Reality Conditions

Monday, April 30, 2007

Teleportation: why you survive

This is a belated follow-up to a post I wrote almost two months ago, in which I polled my readers as to whether teleportation (understood as destroying a body after recording its exact structure, sending the information somewhere else and re-constructing it there) would kill the original person and create a different with false memories, or whether the original person would survive as the teleported one. (If you missed that post you would do better reading it and the comments discussion before this one.) The results were 5-3 in favour of survival (6-3 including myself) but my friends Merrick and DrNitro voted for death, and this post is an attempt to convince them and other skeptics of why I would not be afraid of using such a machine, in the extremely unlikely case that it becomes technologically possible in the course of my life.

Let us first assume without discussion that the “self” does not reside in an inmaterial soul. I think my friends agree with this assumption. Their certainity that the teleportation experiment kills you is grounded in the implicit belief that you are essentially your body, and destroying your body destroys you. But this is not completely exact, because they would probably agree with me that you could survive the destruction of any part of your body, or all of them, with the exception of your brain. If my brain is kept functioning (perhaps in a vat, as in the old Matrix-like philosophical scenario) then all the rest of my body can be destroyed and I will surely survive. So the only question is: Is my survival tied to the survival of my concrete, material brain, or only on the survival of a pattern of brain structure, enconding my personality traits and memories, such that if a new brain comes to exist with this same pattern I continue living in it?

I will give now two arguments (actually, two thought exeperiments or “intuition pumps”) for the second option.

First argument: Suppose we perform the teleportation experiment with a guy –call him Ernest- while he is in coma or deeply anaesthetized. Suppose that we don’t destroy the original Ernest, but only scan his body and send the information to create a duplicate Ernest. (Technical note: as commenter Dmitry remarked, this is physically impossible if the teleportation must copy the exact quantum state of the original, as that is impossible without destroying it. I am assuming that the features of brain structure responsible for the self do not depend on the quantum state.) While both are still unconscious, we lie them side by side and randomly mix them up, so nobody can tell which is the original (not even us, if the randomization and arrengement is made by a computer that doesn’t save the information). Now we prepare to kill one of the copies and awake the other one.

According to my friends, it matters a great deal which copy we destroy. If we kill the original, we are murdering Ernest, and the awoken copy will be just an imitation with faked memories; while if we destroy the copy before awaking it, nothing bad has happened and Ernest goes on living normally. But how can this be? Both bodies lying there are completely identical in every detail that matters. Setting aside random influences that may have changed them since the duplication (which would have affected any of them with no preference) they will react in the same way if awakened, remember the same things, feel the same way. Which body was the original and which the copy is what Daniel Dennett would call an “inert historical fact”. It is a fact purely about the past, that cannot affect anything anymore in the present or the future. How can whether Ernest lives or dies depend on this fact?

To make this intuition stronger, imagine that the experiment is done with the brains. We first destroy Ernest’s body keeping alive in a vat his unconscious brain; we all agree that this doesn’t kill him. Now we duplicate the brain and mix up the two copies. We have in front of us two brains in two vats, exactly alike in all neronal details; any of them if awoken would claim to be Ernest. Unless we believe that there is an invisible soul mystically attached to the original brain of Ernest, how can it matter for his survival which of the two we choose to awake? If thought and consciousness are just brain activity, and the same brain activity would go on in both brains, then any of them we choose to awake will continue Ernest’s life equally well.

This was my first argument. My second one involves a different series of modifications we can make to poor Ernest’s brain. Let’s take anaesthetized Ernest and perform on him any of the following operations. (Assume they are technically possible –even if they are not, I don’t see any impossiblity in principle going on here, surely not more than in the teleportation experiment):

a) “Freeze” his brain so all living signs are completely disappeared, and then “relive” him.

b) Same as above, only that while the brain is “frozen” we cut separate a small part of the brain and then “patch” it together with the rest in exactly the same way it was. (We can decide how large to cut this piece, from a very small one to as much as half of the whole brain).

c) Same as above, only that instead of cutting only a part we cut his whole brain in many little pieces, and then put them back together again.

d) Same as b), only that we duplicate with our teleportation machine the separated piece and use the duplicate instead of the original to reconstruct the whole brain.

e) Same as c), only that we duplicate all the pieces and make the complete brain using the duplicates, or perhaps some of the duplicates and some of the originals.

Now, question for those who believe teleportation is death: In which of all these cases is the brain/person that awakes after the operation Ernest, and in which it is not Ernest but a mere copy and Ernest has died? For me, this is a non-question; the person that awakes has in all cases Ernest’s personality, memories, etc, so he is Ernest and it doesn’t matter which parts of the brain are originals and which not, or whether the brain has had a continuous uninterrumpted existence as a whole object. But for those who disagree with me there has to be a difficult question in deciding where to draw the line: they should say that Ernest has died in case e) (which is very similar to the original teleportation scenario) and that Ernest is still alive in case a), but what of the intermediate cases? Exactly how much of the original brain needs to have persisted for Ernest to survive? Any answer seems to be arbitrary. The simplicity and non-arbitrariness of my answer to these questions seems a good argument for my position.



Thursday, April 26, 2007

More Polish pictures

The webpage of the Quantum Gravity and Quantum Geometry School has put up some good photos from the conference, chosen as a selection from all the pictures taken by participants.

Tuesday, April 24, 2007

Science and Philosophy links

A few links on topics intersecting philosophy and science:

* Matt Leifer argues against the many-worlds interpretation of quantum mechanics from a Quinean philosophical standpoint.

* Lubos points to a paper by Hartle and Srednicki criticizing sharply the way the anthropic principle and related "typicality" ideas are used in cosmology. The gist is that, if we do not know that we were selected as random observers by a physical process, we should not calculate as if we were.

* David Corfield discusses two cultures within mathematics: the theory-builders and the problem-solvers.

* Richard Chapell discusses whether philosophy needs science. He thinks only perhaps in practice, not in principle. I disagree and explain my reasons in a comment there.

* In the latest Philosophers' Carnival there is a special entry featuring Dan Dennett's article "Higher order truths about chmess". I had read it some time ago, and I definitely recommend you to read it as well; it criticizes certain aspects of contemprary philosophy, in a way which could also be applied to contemporary theoretical physics. (It sits well with a remark made by Carlo Rovelli in the talks blogged about previously, that we should focus on problems of physical interest and not in technical investigations about unphysical situations that are good for publishing quick papers. It also links somehow with my comment at Richard's blog.)

Monday, April 16, 2007

Report on the Quantum Gravity School: the discussion

Carlo Rovelli's talk on "Where are we on the path to Quantum Gravity" was scheduled to have two parts, one on the evening of each of the free days we had. He chose a different format: the first day he talked, and the second day he read a list of questions from a sheet of paper that had circulated among the audience on previous days, and gave his opinion on them encouraging people to give theirs and discuss. I think this was an excellent method, and the only problem with it was that we didn't have unlimited time; the discussion session started at 6 pm and the dinner at the hotel closed at 8. As the list had no less than 23 questions set for discussion (some of the first of them raising heated opinions, like the quantum measurement problem!), many of the last got a very short time, and the last six didn't get any discussion at all.

As I think my notes from this discussion session will be of more interest than those of the first talk, I limit this post to sharing these with you. Besides, Francesca has already a brief summary of some points raised in the first talk at this Physics Forums post.

Here, a list of questions written by people and the discussion they got, loosely organised by subjects in the way Rovelli read them:

1) Is there a relation between quantum gravity and the measurement problem in quantum mechanics?

Rovelli mentioned Penrose and t'Hooft as important voices on the affirmative. His own position is that, while regarding the foundational questions in QM as still open, they have no specific relation to quantum gravity; one may try to develop a quantum theory of gravity without needing to solve the philosophical problems. Someone objected that the problems overlap at quantum cosmology, where many people think you have to use the Everettian interpretation or some variation thereof because there is no "external system" to the universe. Rovelli answered distinguishing two meanings of "quantum cosmology" and "the wave function of the universe"; it might mean "a quantum mechanics that is self-contained, including no external observer", and then it relates to the foundations problem, but it has no specific connection with actual cosmology and with gravity; or it can mean "quantum theory of cosmological degrees of freedom", and then you need quantum gravity, but you don't really need to have a philosophy of QM for doing that, as you can have an observer within the universe measuring its cosmological properties and use naive "Copenhaguen" interpretation. I agree that this sounds sensible, but see the next question.

2) Has there been work using decoherence with relation to the classical limit in LQG (or spin foams or the other models we learnt about)?

This was the first of the three questions asked by yours truly. I was inspired to ask it by my conversation with Eugenio Bianchi about the graviton propagator calculation, in which I suggested that instead of fine-tuning the boundary state to ensure it remained semiclassical one could perhaps introduce an environment to keep it classical by constantly "measuring" it. Rovelli said he couldn't recall any work on this, and he didn't seem to think it was a very important idea. Relating it to the previous question, I think it may be important in the following sense: I agree with Rovelli that decoherence does not solve the philosophical problems of quantum theory, but in my understanding it does provide an excuse to forget about them when doing concrete calculations. For example, if you are an Everettian who thinks that the wave function "really" never collapses, decoherence tells you that in practice all results will be indistinguishable from those obtained by assuming a true collapse in measurements, so you can go on using "naive Copenhaguenism" and forget about the philosophy. But decoherence provides this only provided you have an environment, with statistical dissipation and especially a time asymmetry given by a direction of growth of entropy. Otherwise you could never get the appearance of time-asymmetric collapse out of unitary evolution of a time-symmetric theory. Therefore if you are trying to do quantum gravity in a fundamental, "timeless" way, then you may need to think carefully which philosophy of quantum mechanics you endorse and assume in your theory, because you don't have decoherence to provide an "effective equivalence" of the different interpretations. Either that, or you may try to introduce an environment and some kind of decoherence describing it with the "timeless" framework you are using. My question was pointing to this kind of thing. After the discussion someone approached me and told me that there has been work done with decoherence in quantum cosmology to model the passing from the quantum regime to a classical universe. In fact, I knew about this work before, but had forgotten about it.

3) How are singularities dealt with in quantum gravity?

Rovelli summarized briefly the results in Loop Quantum Cosmology that show avoidance of Big Bang singularity, and similar results for black holes. He also mentioned there is a lot of work done in string theory on the same issues. Someone asked whether there was a formal definition of singularities in QG, and Rovelli said that for the moment there wasn't and the usual criterion used for singularity avoidance was boundedness of expectation values of curvature operators.

4) The quantum theory of gravity, unlike the classical theory, has a preferred energy scale given by the Planck mass. Can this result in a broken or deformed diffeomorphism invariance at the level of an effective, semiclassical theory?

Rovelli seemed slightly dismissive of the idea, saying there weren't any reasons to think so. This question was posed by two friends of mine who read this blog, so hopefully they will argue for and defend their idea in the comments ;) .

5) What is the fundamental meaning of symmetry?

I have no notes on the discussion, except an "Unclear", and can't remember anything about it. Comments...?

6) Can Hawking radiation be derived from QG?

Not in the framework used for the famous calculations of entropy from counting area states, which assume a static black hole. Perhaps something will be possible in the dynamical horizons framework.

7) What can kill an approach to QG, aside from experiment?

An interesting question, not only for quantum gravity but for general philosophy of science, though of course the lack of experiments in QG makes it more pressing. Rovelli suggested two possibilities: An approach may die because a different approach is having greater successes, and then most people switch to work in it. Or people may simply become discouraged if fundamental problems persist unsolved for a long time, and the approach fades away.

8) Are there any experiments to test theories of QG?

Rovelli mentioned two possibilities: the "quantum gravity phenomenology" program to test Lorentz invariance at the Planck scale, and predictions from quantum cosmology which possibly may be observable in the fluctuations of the cosmological microwave background.

9) This, Rovelli said before reading it, was the MAIN QUESTION asked in the sheet of paper. Pause for suspense, and then:

"Is there any job for any of us in the future?"

Ha! Laughs (perhaps somewhat nervous laughs?) from the audience. Rovelli granted it might be difficult, but not so terribly difficult, and gave some statistics from his own students: about 60 percent of them had found positions. (But I reckon the statistics for those with recommendation letters from Rovelli may be positively biased!)

10) Has there been any work trying to use the background independent approaches and formulations we have heard about to attempt a background formulation of string theory?

Another question written by myself. I wanted to know if the divide between the sting and the LQG communities is really as large and insurmountable as the blog discussions often make it seem. Rovelli mentioned the Maldacena conjecture and its offshoots as an attempt to provide some kind of background independence in string theory, and string field theory as a previous program that wasn't very successful; but these ideas are not influenced by the other approaches than string theory. He also mentioned some work by Lee Smolin trying to merge stringy and loopy ideas, with little success, and the "loop quantization" of the bosonic string by Thiemann, which wasn't trying to be anything else than a toy model. In conclusion, almost nothing. Perhaps (if I dare to tread in the perilous waters of the String Wars (TM)) I will write some day a post with some more thoughts on the string-LQG divide. Meanwhile, if you haven't read yet the review of the Director's Cut of The String Kings you should do so immediately. Hilarious.

11) Concerning Asymptotic Safety, has Reuter's program been put to test in well understood theories like pure QED or the Electro-Weak interaction?

For some reason I don't have notes for this discussion. Anyone can contribute anything?

12) How do the results of the Asymptotic Safety program cohere with those that indicate a fundamental discreteness at the Planck scale? The fixed point that Reuter finds is obtained following the flow of the effective action all the way to k -> infinity, to much higher scales that the Planck scale, which doesn't seem to play any special role in it.

This was the third and last question I had asked, and it came out of some big discussion I and my friends had after Reuter's lectures. It seems that our discussion had been mirrored by some parallel discussion between Reuter, Rovelli and other "big shots" themselves. Rovelli agreed that it was a very important question, that could perhaps be studied by doing Reuter-style calculations in 3 dimensions, where quantum gravity is well understood. He also said that if there is fundamental discreteness at the Planck scale, this would appear in the effective action as nonlocal terms becoming dominant after that scale. (You are insisting in treating the situation as if there was a continuum, and then you get "nonlocal" dynamics because one discrete element of geometry affects the next one at a Planck scale distance.) This is another topic in which I invite my friends who understand Asymptotic Safety better than I do to contribute in the comments.

13) How does LQG treat spatial distribution of curvature?

Answer: Spin networks are discrete states of 3-geometry; from a spin network state, the 3-curvature can be in principle found and calculated.

14) Are there ambiguities in LQG, and what is their status?

Here I think Rovelli eluded somewhat the question. I would have been very interested in hearing a detailed exposition of exactly how many quantization ambiguities are there in LQG, and whether they are expected to be solved by finding some principled mathematical argument, or by requiring the right semiclassical limit, or by experiment (ie not solved at all). But instead he repeated something he says in his book, namely that, given the apparent inconsistency of general relativity and quantum theory, our immediate goal should not to find the unique and correct quantum theory of gravity, but just to find a consistent theory that includes both GR and QM. Once we have a consistent and well-developed theory we can worry about its uniqueness. [It is impossible to resist thinking that with this philosophy, a member of the "LQG community" loses the right to be snarky about the string landscape...]

15) Are there any problems with the Master Constraint operator?

Thiemann: "I am not aware of any."
Rovelli: "A real Thiemann answer!"

(More seriously, a bit of discussion lead to the acknowledgement of some technical issues which Thiemman trusts will be solved soon.)

16) and 17) Both questions were variations on "the problem of time".

Rovelli gave an answer which will be familiar to those who have read his book Quantum Gravity, and which I find persuasive. The motto is that physics is about relations and correlations of observables between many variables, and it is not possible in general to single out one variable as "time" and discuss the change of all the rest of the variables with respect to this one. One should first learn to do both classical dynamics and quantum mechanics with this "relational" way of thinking, and then apply it to quantum gravity. All this is discussed at length in the book.

Here was where the time constraint of dinner forced us to conclude the discussion. Rovelli read quickly the remaining six questions, which didn't get any discussion time. I write them below in case people wish to discuss them here:

18) Will the fundamental theory of quantum gravity be purely combinatorial, or will it use continuum differential geometry concepts? [This is a very interesting question. I am currently trying to read Thiemann's papers on Algebraic Quantum Gavity, which seem to be the farthest LQG has gone into the combinatorial direction.]

19) Is 3D quantum gravity equivalent to a spin foam model? [Rovelli said "Yes", and went on reading the next question.]

20) What is the heuristic explanation of the relation between LQG and Spin Foams?

21) What is the status of breaking of Lorentz invariance in LQG?

22) What are the observable effects of DSR or violations of Lorentz invariance?

23) Is the Barrett-Crane model correct?

And now, let the comments begin. We have no dinner constraint on this blog, so hopefully we can go on discussing till we find satisfactory answers to all the 23 questions...

Friday, April 13, 2007


I had a long post on the discussion session chaired by Carlo Rovelli almost completely written and saved in Blogger's dashboard, or so I thought. But when I tried to sign in today to finish it and post it, Blogger forced me to upgrade to the new version using a Google account -and after going through that, I found my post was almost completely gone from the memory, with only the first paragraph remaining. I don't know if it is somehow Blogger's fault and related to the account switching, or if I was really absent-minded enough to not save everything I had written and still be completely convinced that I had saved it. But anyway. This means that you won't be seeing the post on the discussion session today, as I feel too pissed off and tired to rewrite it now; I promise to do it in the weekend. My apologies.

Meanwhile, to keep the "reports from the QG school" series alive, I write a short post informing you of an addition to the English language we came up with during the school. The neologism we coined is upstuff. It has a very simple and beautiful definition:

Upstuff is what you are making when you make up stuff.

So it has a similar field of meaning that "bullshit" or "crap" (applied to talk). But these are completely negative words, while "upstuff" is neutral or even positive in evaluation. Sometimes it is fun to make up stuff and to listen to people who make up stuff. If you have friends who are slightly geeky (and share a taste in hunour with some of my own slightly geeky friends), you might be familiar with a situation in which an informal question or demand for information is answered with an inspired, lenghty explanation randomly made up in the moment. This is a perfect example of good upstuff. A concrete case in point is this wonderful post at the Volokh Conspiracy. (For my Argentinian readers, "fruta" as in "mandar fruta" is a good translation for "upstuff", although perhaps less positive in connotation.)

I think this is a word and concept that the English language sorely needs, as was proved by our very frequent use of it in the days after coining the word. I rely on you Dear Readers to use it and propagate it widely.

The serious reports on the physics will resume, as promised, after I find time for rewriting the report on the discussion session, which you can expect to see it posted on Sunday or Monday. I promise it will not be upstuff.

Tuesday, April 10, 2007

Report on the Quantum Gravity School: the lectures (2 – Asymptotic Safety)

I had promised to write about Martin Reuter’s lectures on Asymptotic Safety. These were the “surprise hit” of the school; Reuter had only five lectures slots assigned, less than many other speakers, but it was the results presented by him which arose most excitement and discussion. I would have been happy with one or two more lectures on the subject. The time spent answering interested questions forced him to leave out of the program the topic of fractal dimension of spacetime at high energy scales.

Let me attempt a brief summary of the Asymptotic Safety approach to quantum gravity, as I understood it. (There may very well be inaccuracies and even gross mistakes; I expect you to point them out if you see them). The cornestone of the program is the hypothesis, first proposed by Weinberg, that the renormalization group flow for gravity might have a non-Gaussian fixed point when examined nonperturbatively. That would mean that the quantum theory would be well-defined despite not being perturbatively renormalizable.

Consider a “theory space” formed by all possible diffeomorphism invariant action functionals of the spacetime metric. You can “coordinatize” it by the values of dimensionless coupling constants of different terms, where the dimensionless couplings are constructed from the dimensional ones dividing them by the energy scale k at which you are thinking the theory (to the relevant power). For example, you would have the Einstein-Hilbert action with couplings G and Lambda (suitably rendered dimensionless), plus terms with any power of the curvature scalar, and of the square of the Ricci tensor, and so on. You can define on this space the Exact Renormalization Group Equation (ERGE) which determines the flow of the effective action for gravity in this space. The effective action is the action from which all interactions at scale k can be calculated accurately at tree level. Varying the scale k, the couplings start “running” and some may be turned on or off. If the flow of the effective action, for k going to infinity, reaches a fixed point at which the couplings are not all zero, this is a non-Gaussian UV fixed point and the theory is said to be assymptotically safe. If in addition the flow towards the fixed point is attractive in only a finite number n of dimensions in theory space, the “bare action” you find at infinite k will have only n free parameters, and the exact quantum theory will be as predictive as a perturbatively renormalizable theory with n adjustable parameters is.

Of course, solving the ERGE exactly is out of the question; it is an infinite system of coupled differential equation. The strategy Reuter uses is “truncation” –arbitrarily decide to consider only actions with a given number of terms of a given kind. For example the first and most brutal truncation is the Einstein-Hilbert one: consider only the flow of the two terms of the EH action, with couplings G and L (the L is supposed to be read as "Lambda" and represent the consmological constant). It would be an abuse of language to call this an “approximation”, because a priori there is no reason to believe that the results of the exact flow will be close to those of the truncated flow, or that taking more terms will yield better and better approximations, as long as there are still an infinite amount of neglected terms. To a skeptical mind, this renders the whole program worthless. But Reuter managed to convinced many of us nevertheless that the program was being highly successful. I will explain now the results with which he archivied this effect.

First: the flow of the EH-truncated renormalization group does have a non-Gaussian UV fixed point. The trajectories flowing back from it with decreasing k spend a lot of “time” in the regime where the dimensionless couplings are small. In these region the flow looks “classical”: the dimensionful G and L are constant.

Second: There is a cutoff scheme involved in the calculation. For the exact ERGE, the results are independent of the cutoff scheme, but this is not guaranteed to happen in the truncated calculation. However, Reuter and his collaborators find that the results they have obtained are in fact independent to a high degree of the cutoff used. They take this as partial evidence that a similar fixed point exists in the full, nontruncated theory.

Third: The “next order” of including in the action a third term, proportional to R^2, has been carried out. It must be stressed that there is no reason at all to suppose that the results with this term included would resemble those without it. Instead of two coupled differential equations we have three now, so the situation is much more complicated. However, surprisingly enough, essentially the same fixed point is found! The values of dimensionless G, L on it are almost exactly the same than those at the fixed point found in the EH-truncation, and the coupling of the added term is very small at the critical point.

Fourth: There is very recent work which extends the previous results to actions containing all powers of R up to R^6. The system of 7 coupled diffential equations is now hugely complicated, and if the exact theory did not have a fixed point it would be “magical” that the flow leads to the same point as the previous truncations did. But it does! The GL-projection of the flow near the fixed point is still essentially the same as the one found with the original EH-truncation. Moreover, the dimension of the “attractive hypersurface” is only 3, which means that the bare action has only 3 independent parameters instead of 7 within this truncation. This gives hope that the exact theory may be predictive.

These results had us all very excited! Reuter also talked about some implications for cosmology that arise if we assume the EH-truncated flow to be a good approximation. One important one is that, if the RG trajectory realised in Nature has a “long” classical regime at all, then the physical cosmological constant L is automatically constrained to be much smaller than the physical Newton’s constant G. Thus the smallness of L poses no extra “naturalness” problem beyond the mere existence of a classical regime. Another one is that Reuter expects the truncation to break down as an approximation in the infrared, at length scales much larger than the “classical” regime. Nonlocal terms would presumably begin to act there. A dimensional argument shows that the scale at which this should happen is the scale of the physical cosmological constant! Reuter therefore makes a (very tentative) prediction of new physics at the Hubble scale, and even speculates on a relation to alternative MOND-like theories to dark matter.

Much more work would be needed to see if there is anything substantial in this last speculation, and in the approach as a whole. The exciting thing is that it is a little explored path, which despite being fully "background independent" uses techniques familiar from ordinary QFT, and may be able to make contact with it more easily that models which introduce discrete physics like LQG or spin foams. Of course, even if the exact renormalization group flow has a fixed point with all the required properties and quantum gravity exists as a theory by its own right, this doesn’t mean that this is realised in Nature! String theory provides a very different UV completion to gravity, and if it is true I guess it would render the UV fixed point of “pure gravity” physically irrelevant. But if one of the main motivations for string theory in the first place is the non-renormalizability of pure gravity, then Reuter’s results are making this motivation rather shaky.

Sunday, April 08, 2007

Report on the Quantum Gravity School: the lectures (1)

I will not copy or summarise the program of lectures we had, as you can read it here. From my point of view, there were three sets of lectures that were the “main course” of the school, which were: Thomas Thiemann on Loop Quantum Gravity, Martin Reuter on Asymptotic Safety and Laurent Friedel and Etera Livine on Spin Foams (these last two sets of lectures can be seen as the first and second part of one set, as Friedel covered mostly 3D spin foams and Livine talked about 4D models). The other lectures, though sometimes very interesting, covered more peripheral or mathematical topics.

In the Spin Foam lectures, Friedel defined the basic structure of spin foam models, introduced the diagrammatic notation used for them, and discussed 3D quantum gravity extensively as an example, both without and with matter. It was only by the end of the last lecture that he reached the connections of the latter case with an effective non-commutative field theory with deformed Poincare invariance, which is probably the most exciting ofshoot of this research. Livine discussed four-dimensional models, which arise from writing gravity as a constrained BF theory. He centered on the Barrett-Crane model, and sketched the calculation of the 10j symbol, showing that from it the Regge discretization of gravity arises naturally but with extra “bad” terms. He them talked about the calculation made by Rovelli and his collaborators of the graviton propagator from spin foams, which eluded this problem by introducing a boundary semiclassical state with a phase that, when the calculation is carried out, cancels exactly the “bad” terms of the 10j symbol.

I may add some personal remarks here. When I first heard about the graviton propagator calculation I was excited, but I was unsure as to whether that phase had not been but “by hand” to ensure a nice result which otherwise the theory refused to provide. That is often the problem when you don’t actually work in a field (and you lack the experience and smartness required to check claims by yourself if you don’t work in it): you read a paper and if it gives you this kind of suspicion, you have no way of deciding whom to trust. This is one reason why it is so great to travel to conferences and get an opportunity to discuss face to face with people who don’t mind answering your questions even if they are naïve. In this case it was a dinner table conversation with Eugenio Bianchi that reassured me that the calculation was sound. The phase of the boundary state is not arbitrary or chosen by hand: it is the correct phase to use for the state to be really semiclassical, being peaked not only in the “configuration variables” that specify the classical boundary geometry but also in the “momentum variables” conjugate to them. In fact, in the LQG lectures Thiemann constructed a precise mathematical definition of “semiclassical states” and, according to Bianchi, the state that Rovelli, he and the rest used was the same kind of state, independently found by physical ansatz instead of rigourous mathematical definition. (All this was in fact actually explained in their paper; but reading it after a personal explanation is so much clearer!)

Going back to the lectures, the most intensive ones were Thiemann’s twelve lectures on canonical Loop Quantum Gravity. I certainly learnt a lot from them, and not only abouth LQG per se but also about more general things like constrained systems and how a quantum algebra is constructed from a classical one. The Master Constraint program for dealing with the Hamiltonian (which replaces the constraint at each point of space by the integral over all space of the square of the constraint) was introduced, and after some discussions of the subtleties and ambiguities to be solved, Thiemann enunciated (without proving –that would have probably another 12 lectures!) an important theorem: A particular “quantum Master Constraint operator” was defined in such a way that satisfies all desired properties, including finiteness, dipheomorphism invariance, and most importantly, good semicalssical behaviour. By this Thiemann meant that given a classical field configuration (a pair A, E of Ashtekar variables) one can find a semiclassical state (built as a superposition of spin networks which peaks on it) that makes the expectation value of the MC operator agree with the classical value of the MC to within any desired accuracy. (It is important for this that the classical state and the semiclassical one that approaches it are not physical states, in which the constraint vanishes).

After this, Thiemann also defined in a formal way the scalar product in the physical Hilbert space, which suggestively can be seen as the “time integral” of a transition amplitude. He commented on the possibility that spin foam models might benefit from using the master constraint instead of ordinary constraints, something that has not been tried (and I have no idea how it could be tried). He also described a way to compute expectation values of the volume operator to arbitrary precission in semicalssical states, and mentioned (unfortunately briefly) his more recently developed "Algebraic Quantum Gravity". After the lectures ended I imprudently tried to ask him (in personal conversation) a question concerning “the unsolved problem of the classical limit of LQG” and cut me by saying that the problem was already solved! What emerged from our follwing conversation (which on my side had a rather bewildered face) was this: the “problem of the classical limit” consists in showing that there exist in LQG physical states that, looked at large scales, resemble a nice classical manifold on which GR holds; the semiclassical behaviour of the Master Constraint operator described above implies, by some subtle argument involving projection which I could not follow, that there will be physical states with this property; therefore, the problem is solved. It does not matter at all that most combinations of spin networks, or even most physical states, will not give anything resembling a classical state at large scales. This is the same that happens in ordinary quantum mechanics: coherent states, with nice semiclassical properties, are a very particular kind of state, and most combinations of large number of individual quantum objects do not look at all like anything classical. It is enough that there be nice semiclassical states, not that they be generic.

Of course, this does not mean that one knows how to write a physical state approaching Minkowski (or Schwarzschild or any other classical solution). One doesn’t even know how to write any physical state! But I think that Thiemann’s argument does show, somehow, that this problem is merely technical and that there is no fundamental problem in LQG with respect to the existence of the classical limit. I am interested in hearing my readers’ perspectives on this.

This post is already rather long, and I still have much to say about Martin Reuter’s lectures on Asymptotic Safety, so I think it is a good idea to stop here for the moment. Expect the next post within a couple of days.

Thursday, April 05, 2007

Report on the Quantum Gravity School: the pictures

Being back from Poland only since yesterday, I start here a series of posts reporting on the Quantum Gravity and Quantum Geometry School I attended there. This first one is just for putting up some of the best pictures I have from the two weeks, as many people have been asking me for them. As you can see, Zakopane and its surroundings (the Tatra mountains) are a quite wonderful place.

This group picture of those of us who made it to the peak was taken by Carlo Rovelli.

Thomas Thiemann solving the canonical constraint equations for quantum gravity.

John Barrett and Ileana Naish-Guzman on a long hike we made on the first free day.

Picture taken shortly after the previous one. I urge you to see both on full size by clicking on them; they may easily be the best photos I have taken in my life.

A bunch of happy and slightly inebriated physicists after dining out on one of the last nights

The next post will briefly summarize some of the most important lectures, and the following one will describe at length the discussion session "Where are we in the path to Quantum Gravity?" chaired by Rovelli. Stay tuned!

UPDATE: Oooops, it seems you cannot enlarge the pictures by clicking on them. Well, if you really want to see them just email me and I will send them.