127. Ashtekar at Perimeter Institute
ASTRO, HEP-TH/PH — By Dmitry Podolsky on December 8, 2008 at 1:47 pm
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Abhay Ashtekar has recently visited the Perimeter Institute and gave a couple of talks – about loop quantum gravity of course, since he is one of the major players in the LQG field (considered to be its inventor). I think, both of the talks are worth watching (or at least scanning through his transparencies available as PDF file at PIRSA) for a person who wants to understand what LQG is about. If you do not have an intention to watch them 
, I shall explain you what both of them are about.
1. Big Bang singularity
The first talk is for generic audience (i.e., promotional one rather than technical). It is devoted to the discussion of possible resolution of the cosmological singularity in a full quantum gravity theory (he certainly means LQG by that).
Ashtekar wants to discuss only isotropic homogeneous cosmological models and their quantization a la Wheeler – de Witt. This seemed always suspicious for me, because, as we know from the works of Belinsky, Lifshitz and Khalatnikov, in the quasiclassical approximation spacetime becomes essentially anisotropic in the vicinity of the cosmological singularity (its metric is given by famous BKL general asymptotic solution of the Einstein equations near the singularity). Listening his talk, I arrogantly concluded that Ashtekar wants to quantize Friedmann equations just because he is able to do that, not because the physics of the problem requires him to. No single mentioning of inflation, horizon-flatness-entropy problems. In overall, it is quite unclear what is the physics behind his talk and why it is interesting (apart from mentioning the magical word “Big Bang singularity”).
2. Black hole singularity and information loss
His second talk is more technical (and therefore – more interesting). It is somewhat surprising to me, but the results are not based on LQG in any way. The talk is about the resolution of spacelike singularities in a full quantum gravity theory. (If you want to know how AdS/CFT is dealing with the issue, please follow the recent discussion on Dirac Sea Shores featuring Moshe Rozali, Lubos Motl and many confused people including myself.)
The talk is based on speaker’s recent PRL paper. One key idea is that if we take the whole history of evaporating black hole into account, event horizon does not exist, since it’s the feature of the global spacetime. On the other hand, trapped surfaces are there during a finite amount of time and dynamical horizons do exist.
He is considering dilaton gravity in 1+1 dimension (dilaton+gravity+massless scalar field). Gravity depends only on the scalar curvature, so essentially he has three coupled differential equations for three scalar variables. He first considers the collapse of the scalar field and concludes that the only relevant degree of freedom is the distribution of the scalar field (which is of no surprise – since gravity in 2d is topological 
)
The corresponding classical solution for the scalar field is regular everywhere, but there is one point where metric is singular. He wants to interpret it as a black hole singularity (why?).
Then, he takes his classical equations, promotes them to the equations for the Heisenberg fields and solves by bootstrapping (taking a seed metric, calculating trace anomaly, substitute it back to the equations, find the response of the metric etc.) Considering mean field approximation and behaviour of solutions of the equations of motion at future infinity, he concludes that the out state is pure state and there is no information loss in the system.
His talk has left me with many questions…
- Why does he use mean field? When is it applicable? What would be the next correction to the mean field?
- Why does he interpret the singularity in classical EoMs as a BH singularity? Where is the horizon (whatever, dynamical or event?) If there is a dynamical horizon, how is it formed with time?
- Where is the Hawking radiation? Why is its spectrum thermal? What are the corrections to the thermal law and where do they come from? (If information is recovered, certainly, there should be some corrections to the Hawking radiation.)
15 Comments
Dear Dmitry,
a pleasant guy, by looking at pieces of the videos. In some sense, I must have been happier at the college times when people, including Prof Ashtekar (promoted by a well-known Czech relativist, prof Bi??k, who co-taught me GR in Prague), were unreachable big guys somewhere in the skies.
Well, today they’re still well-known physicists but as students, they would probably not earn an A in my class of QG.
Concerning the first talk, it is not clear to me why it’s interesting, either. These ideas are based on oversimplifications that often look more dramatic than necessary even for knowing how to solve it (which is much more modest than the requirement of being true), and that surely seem to completely miss all the tough and conceptually appealing physics of the early cosmology – inflation, the vacuum selection in the Planckian era, tunneling from other vacua, horizon complementarity and so on and so on.
On the other hand, I sense a kind of terminological confusion in your criticism of the WDW equation. WDW doesn’t mean that you only consider uniform isotropic cosmologies (like in “loop quantum cosmology”, which is an approach that doesn’t even follow from “loop quantum gravity” – even if it did, it would still be wrong).
WDW is much more general, it is essentially H psi = 0, and the uniform approximation is a “minisuperspace approximation” of it, not a universal story. I personally believe that in some sense, WDW is a legitimate approach to the full theory useful in the cosmological regime, when supplemented with all the correct variables of the full theory. By the full theory, I probably mean something entirely different than Prof Ashtekar.
Nevertheless, your comment about superseding WDW by those Soviet – or, in a more friendly way, Slavic – physicists is surely a source of national self-confidence!
Concerning the second talk, I share your questions, besides others. I don’t even see why an evaporating hole doesn’t have an event horizon. I thought that the Penrose pictures make it clear that it does. At any rate, there seems to be this obsession with the classical singularities – where the relativists seem to hide all their religious feelings (and they identify all singularities with one another and with all the problems). I just don’t have this obsession and the identifications seem plain wrong. The singularity is very microstate-dependent (which was your BKL point in the first talk, too, by the way), the physics around is probably nonlocal, and the new non-semiclassical effects must start right below the horizon.
Best wishes
Lubos
Dear Lubos
Well, yes, in this particular note by WdW I meant the minisuperspace approximation. I know your views on WdW from your posts. As for me, I believe that even the general (not the minisuperspace approx., which is ridiculous) ADM quantization is unsatisfactory. There is always the question what is behind the horizon. You want to push complementarity (there is nothing interesting behind the horizon, therefore, the ADM formalism is the only thing one really needs to know), while from the studies of eternal inflation I learn that the spacetime causal structure behind the horizon may be very non-trivial.
Cheers
Dear Dmitry,
I completely agree that the space behind the horizon can have a very complicated causal structure. That’s actually a part of the problem and a hint that it is not quite physical.
The structure may be complicated to some extent but it is likely that all this structure is just an “effective geometry” that becomes less accurate as you go deeper to these unexpected corners. Even classically, one has to be careful about all kinds of instabilities, e.g. at Cauchy horizons, which often occur inside whenever the structure is complicated (e.g. the inner horizon of a Reissner-Nordstrom hole).
If complementarity is true, you can’t beat it just by wishing for the complicated causal structure inside to be fully physical. And when the Universe is really tiny (early cosmology), I am afraid that a WDW-like treatment using all the relevant degrees of freedom will be pretty much inevitable to get the initial conditions etc.
Have a nice Tuesday, Lubos
Hi Lubos
How is that?
Yes, but inflation is different story: matter modes and causal structure at superhorizon scales are more or less frozen, so nobody really cares about those instabilities.
Cheers
Heres a foundational question I never understood with people who are enamored with WDW for cosmology..
Lets say you add the relevant degrees of freedom from the full QG theory to the WDW model to see what it tells us.
Exactly why are we supposed to believe those D.O.F remain approximately valid after we’ve taken the minisuperspace approximation? Tremendous violence is being done to the space. One would think those mostly quantum degrees of freedom would react most strenously to precisely this sort of operation?
Hi Haelfix
I hope I understood your question correctly. If so, my answer is the following.
1) you prepare a very very specific state (density matrix) such that all relevant dynamics happens within one causal patch. Is it possible to prepare such a state? My impression is: yes, sure, you can cook whatever you want by constructing linear combinations of states from the full Hilbert space of the quantum theory whatever you mean by that. Is it correct initial state which describes our Universe in the very beginning of our evolution? My impression (coming from studies of eternal inflation) is that the answer is negative.
2) you set the density matrix free and it evolves with time. ADM is good enough as long as the dynamics develops in a single causal patch, i.e., nothing crosses the horizon.
This criterion shows you when and where minisuperspace approximation is applicable.
Cheers
Dmitry: “How is that?”
Well, my reasoning is that if a tough new causal/topological subtlety evolves in spacetime, you must inevitably go through a process where your physics intuition can go wrong.
In the Reissner-Nordstrom case, there are, for example, many diagrams like the infinitely prolonger one that is almost certainly unphysical – it just looks cute which is why we draw it.
But even if you return to more modest Penrose diagrams, one must be careful about their portions that haven’t been “checked”. Of course, no one has checked – and no survivor ever will check – the Cauchy horizons inside RN black holes etc. We don’t have any experimental data from them and I would argue that we don’t have even any string-theory data about them.
Whether GR can be trusted to these deep corners of spacetime is an open question for me. What I mean is that I am not aware of a controllable approximation of string theory that would cover both exterior and interior of a RN black hole and allowed you to argue that all the classical GR intuition inside is correct – the reliability already breaks at the exterior event horizon.
Concerning inflation & instabilities, I didn’t mean that these problems are explosive in combination. I was just mentioning two important early cosmology problems. And inflation & causal structure is a tough problem that we only understand qualitatively – why it solves the horizon problem.
I think that we don’t really know how independent the different patches of the Universe in this (de Sitter) space are. These are questions discussed above. Do you think you fully understand where the things come from? How do you prove that you can prepare a causal patch in any way you want, and how do you demonstrate a problem when you try to prepare more than that? Why is there exactly a boundary between these two tasks, a boundary that seems to violate locality that otherwise holds?
Dear Lubos
I think, the measure of independence is related to exponentially decaying superhorizon modes which are usually neglected in our analysis. Basically, the question is how rapidly quantum modes become classical after they leave the Hubble scale – the general lore is that a couple of efoldings is enough.
I would expect that the situation in dS somewhat resembles the one realized near black hole: one has Hawking radiation and (probably) exponentially small corrections to the thermal distribution of outgoing quanta. These tiny exponentially small corrections in principle should carry information about subhorizon physics (and that is, I think, the resolution of the information loss paradox in black hole).
Similarly, you have an information loss in dS – superhorizon modes can be effectively considered classical. Nevertheless, if you have (or will have) access to the overall 3d volume of the Universe (for example, cosmological constant decayed everywhere and eternal inflation stopped everywhere), you can recover all the information about initial state.
Cheers,
Dmitry.
Nude Socialist
http://www.newscientist.com/ar.....?full=true
just printed an article about Ashtekar’s cyclic cosmology. I don’t know what you think about the text but my impression is that it not only has wrong answers to most questions but it contains no rational logical step whatsoever. I just don’t recognize that this is supposed to be science.
They say all the conceivable wrong things they can say about singularities in GR. But they also completely misinterpret everything about the history of cosmology and physics in general.
For example, cyclic cosmology has been studied since the 1930s (Einstein, recognition of the importance of the 2nd law that makes the cycles ever longer, all the basic things that they seem to be ignorant about, too), and even in the present context, LQC surely doesn’t belong among the more justified or interesting frameworks to study this ill-motivated idea (ekpyrotic braneworlds etc. are slightly more non-vacuous representations of the idea even though one couldn’t exactly say that they’re motivated, either).
LQC is even more ludicrously oversimplified a toy model of non-reality than LQG, there is no reason to think that any of its conclusions have anything to do with the actual answers about gravity – not even if one assumes that LQG is correct (because LQC doesn’t follow from LQG). They say a lot of things about the Planckian and infinite densities and the behavior of the Planckian small Universe that can be either right or wrong. But they are definitely not new as possibilities and they present no rational arguments to support one answer or another.
It just looks like a pile of mostly verbal semi-mathematical masturbation without any logic or merit. Many people have said and written similar things with similar words and what Ashtekar et al. are saying clearly doesn’t deviate from the random noise in this context. There are hundreds of papers about similar issues every year that are manifestly much better than all the papers mentioned in the Nude Socialist article. I am kind of concerned about these things because the media are helping to destroy meritocracy in the field.
Dear Lubos
My impression that grew out of reading some LQG papers was similar to yours, although I have to admit – loop variables seemed interesting for me. So I decided to talk to Lee Smolin when I was at CITA.
What I knew at that point is that 1+1 quantum gravity (and 2+1 quantum gravity, although people overestimated the significance of Witten’s work on Chern-Simons formulation) were fairly well understood. During our conversation with Smolin it turned out that LQG people do not quite know how to map their loop formalism to what is now known about 1+1 gravity (say, Knizhnik-Polyakov-Zamolodchikov work).
Then, Lee said to me – you have to forget that and focus on how many wonderful things are done in LQG. I am not exaggerating and reproduce his wording exactly (Dick Bond also heard the whole conversation and took an active part in it). I understood that I have nothing to discuss with Mr. Smolin further.
My second experience with LQG people was related to the issue of citations. I asked one LQG guy from Poland to cite my paper which was relevant to the physics he discussed. In reply, he explained to me that he cannot do that, because I did not cite a single LQG paper in mine.
What I have concluded is that the theory of LQG and LQG activity is more like a social phenomenon. (Still, I have to admit again that there are Ashtekar variables which look somewhat compelling to me even nowadays.)
Let us be constructive – the media have its own rules, and LQG people understood somewhat better than us how to exploit those rules. Why don’t we learn those rules, too?
Cheers
Dear Dmitry,
I’ve studied these LQG-like things at some moments because they looked interesting to me, too – although it was partially a social issue because I couldn’t possibly believe that dozens or hundreds of somewhat well-known people would be spending their time on something that had no merit.
And I’ve talked to Lee Smolin many times, too, and have been repeatedly the only person in a well-known MA city who would invite him for a visit etc.
I don’t believe that one can get too far with the media’s influence on science by adopting the rules of the media. It is true that other people may become influential in the media if they try and are able to play their rules. But what is not true is your implicit assumption that by this strategy, media will systematically promote the right things. If the rules of the media reject any kind of meritocracy, it is simply rejected and you can’t fix it by learning the non-meritocratic rules.
So I think that the attempt should be to try to convince/force the media to adopt the right rules of game rather than increasing the portions of the society that adopt the wrong rules.
Best wishes
Lubos
In turn, I think that your point is the ultimate correct one
for a person who has a power to drastically change the world. My point of view (maybe, wrong one) is that Life is a thermostat and we are gas molecules in this thermostat. Of course, one molecule can be very proactive (and be able to somewhat increase the temperature of the system), but most probably the effect would be suppressed by the size of the system 
Hi Dmitry, sure, I realize that this is about power-dependent things. Still, one has the option of creating “science-merit-oriented” media or helping those media that seem to be doing better job in this than others.
That’s for sure, as well as creating new science-merit-oriented media.
Cheers
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