it student-only makes it easier to dare to ask potentially stupid questions and voice one's opinions. We had already had one such meeting in Cambridge several months ago, and this second experience was as good as or better than the first.

This time we had four seminar-like talks, plus an open discussion session on the topic "Are the foundational problems of quantum mechanics relevant for quantum gravity?" Starting with the talks: Leron Borsten talked on the entropy of black holes in supergravity theories, and intriguing connections it has with entanglement in quantum information theory. There is no clear picture yet in which to view the black hole entropy as entanglement entropy, but there are some identities or isomorphisms between the mathematical description of both concepts that do not look as a coincidence. Yousef Ghazi-Tabatabai talked on an approach to interpreting quantum mechanics which seemed related to the ideas pushed forward by Rafael Sorkin in his plenary talk at Morelia.

Frank Hellmann (who also must be given the lion's share of the credit for organizing the colloquium) talked on "Partial Observables", an approach to defining quantum observables in generally covariant theories and, potentially, solving the problem of time. It has been long championed by Carlo Rovelli, with whom Frank worked before coming to Nottingham. The talk explained how observables that are evolving in a conventional framework can be recast as Dirac observables when the dynamics is written in a generally covariant way. These are fit to answer the question "If the system is in physical state Rho, what is the probability of seeing the correlation (x,t)?" (where x,t are the variables of the classical configuration space). The answer to this question is Tr (Rho P(x,t)), where P(x,t) is the operator that projects states into the physical state which is itself the projection, onto the physical Hilbert space, of the kinematical state corresponding to correlation (x,t). Sadly little time was left by the end of the talk for Frank to discuss the thorny case of multi-time measurements, which is the real centrepiece of his paper.

Eugenio Bianchi gave an excellent talk on Perturbative Regge Calculus and Loop Quantum Gravity. It was a version of the talk he gave at Morelia, but with the math replaced by the concepts, which was much better! I think this stuff is extremely important and I am hope to start working into it in the future, so I will summarise the talk in more detail than the previous ones. I would be extremely happy to receive comments discussing it or pointing out mistakes in my exposition.

Loop Quantum Gravity is an essentially non-perturbative theory. Any attempt to find a "semiclassical limit" and connect it to established physics is complicated by the fact that semiclassical physics is essentially perturbative; so there is the problem of even mathematically connecting the two frameworks, before a concrete calculation to see if they agree can be done. One way of doing this connection is the boundary amplitude formalism introduced by Rovelli. Take a kinematical semiclassical state, a kinematical state given by a superposition of spin networks which is a Gaussian peaked on on a classical spacetime (and choose this to be flat space). Fix this as the state on the boundary of a region, and you can compute correlations of observables, measured in the boundary, due to the dynamics in the interior. Use a spin foam model to specify the dynamics: for example, the Barrett-Crane model. You can then calculate, based on a nonperturbative theory, semiclassical correlations of your dynamical variables, which are spins jmn. You obtain results. However, you don't know if your initial theory that defines the boundary state (LQG) is correct, nor if the spin foam model you have chosen to encode the dynamics is correct, and besides that as the whole conceptual and calculational framework looks very different from things used in other areas of physics, you would really really want something to compare your results to as a check.

Enter Perturbative Regge Calculus. Regge Calculus is an approximation scheme to GR in which the curved manifold is replaced by a skeleton triangulation, with the geometry encoded in the discrete edges and vertices. As Eugenio stressed, it can also be thought of as exact (not approximated) GR but with piecewise flat metrics instead of continuous metrics. Choose a triangulation that discretizes flat space; it is described by the connectivity C and a set of edge lengths Li. Now add small perturbations to the edge length variables, and quantize these perturbations. You are now doing Quantum Perturbative Regge Calculus, which is a straightforward background-dependent, perturbative quantum theory, in which all the standard rules of the game apply. Change your variables from edge lengths to face areas, and calculate the quantum area-area correlations on the boundary of a region. Compare them with the fluctuation in spins jmn calculated from the non-perturbative theory. Are there equal?

The answer is that, for the Barrett-Crane model dynamics, all quantities compared between both calculations up to the 3-point function match exactly, provided that one identifies the spins used as variables in LQG with the areas used in Regge calculus, up to the factor 8 Pi G b, with b being the Imirizi parameter! This is an independent and nontrivial check of the famous LQG spectrum area, which was derived at a purely kinematical level. Here the dynamics is necessary to ensure the right correspondence between areas and spin variables. For example, if one uses a non graph-changing Hamiltonian to define the dynamics, the correspondence is not recovered. The calculation with the new spin foam model recently proposed by Rovelli, Pereira and Engle, which cures certain problems with the Barrett-Crane model, is still not completed and its results are eagerly awaited.

It should be stressed that, though nontrivial, this check does not amount yet to confirming that LQG has the "correct" semiclassical limit. The only perturbative theory of quantum gravity that has right to be acknowledged as "correct" (because it uses uncontroversial quantum field theory principles in an unobjectionable way) is the Effective Field Theory approach popularized by Donoghue. It is not known if quantum perturbative Regge calculus is a sort of discrete equivalent of this; understanding the connection between them would be a key step forward. But the calculation Eugenio talked about has great importance by itself, because it shows that a fully nonperturbative approach to quantum gravity, when used in conjunction with a semiclassical state, can give the same answers as a better understood perturbative approach.

As this post is getting longish, I will break it here and post in one or two days about the discussion on the relation between foundations of QM and QG. Stay tuned.


Wednesday, September 05, 2007

Answering my Readers: the Catechism of the Eastern Orthodox Church edition

Alana has asked me to give my opinion, from a scientific point of view, on an argument for the existence of God that she copies from the Catechism of the Eastern Orthodox Church. The Catechism seems to be a sort of FAQ about the basic doctrines of this church, and according to this website it has non-official status. Its author is one one Rev. Constas H. Demetry. The non-official status is fortunate, because as a good “Neville Chamberlain atheist” I do not wish to offend anybody’s faith, least of all that of a commenter who was nicely asking a question, and I must say that I will be highly critical of Demetry’s level of both scientific knowledge and philosophical acumen. I understand that one cannot expect very complex and precise philosophical arguments from a FAQ, but one should at least avoid elementary mistakes.

The paragraph Alana quotes (adding the conclusion of the argument, which she didn’t quote) says:

Q. About subtopic (a), How is it proved from the existence of the universe that there is a God apart from it?

1.) The universe, (the earth and the heavenly bodies) could not come into being of itself because it consists of matter, which is inert. (A body is called inert, when it of itself, without external influence, cannot change its state.) Therefore there must be a personal Power apart from it, which gave it its beginning. And this personal Power is God.

The conception the Reverend has of matter seems taken straightly from scholastic philosophy, with no contamination from modern science. It is unclear what is to be understood by the “state” of a body, but on any natural reading, the assertion that matter is inert in the defined sense is false. As a very simple example, take an lump of an unstable element, such as uranium; left to itself and without external influence, it will emit spontaneously (at times not predictable except in a statistic, probabilistic way) a radiation of particles (radioactivity) and its atoms will transform gradually into different ones. Contrary to what I hastily wrote in a comment to the previous post, this also can happen to elementary particles: the muon, for example, transforms spontaneously into an electron, a neutrino and an antineutrino, even though it is currently believed to be elementary (not composed of more basic particles). There are hundreds of other examples one can give of material systems that change their state without external influence, and one does not need fancy complicated physics: how about a digital clock, continuously updating the display? An ordinary alarm clock, suddenly ringing? A volcano erupting? And so on…

But leaving aside all this, the argument is still an obvious non sequitur. Substituting the definition of “inert”, the structure of the argument is:

(1) Matter cannot change its state without external influence.
(2) Therefore, it could not come into being of itself.
(3) Therefore, there must be a personal Power apart from it, which gave it its beginning.

How does (2) follow from (1)? (1) is only about how matter can change, while (2) is about how it can begin to exist. Okay, perhaps we can allow for “coming to exist”, as a subspecies of change, though it sounds strange. But (3) certainly doesn’t follow from (2) and (1). No argument is made to show that matter could not have existed forever. Even if such an argument could be made, it still wouldn’t follow that it was created by a personal power. “Personal” qualities (consciousness, intelligence, purposefulness, etc.) are empirical features of the world that we see exemplified in only a few beings on the surface of a tiny planet. To attribute them, without any argument, to the unknown First Cause of the universe is to make a gigantic leap in reasoning that cannot be left unjustified.

I see this as the main stumbling block of cosmological arguments for a deity, even those that are much more sophisticated than this one. I do not find the case for a First Cause or a Necessary Being persuasive (I think I can conceive perfectly well an infinite regress of causes or explanations), but even if there is an Ultimate Explanation, maybe it takes a “formal” nature more akin to a physical or mathematical principle than to a Being; and even if it is a Being of sorts, I have never seen any good reason to suppose it to be a personal one. Most of the arguments for this that I have seen depend on a spurious dichotomy between Matter and Persons (or in other words, between mechanical and teleological explanations), together with a spurious conception of Matter as “inert” and Persons as “active” (or in other words, of mechanical explanations as always needing further ones, while teleological ones get a free pass as acts of will.)

All these are concepts and distinctions that fit perfectly into the scholastic, medieval view of the world and very badly into the modern scientific one. I’m not saying that modern science can prove medieval philosophy to be “wrong”, except in a few peripheral matters. One can always start from a philosophical system, declared to be a priori known, and interpret the whole of world and science according to it. But I find it more reasonable to begin with modern science as a solid starting point (there is much more agreement among scientists that among philosophers, after all!) and then try to build up a philosophy that squares well with it. And according to such a naturalistic philosophy, purposes and intentions are not free-standing fundamental metaphysical categories but just features of the way we describe and explain at a high, emergent level the behaviour of some very complex material systems –us.

I have sidetracked, however, discussing more general cosmological arguments and my opinions on them, rather than concentrating on Rev. Demetry’s arguments. This is sensible, because Demetry’s next arguments are unbelievably silly. The Introduction to the document does not give any dates, but one can infer from it that Demetry lived in the twentieth century, and not too long ago. Were it not for this, this argument would make me think he was writing in the sixteen hundreds. His scientific knowledge has not surpassed that stage:

2.) The Universe, according to the astronomers, moves, and moves regularly, and in circles (rotates). This rotating movement needed a power apart from the universe to produce this motion, and, in order that the power should not be exhausted or become larger or smaller, a Personal and Omnipotent Power is needed to renew the power which is lost on account of the friction of the motion, and to regulate it so that the motion might always be uniform.

The Universe rotates??? God renews the power lost in the friction???

*shaking my head in disbelief, as if having seen a living fossil in the wild.*

Demetry seems to be taking a leaf from Isaac Newton, who argued that God’s action was needed to keep the solar system perpetually moving because otherwise the perturbations that some planets cause to the orbits of others would make it unstable. But even Newton (and Kepler before him) knew that the planets do not move in circles but in ellipses. And the idea of the whole universe rotating is even more obsolete: it only makes sense in the geocentric cosmology that Copernicus and Galileo overthrowed. It is not only the Reverend’s philosophy that is medieval… Of course, even in Newton’s days his argument was attacked on philosophical grounds by Leibniz, who said it was diminishing of God’s perfection to have to tinker continuously with his creation like a clumsy watchmaker. The point was rendered moot when later it was proven that Newton’s calculations were wrong and that the Solar System can survive by itself without any external tinkering. Nowadays arguments for God from misunderstandings of physical cosmology invoke more usually the Big Bang; their philosophy is not much better (see the link for my comment), but their science is at least updated.

I will not go on with Demetry’s next arguments for the existence of God, which are not much better than the ones above. I will, however, quote a passage that made me jump in my seat when I saw it, from the section on the Trinity. We read:

Q. Can we understand the Holy Trinity?

A. No, because it is a mystery.

Q. What is a mystery?

A. A mystery is a truth which we cannot understand.

So far so good; I would certainly accept that there are many truths we cannot understand at present, and maybe there are some that we cannot even understand in principle (though this would depend on how we understand “truth”; deep philosophical waters await there). Of course I would reject that the Trinity is one such truth, and moreover I would reject that we can ever have warranted belief in a truth if we believe we cannot even in principle understand it; one could also wonder what is meant exactly by believing something you do not understand, beyond repeating the words in an empty way. But certainly there is material there for a thoughtful philosophical or theological discussion. Look, however, how Rev. Demetry tries to argue this matter:

Q. Is it right that we should reject everything which we cannot understand?

A. No, because there are many things which we do not understand, but which exist, and which we use continually; for example, magnetism, electricity, gravity, etc.

*blinks and stares*

Snarky reaction: “Well, the fact that you don’t understand them doesn’t mean anyone else can’t, after just a couple of years of basic physics courses!”

More serious reaction: We do understand magnetism, electricity, and gravity; I can write, in just a couple of lines, the equations that these phenomena satisfy in all conditions that have been studied so far. Of course, this understanding is not complete: we don’t know for sure if these same equations hold in other conditions we haven’t tested yet; indeed, we have reason to believe they don’t hold –for example- at very small length scales, and we do not understand what equations replace them. But exactly to the degree to which we don’t understand these phenomena, we lack as well any warranted beliefs about them. To the extent that we don’t understand gravity at the quantum scale, we do not hold the belief that gravity “exists” at that scale, and in that sense we “reject” it, or at least we remain agnostic. So as an analogy to the Trinity, this is absolutely dreadful and backfires completely against the Reverend: following the analogy would be a good reason for me to not believe in the Trinity. Even knowing next-to-nothing about the theological conception of the Trinity, I am sure I could write a better defense of it than this one, in the spirit of Sean's recent post.

I hope I have answered Alana’s question without being too aggressive or dismissive. I do not think that religious people are necessarily stupid or even irrational (see here), and I think some theological arguments deserve to be taken seriously. But I'm sorry to say that I cannot take seriously those of Rev. Constas H. Demetry.

By the way: Readers asking questions or petitioning for posts on subjects are a good way of making me overcome my natural blog laziness. So, is there any other topic you would like to see discussed here?

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