### 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...

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...

## 6 Comments:

It's well-known lore among various parts of the physics community that you cannot simply square the constraints and obtain anything useful. I believe this is stated, for example, near the beginning of Henneaux and Teitelboim. Can Thiemann demonstrate any nontrivial

quantumeffects of traditional quantization in his "master constraint" formalism? It would be helpful to see a calculation involving some sort of anomaly, for example.(There is some discussion of this here).

By aaron Bergman, at 11:42 PM, April 16, 2007

Hi Aaron,

You might try to have a look at Thiemann and Dittrich's series of papers "Testing the Master Constraint Programme". In particular the last two (http://arxiv.org/abs/gr-qc/0411141 and http://arxiv.org/abs/gr-qc/0411142) apply it to free and interacting QFTs and claim to get satisfactory results.

But perhaps the case of free fields (where the ususal results are recovered) does not count as nontrivial, and you will find his treatment of the interacting case unsatisfactory because an LQG-like representation instead of the Fock one is used. Also, there is no discussion of cases with anomalies.

Regarding the discussion you link to, Jacques Distler's main complaint is that with quantization techniques as nonstandard as Thiemann uses there is no clear relation of the results to the original classical theory. Thiemann's program is to ensure the classical limit by demanding that the master constraint operator must have the right expectation value on semiclassical kinematical states. As I said a few posts ago, he claims this to be enough although I can't really understand why.

(Can any of my readers give better answers? I do not work really on LQG, though I am interested in it and trying to learn more. I'm sure many of my readers are better qualified than I am to serve as spokepersons for the "LQG community" in this kind of discussion...)

By Alejandro, at 12:40 PM, April 17, 2007

I don't mean to be harping on these things to you incessantly, but these points seem to me to be sorely neglected in communication between LQGists and the rest of the high energy community. Disappointingly, I didn't here them raised in the recent KITP program (although I might have missed it.) Some people I talk to talk as if Thiemann's program is the essence of canonical LQG while others (well, 'other' actually) have told me it makes no sense and that other directions are where I should look for the good stuff in LQG (say, spin foam stuff.)

As I said, this whole program goes against all the usual adages I've heard when quantization is discussed, and the failure to, say, reproduce the anomaly in 2D isn't particularly encouraging.

By Aaron Bergman, at 4:37 PM, April 17, 2007

I certainly agree that more communication is needed between the LQG community and the rest. A friend with whom I was discussing this today said that people used to the tools of QFT in a background and those pusuing background independent approaches talk sometimes in different languages. This may be so but in any case all languages should, if valid, describe the same physics, and given that the LQG group is less mainstream it is their responsability to engage the others, answer their criticisms and explain their results in a languange the others can understand. Otherwise the divide will only become greater and greater.

So don't apologize for "harping"... I only whish more people were asking that kind of questions, and more were answering them on our side.

I think the problem with Thiemann's approach that explains the sociological oddness you mentioned is that very few people outside his group of collaborators understand it fully. The positive or negative impressions may be more based on just "trust" or "mistrust" than on a careful critical evaluation.

By Alejandro, at 6:39 PM, April 17, 2007

On second thoughts, I am not really in any position to assess whether most LQGers understand Thiemann or not -my only evidence is talking with a few other grad students, who wouldn't be expected to understand everything if they don't work in that area... So don't quote me on that last paragraph.

By Alejandro, at 10:16 AM, April 18, 2007

To my mind one and all must browse on it.

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By Melvin, at 5:05 PM, November 22, 2011

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