### Reviewing Quantum Gravity

Last week two leading researchers of the LQG community published papers that review the state of the field from different perspectives and with a different focus:

Abhay Ashtekar: Gravity, Geometry and the Quantum

Lee Smolin: Generic predictions of quantum theories of gravity

Marcus has asked me to make a comment on the second of them, but I will include also the first because it will enable me to sneak in a question that has puzzled me for a while about the results in singularity resolution within Loop Quantum Cosmology. I should start by saying that I am no expert in LQG, not even in the measure a graduate student working directly in it would be; I work in quantum field theory in curved spacetime, not quantum gravity proper. True, I am a member of a research group with an important LQG component, and I have a great interest in the developments made in the theory; but I have not studied it “seriously” (which means: beyond reading several review articles and Rovelli’s

OK, no more disclaimers. Smolin’s paper is focused on generic predictions from background independent quantum theories of spacetime. It starts listing four assumptions these theories are based on: quantum mechanics, background independence (partial, because some structures like dimension and topology may be fixed), discreteness and causality. And here comes my first question: I thought one of the main selling points of LQG was that the discreteness of spacetime is not an assumption of the theory but a natural consequence of a background independent quantization of grvity. In fact, when Smolin lists the theories he has in mind he includes causal sets, dynamical triangulations and consistent discretization models, but not canonical loop quantum gravity proper. The formal description of the theories made later, however, seems appropiate only for the latter, describing Wilson loops, spin networks, and so on. If these feature in causal sets or CDT models, I was not aware of it.

Likewise, the “well studied generic consequences” discussed in Section 3 are three results classically associated with canonical LQG: ultraviolet finiteness due to discreteness, elimination of spacetime singularities (these are discussed at much more length in Ashtekar’s paper) and horizon entropy. I am surprised that Smolin seems to regard the last of these as a settled matter, with the “correct” way of doing the calculation already known as being the one that gives the same Immirizi parameter implied by classical quasinormal modes. That is not the impression I obtained from a seminar we had a couple of months ago. A fourth generic consequence, of which I was not aware of previously, seems to be a natural role for the cosmological constant in the theory; the description of this is intriguing but too sketchy for me to follow, so I guess I’ll have to llok at the 59-pages long referenced paper.

Section 4 mentions briefly the results in recovering a classical spacetime for long distances: Rovelli’s “gravitons from LQG” calculation, Freidel and Levine’s result of DSR as flat limit of 2+1 QG, Loll et al.’s results on the large distance limit of CDTs with 3+1 emergent dimensions, and work using noiseless subsystems techniques. Section 5 is on “Possible new generic consequences”, which are more speculative than those in previous sections. The first is DSR (doubly or deformed special relativity) as classical limit of QG in 3+1 dimensions. Smolin mentions possible experimantal tests of this idea, but downplays a bit what are (in my impression) large technical and conceptual problems to understand fully what DSR

In general, the impression I have is that all the “generic predictions” Smolin discusses in section 5 are at this stage more speculations than predictions, even tentative ones. The strongest generic results of the LQG program seem to me the discretization of spacetime giving finitenesss to the theory and the resolution of singularities. This last issue brings us to Ashetekar’s paper.

This paper starts with a brief revision fo the formal structure of LQG, and then applies it to homogeneous and isotropical cosmology. In Loop Quantum Cosmology, the spacetime is first assumed to have the usual symmetries so there is effectively only one degree of freedom (the scale factor) and then this variable is quantized following an analogous procedure as the degrees of freedom in the compelte theory. One might of course question whether the operations of quantizing and imposing symmetry “commute”, so the results found this way would be preserved for cosmology in the full theory; but leaving that aside, the results found in LQC are indeed impressive. Starting with a semiclassical state approaching a Friedmann clasical solution at late times, with a scalar field added as a non-geometrical degree of freedom, and evolve it backwards towards the Big Bang. What you find is that the matter density increases until reaching approximately 2.5 times the Plack density, and then it bounces and starts to decrease again, approaching another classical (collapsing) universe in the distant past. The singularity is avoided by the effect, at Planckian distances, of what Ashtekar calls an effective repulsive gravitational force arising from the quantisation of the geometry, akin to the effective repulsion between fermions arising from the Pauli principle.

This result is without a doubt important and exciting, especially because similar effects may resolve black hole singularities as well. However, the idea that a bounce from the collapse of a previous classical universe is a realistic scenario for “what happened before the Big Bang” is one that creates a host of problems in my opinion. First, our universe is known to be in an accelerated expansion that will not recollapse to a Big Crunch, quite the opposite; then why did the previous universe collapse? To postulate as "cosmic initial condition" a large classical universe collapsing seems even stranger than a singularity to me. Leaving aside this quasi-metaphysical worry, I see a serious potential problem in the second law of thermodynamics. A realistic collapsing universe would almost certainly be increasing its entropy to a maximum, ending in a very "messy" state with lots of black holes; not the kind of smooth, low entropy state we have at the beginning of our universe. Of course the calculations Ashtekar presents can't address these problems because they restrict to a case with imposed homogeneity. I would be surprised if the apparent mirror symmetry between the collapsing and the expanding phase persists when anisotropy is allowed, as this would seem to be against the Second Law. (You would be right in presuming that my worries about time asymmetry and the low-entropy beginning of the universe were spawned by reading Penrose; see this Physics Musings recent post). A similar question arises if black hole singularities are resolved with a similar bounce: does the black hole transform into a white hole after passing through the Planckian regime? But don't white holes violate the Second Law?

In summary, the elimination of singularities thanks to the loop quantization seems compelling, but the bouncing mechanism puzzles me because in a realistic scenario I don't see how to reconciliate it with the Second Law. Any ideas?

Abhay Ashtekar: Gravity, Geometry and the Quantum

Lee Smolin: Generic predictions of quantum theories of gravity

Marcus has asked me to make a comment on the second of them, but I will include also the first because it will enable me to sneak in a question that has puzzled me for a while about the results in singularity resolution within Loop Quantum Cosmology. I should start by saying that I am no expert in LQG, not even in the measure a graduate student working directly in it would be; I work in quantum field theory in curved spacetime, not quantum gravity proper. True, I am a member of a research group with an important LQG component, and I have a great interest in the developments made in the theory; but I have not studied it “seriously” (which means: beyond reading several review articles and Rovelli’s

*Quantum Gravity*textbook without following the more technical parts of the math, and assisting to several seminars and to the Loops 05 conference). So my comment on these papers can’t be an “informed critical comment”; it will be more like a “summary plus personal subjective impressions and questions”. I’m not sure if that is what Marcus wanted, but it’s the best I can make. I hope that people with more knowledge than me will jump in and correct any mistakes.OK, no more disclaimers. Smolin’s paper is focused on generic predictions from background independent quantum theories of spacetime. It starts listing four assumptions these theories are based on: quantum mechanics, background independence (partial, because some structures like dimension and topology may be fixed), discreteness and causality. And here comes my first question: I thought one of the main selling points of LQG was that the discreteness of spacetime is not an assumption of the theory but a natural consequence of a background independent quantization of grvity. In fact, when Smolin lists the theories he has in mind he includes causal sets, dynamical triangulations and consistent discretization models, but not canonical loop quantum gravity proper. The formal description of the theories made later, however, seems appropiate only for the latter, describing Wilson loops, spin networks, and so on. If these feature in causal sets or CDT models, I was not aware of it.

Likewise, the “well studied generic consequences” discussed in Section 3 are three results classically associated with canonical LQG: ultraviolet finiteness due to discreteness, elimination of spacetime singularities (these are discussed at much more length in Ashtekar’s paper) and horizon entropy. I am surprised that Smolin seems to regard the last of these as a settled matter, with the “correct” way of doing the calculation already known as being the one that gives the same Immirizi parameter implied by classical quasinormal modes. That is not the impression I obtained from a seminar we had a couple of months ago. A fourth generic consequence, of which I was not aware of previously, seems to be a natural role for the cosmological constant in the theory; the description of this is intriguing but too sketchy for me to follow, so I guess I’ll have to llok at the 59-pages long referenced paper.

Section 4 mentions briefly the results in recovering a classical spacetime for long distances: Rovelli’s “gravitons from LQG” calculation, Freidel and Levine’s result of DSR as flat limit of 2+1 QG, Loll et al.’s results on the large distance limit of CDTs with 3+1 emergent dimensions, and work using noiseless subsystems techniques. Section 5 is on “Possible new generic consequences”, which are more speculative than those in previous sections. The first is DSR (doubly or deformed special relativity) as classical limit of QG in 3+1 dimensions. Smolin mentions possible experimantal tests of this idea, but downplays a bit what are (in my impression) large technical and conceptual problems to understand fully what DSR

*means*, let alone what it predicts. Next come Smolin’s pet speculation on matter as emergent from geometry (ridiculed by Lubos here; I as a rule take with suspicion anything Lubos says outside from technical areas of string theory, but in this case it does seem to me that, at the least, Smolin’s idea needs quite a lot of more hard working on until we can say that matter as we know it can arise from geometry). Follows a discussion on disordered locality, which excites Smolin becase he hopes it may explain puzzles like dark matter (via some MOND-like model) and the Pioneer anomaly, as he explained in a Loops 05 talk. This seems very optimistic to me; intuitively I would expect non-local effects, if they persist at low energies, to mess up the theory and perhaps make it inconsistent with our present well tested low-energy local physics, instead of magically creating exactly the kind of effect that accounts for the few anomalies we presently cannot explain. Surely, a lot of more work needs to be done here. Finally there is a simple calculation attempting to relate disordered locality to the cosmological power spectrum.In general, the impression I have is that all the “generic predictions” Smolin discusses in section 5 are at this stage more speculations than predictions, even tentative ones. The strongest generic results of the LQG program seem to me the discretization of spacetime giving finitenesss to the theory and the resolution of singularities. This last issue brings us to Ashetekar’s paper.

This paper starts with a brief revision fo the formal structure of LQG, and then applies it to homogeneous and isotropical cosmology. In Loop Quantum Cosmology, the spacetime is first assumed to have the usual symmetries so there is effectively only one degree of freedom (the scale factor) and then this variable is quantized following an analogous procedure as the degrees of freedom in the compelte theory. One might of course question whether the operations of quantizing and imposing symmetry “commute”, so the results found this way would be preserved for cosmology in the full theory; but leaving that aside, the results found in LQC are indeed impressive. Starting with a semiclassical state approaching a Friedmann clasical solution at late times, with a scalar field added as a non-geometrical degree of freedom, and evolve it backwards towards the Big Bang. What you find is that the matter density increases until reaching approximately 2.5 times the Plack density, and then it bounces and starts to decrease again, approaching another classical (collapsing) universe in the distant past. The singularity is avoided by the effect, at Planckian distances, of what Ashtekar calls an effective repulsive gravitational force arising from the quantisation of the geometry, akin to the effective repulsion between fermions arising from the Pauli principle.

This result is without a doubt important and exciting, especially because similar effects may resolve black hole singularities as well. However, the idea that a bounce from the collapse of a previous classical universe is a realistic scenario for “what happened before the Big Bang” is one that creates a host of problems in my opinion. First, our universe is known to be in an accelerated expansion that will not recollapse to a Big Crunch, quite the opposite; then why did the previous universe collapse? To postulate as "cosmic initial condition" a large classical universe collapsing seems even stranger than a singularity to me. Leaving aside this quasi-metaphysical worry, I see a serious potential problem in the second law of thermodynamics. A realistic collapsing universe would almost certainly be increasing its entropy to a maximum, ending in a very "messy" state with lots of black holes; not the kind of smooth, low entropy state we have at the beginning of our universe. Of course the calculations Ashtekar presents can't address these problems because they restrict to a case with imposed homogeneity. I would be surprised if the apparent mirror symmetry between the collapsing and the expanding phase persists when anisotropy is allowed, as this would seem to be against the Second Law. (You would be right in presuming that my worries about time asymmetry and the low-entropy beginning of the universe were spawned by reading Penrose; see this Physics Musings recent post). A similar question arises if black hole singularities are resolved with a similar bounce: does the black hole transform into a white hole after passing through the Planckian regime? But don't white holes violate the Second Law?

In summary, the elimination of singularities thanks to the loop quantization seems compelling, but the bouncing mechanism puzzles me because in a realistic scenario I don't see how to reconciliate it with the Second Law. Any ideas?

## 12 Comments:

I would think it most natural that on both sides of the bang you have a thermodynamic arrow of time pointing away from the bang.

I haven't read the other two papers yet, but I have started looking at the positive cosmological constant one, and that's really very nice (though I am suffering from review fatigue, I need to start dvelving a bit deeper...). The cosmological constant really does look very natural in the LQG context. His streamed lectures at PI are based on this paper.

By fh, at 11:53 PM, May 08, 2006

Interesting idea, fh. I had not thought of it. So could we equally view it as two different universes expanding from the Big Bang each into its own future, but each one views the other as being in the past? This is giving me a headache...

By Alejandro, at 12:45 AM, May 09, 2006

I would say so. The key point is that observation is an internal process in each direction.

Here is a related (VERY handwaving) observation, imagine the particles in a box are all in one half of the box. So increase of entropy tells you that with near certainty they will distribute into the future.

But if you take that microstate and run it "backwards" they will of course also distribute and entropy increases backwards! Thus the low entropy state does not really define a time direction, what defines the time direction is that in the past we had a wall in the box and the backwards evolution is different from the forward evolution.

(In fact you can give a time reversal invariant version of the second law by simply saying that fluctuations from equilibrium are rare with decreasing probability the further away they are.)

The big bang is a low entropy state but without the wall, on both sides of that state entropy increases and defines the *local* time direction, and there is no God/singularity to cut of the other branch and therefore the *local* time direction is no longer defined globally.

This is of course borderline metaphysical...

By fh, at 9:05 PM, May 09, 2006

thanks for discussing both papers, alejandro,

In Ashtekar's picture of a prior collapse phase, I am not sure that it has to be an entire universe that is collapsing, Might be just part of one, in effect a black hole.

As you point out, as far as is known entire universes don't collapse, if they are like ours. But parts of them do, and might provide the prior collapse phase. A familiar idea now, I think. You will have plenty of objections to raise about it, if you wish to challenge.

By marcus, at 9:21 PM, May 09, 2006

about your second law objection, alejandro.

From a relational standpoint, where the entropy is AS SEEN BY A STIPULATED OBSERVER, I do not quite see what the problem is.

there is an observer outside the hole horizon in world A and he sees stuff fall into the hole---he sees entropy increasing and is happy: All is well with the world.

then there is also an observer in world B who is subsequent to the "bounce" and who sees the entropy there where he is increasing. So he too is happy.

there is no superbeing who can watch the whole process, someone for whom the entropy has an absolute meaning, and who might be disturbed to see the very high entropy in the black hole suddenly "turn inside out" and become very low entropy at the beginning of world B expansion. the laws of thermodynamics were not set up for the convenience of such a being but for humanoid observers like us in our respective worlds.

Please object. It is all the better that you are not officially studying quantum gravity. As a rough approximation it is only amateurs who can think---or professionals who can think like the amateur

By marcus, at 10:42 PM, May 09, 2006

a propos reviewing the reviews,

Ashtekar just posted a SECOND survey, for nonspecialists---he says for philosophers of science.

http://arxiv.org/abs/physics/0605078

The Issue of the Beginning

By marcus, at 4:54 AM, May 10, 2006

fh: Very interesting explanation. If I understand correctly, the idea is that we have a low entropy state (the BB, or as close as we can get to it with the quantized theory) and moving away from it we increase entropy in both time directions. All the other arrows of time (e.g. the psychological arrow of time for observers) go with the thermodynamical one, so observers in both universes see an expansion that increases entropy. There is no globally defined arrow of time.

marcus: I find your position more difficult to understand. Firstly, you seem to be mixing the cosmological case and the black hole case, which I would prefer to keep separate. In the first one we quantize the Friedmann equation for a spatially homogeneous and isotropical spacetime, in the second we quantize the equations for collapse to a BH, a situation isotropical but not homgeneous. I know Smolin has speculated that new homogeneous universes emerge from black hole singularities (his fascinating Darwinistic cosmology), but is there any solid reason to suppose so? I would imagine a white hole to be more likely at the other side of a BH singularity, with the same sort of mirror symmetry that appears to hold in the cosmological case.

So let's stick to the cosmological case. Your position here is different from fh's. For him entropy increases moving away in both directions from the Planckian regime. For you it decreases in one direction and increases in another one. The second direction is the one of our universe, and observers in it see it as expanding and increasing entropy. The first one is the one of the "previous" universe, and observers in it see it as collapsing and increasing entropy. This leads naturally to the question of how can the very high entropy of the ending point of the previous universe turn into a very low entropy point to start our present universe. And you answer that entropy is observer-relative so it doesn't matter. I am not too satisfied with this. Compare with the black hole entropy calculations in LQG, which ask how many microstates of geometry have the same macro description as a BH of a given area, and interpret this number as the entropy for an observer external to the BH. The same sort of calculation could be made in the cosmological case: take the geometry state during the Planckian regime "bridging" the universes, and ask, what is the degeneracy of that state? I would like you to explain in more detail how the collapsing observer can obtain a high value for this quantity and the expanding observer a low one.

Thanks for pointing to the new Ashtekar paper. I'll have a look at it.

By Alejandro, at 11:57 AM, May 10, 2006

" I find your position more difficult to understand. Firstly, you seem to be mixing the cosmological case and the black hole case, which I would prefer to keep separate. In the first one we quantize the Friedmann equation for a spatially homogeneous and isotropical spacetime, in the second we quantize the equations for collapse to a BH, a situation isotropical but not homgeneous. I know Smolin has speculated..."

My reading of the current research (since 2004) and Ashtekar's statements is that you cannot separate those two cases.

the analysis that people use in their papers overlaps---some authors who are dealing with BH collapse will say "now we will use the LQC equation...etc etc..."

Smolin speculations about the connection of these two cases go back to 1995 and 1996. He has not been doing the current research on this. His speculation from back then are water under the bridge and do not characterize present work by others.

I cant easily cite papers, recent authors are (of course) Bojowald, Viqar Husain, Oliver Winkler, Parampreet Singh, T. Pawlowski, Leonardo Modesto, several more.

You would be very right to say that nobody explicitly connects these two cases but neither do they keep them separate. they seem to be allowing for the possibility that they are connected.

the trend recently has been to consider increasingly complex collapse and expansions, to gradually relax the simplifying symmetry assumptions, to include matter in various ways---short of full generality. This program is being carried out in both cases: BB and BH.

Because more complicated versions of collapse and expansion are being studied this also makes a pat division of cases more problematical----one can no longer so easily say "well, BB is this analysis and BH is that other analysis, so it is clearly different" because both research lines are broadening out.

If you decide you want to keep these two cases quite separate in your mind that is OK with me :-)

I like your style of thinking even though on this particular issue i would not be able to discuss.

Instead, I will try to subvert you by pointing to a delicate nuance in what Ashtekar said in his most recent paper (he is averse to risk and speculation so he has taken a long time to come around to where he will allow for the possibility of some connection between blackhole and cosmological cases, you will see how admirably guarded he is!)

I will go fetch the quote and make another post. Or, if the nuance seems so faint that it wouldnt make any sense to you, I will give up for the time being.

By marcus, at 5:30 PM, May 10, 2006

have to give up for the time being. i was thinking of his "discussion" section at the end---pages 13, 14.

suggestive but carefully elusive. old fox is too wise.

He does make a nice analogy between the Fermi-Dirac pressure that supports white dwarves and quantum geometry pressure. I will quote it just for fun even though it does not support my point.

As reminder this is from new Ashtekar prepring

The Issue of the Beginningwhere in conclusion section he says:"a new repulsive force comes into play when the core approaches a critical density, halting further collapse and leading to stable white dwarfs and neutron stars. This force, with its origin in the Fermi-Dirac statistics, is

associated with the quantum nature of matter. However, if the total mass of the star is larger than, say, 5 solar masses, classical gravity overwhelms this force. The suggestion from LQC is that a repulsive forceassociated with the quantum nature of geometrymay come into play and could be strong enough to counter the classical, gravitational attraction, preventing the formation of singularities... "his italics

nothing in the conclusions you can actually pin down

will try later if all right with you

By marcus, at 6:18 PM, May 10, 2006

I admit that I haven't read many of the papers on the topic, I had just assumed that the cosmological and the black hole cases would be different, and that whatever is it that emerges from the Planckian regime in a BH collapse would still be within the same old universe the BH was, not form a new one. A short lookup makes this seemingly supported by Figures 3 and 4 and their discussion in Ashtekar's beautiful paper:

http://arxiv.org/abs/gr-qc/0504029

My reading is that what emerges from the singularity is in a separate universe only in the ideal, unphysical case of a black hole taking infinite time to evaporate.

Anyway, the distinction or not of BB and BH analysis was a side issue, my main interest in my previous comment was to understand better your idea about the observer-dependence of entropy solving my question in the post.

I also like the Fermi repulsion analogy. It gives a nice intuitive feeling for the bounce.

By Alejandro, at 12:54 AM, May 11, 2006

you say "beautiful" paper

http://arxiv.org/abs/gr-qc/0504029

I was quite disappointed by this paper (which was co-authored by Bojowald and Ashtekar)

I think that there has since been a shift by both Bojowald and Ashtekar towards recognition of the possibility that time evolution can fork at a BH collapse and the planck regime at the pit can be a "bridge" in Ashtekar's words to a large tract of classical spacetime.

Basically I use that paper on BH evaporation that you cited (gr-qc/0504...) as a zero-point or benchmark to gauge progress.

So far, I think that one can neither say there is a BH/BB connection, nor say there is not one. Quite a few people have studied it from both sides, in a LQC/LQG context. (When people study BH graviational collapse in LQG they use symmetry reduced simplified models similar to LQC and sometimes cite LQC---there is a rough formal similarity.)

Actually it occurs to me that it might be a good PhD problem to try to prove that in LQC formalism it is forbidden for a BH collapse to result in a BB bounce.

there may be some obstacle. If it is not somehow forbidden then it may happen.

sorry, have to go

By marcus, at 2:14 AM, May 11, 2006

Alejandro, you kindly asked my view about that application of the second law. I have just a moment and then must go help with supper. (company)

I do not think I can say anything very enlightening and so must be very brief.

I think one must look at it from the two viewpoints, the observer outside the horizon of the collapse (who sees the BH)

and the observer who is subsequent to the onset of expansion (who infers back to a BB)

I don't understand how there can be any other observers besides these two and they are very different in their perspective. So I want to ask what does entropy mean for these two different watchers? And how does the second law apply for each of them?

I do not see that there is a contradiction, or that thermodynamics is violated.

but my instinct is to defer to you---I think your combination of philosophical and physical smarts can illuminate this (no flattery, simple fact) . So my idea right now is not to try to argue, but see if you have anything to say.

entropy is about coarse-graining, from whose perspective is the coarse-graining? Mr A or Mr B? and does it matter?

thanks for having this blog and its implied hospitality to such a question

By marcus, at 2:37 AM, May 11, 2006

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