I’ve been spending most of my time recently trying to get unconfused about Euclidean spinor fields, will likely write something here about that in the not too distant future. Some other things that may be of interest:

- I did an interview a couple days ago with Fraser Cain, who runs the Universe Today website. He had some excellent and well-informed questions about the state of HEP physics. I regret a little bit that I focused on giving an even-handed explanation of the arguments over a next generation collider, didn’t emphasize that personally I think building such a thing is a good idea (if the money can somehow be found), since the alternative would be giving up and abandoning this kind of fundamental science.
- On Monday, the Simons Center celebrated its 10th birthday, talks are here, giving a good overview of the kinds of math and physics that have been going on there during its first decade.
- For the latest on the formulation of the local Langlands correspondence in terms of the geometry of the Fargues-Fontaine curve, Peter Scholze is teaching a course now in Bonn, website here.
- Kirill Krasnov has a book out from Cambridge, Formulations of General Relativity. If you share my current interest in chiral formulations of GR and twistors, there’s a lot about these in the book. For a more general interest survey of what’s in the book, see Krasnov’s lectures last year at Perimeter (links and slides are on his website).
- A couple weeks ago, a very well-done explanation of what’s been going on around the black hole information paradox written by George Musser appeared at Quanta Magazine. Periodically in recent years I’ve tried to follow what’s up with this subject, generally giving up after a while, frustrated especially at not being able to figure out what underlying theory of quantum gravity was being studied. All that ever was clear was that this was about low-dimensional toy model calculations involving some assumptions that had ingredients coming from holography and AdS/CFT.
Musser’s article makes quite a few things clearer, with one striking aspect the news that:

researchers cut the tether to string theory altogether.

which I gather means that any foundation in AdS/CFT is gone, with what is being discussed now purely semi-classical. I don’t understand what these new semi-classical calculations are, and whether optimistic claims that the information paradox is on its way to a solution are justified (history hasn’t been kind to previous such claims). In recent years the pro-string theory research argument has often been that while there no longer were any prospects that it would tell us about particle physics, it was the best route to solving the problem of quantum gravity. It will be interesting to see what the effect will be of that cord getting cut by leading researchers.

If you think it’s a good idea to follow discussions of this kind of thing on Twitter, you might enjoy threads from Sabine Hossenfelder and Ahmed Almeiri.

My understanding of the new semiclassical calculations is that by computing the gravitational path integral over an ensemble of n boundary conditions, and allowing topologies which connect the boundaries, one can reproduce the Page curve when n is analytically continued to 1.

These new topological terms (“euclidean wormholes”) can be computed ‘easily’ in 2d JT gravity and the page curve is reproduced there. The problem is that no one knows what exactly to make of these topologies that don’t factorize and it’s not obvious that effects in 4D won’t spoil the magic. On page 29 of https://arxiv.org/pdf/1911.11977.pdf the authors suggest this isn’t an issue, “2d gravity is convenient for drawing pictures, but the topological argument relating replica wormholes to the island extremal surface is similar in any spacetime dimension: one just replaces each point in the discussion below by a sphere.”

It seems the interpretation of the euclidean wormhole topologies in the limit n->1 is somehow related to an ensemble average of chaotic quantum systems and it is not clear that the gravitational path integral can be interpreted as a semiclassical limit of any single quantum system. I really don’t understand the connection between the SYK model and JT gravity which seems central to this idea.

I found these talks by Douglas Stanford to be illuminating:

1) Conceptually helpful https://www.youtube.com/watch?v=-hfcApA9s8Q

2) Technically helpful https://www.youtube.com/watch?v=Yi2hx0GH624

Patrick Bryant,

Thanks. My problem here is that the claims being made all are about “doing the gravitational path integral”, but the whole problem of quantum gravity is that in 4d that (summing over all geometries using the classical action) is something no one has made sense of, and nothing is being said that addresses that problem.

In 4d you can decide to give up on the full sum, just look at classical solutions and do a semi-classical calculation, but this doesn’t touch the underlying quantum gravity problem. It sounds like this is what is being done here in a simpler context. Maybe it resolves the question of how to make sense of the semi-classical calculation in a black hole background, but I don’t see anything addressing the problem of how to actually quantize the gravitational degrees of freedom.

There are (at least) two other lines of recent developments that relate to AdS/CFT and black hole physics. Both of them are very much tethered to string theory and are concerned with black holes in more than 3 space-time dimensions.

1. One is the program of microstate geometries/fuzzballs. See this recent review

https://arxiv.org/abs/1902.07176

and this Quanta magazine article from a few years ago

https://www.quantamagazine.org/how-fuzzballs-solve-the-black-hole-firewall-paradox-20150623/

2. There has also been a flurry of activity showing how to use holography to successfully relate exact QFT path integral calculation to learn about the dual AdS black holes. See this review for a nice (but already outdated) summary

https://arxiv.org/abs/1902.07176

Of course, given the premise of this blog, I suspect that you may label both of these research programs as “not even wrong”.

S=k_B log(W),

Your point seems to be that some people have not given up on hopes that they can use AdS/CFT to produce a viable quantum gravity theory describing our world (dS, four large space-time dimensions). Back in 2006 when I wasted a lot of time arguing with string theorists like Lubos Motl about this, it was a nine year old idea that was going nowhere. Now it’s a 23 year old idea which has gone nowhere. As for claims that this line of work can solve the information paradox, the five year old Quanta article you refer to has

“If Samir says he has a solution to the paradox, he is linguistically correct. He’s also in good company,” said Marolf. “There are lots of people with resolutions to the paradox. Whether it’s the way physics actually works in our universe remains to be seen.”

On the information paradox front, the newer Quanta article tells a different story: apparently the resolution of the paradox is semi-classical, nothing to do with string theory or hopes of getting quantum gravity (4d, dS) out of AdS/CFT.

Peter wrote:

I think you’re right. That’s not

necessarilybad. If folks could figure out how to solve the black hole entropy problem “semiclassically” – without inventing a full-fledged theory of quantum gravity – they could find a solution that applies to many candidate theories. It could be a bit like thermodynamics versus a detailed theory of the microscopic structure of matter: thermodynamics tells you less, but its results are more general, so the further you can go on solving a problem using just thermodynamics, the more robust your solution will be.However, the analogy to thermodynamics is weak, because in thermodynamics we know the rules of the game, whereas it would take a lot of work to isolate and clarify the principles underlying the calculation described in the

Quantaarticle. As they say:I think the title of the

Quantaarticle is only accurate if one reads it very generously. We are not near the end of work on the black hole information paradox.It’s great to hear Kirill Krasnov has come out with a book on formulations of general relativity. We used to work together on spin foam models of quantum gravity, and we kept playing around with different formulations of general relativity, trying to find one that worked best for our purposes. I’d sort of lost touch with him in recent years until he came out with a paper on octonions and the Standard Model, which focuses on the importance of SO(9). I’ve been talking to him about that recently… but he didn’t tell me he’d come out with a book on GR! It’s a good thing I read this blog.

I’ve slipped behind in trying to understand the ways in which my fellow theorists are torturing black holes these days. Coming at the problem from the quantum information side, I never quite followed the arguments or grasped the underlying intuitions, I think. When “ER = EPR” came out, for example, I just didn’t get it — it sounded like they would have had a wormhole between any two correlated systems in the Spekkens toy model, which is just silly. A lot of what I read since then seemed more likely to give a geometric description of certain types of many-body entangled states, rather than to turn entanglement into spacetime. (I know multiple people who knew John Wheeler, and we’ve had plenty of long chats about “it from bit” aspirations, so I

amcoming at “it from qubit” from a sympathetic place.) And for weird reasons of my own, I distrust the applicability of any conclusions from AdS, whether or not a gauge/gravity duality is invoked. The new “replica wormholes” effort seems to rely a lot on AdS still, even when it’s not being stringy, doing things like gluing AdS to Minkowski in order to provide a place for radiation to escape into. I’m not sure how I feel about that!This is probably a very smart tactic being employed by some very smart people, but it also gives me the feeling that somebody is going to pop out from behind the corner and declare that the total number of black holes in the Universe is now -1/12.

I read through Kirill Krasnov’s 6d/7d model. As he mentioned in his talk, it could be related to the topological strings. Nevertheless, I believe it must be related to the so-called 6d (2,0) SCFT and its 7d dual. Some twisted version of the 6d theory is also called Theory X by some mathematicians. Here the cosmological constant naturally presents itself through the Omega parameters of Nekrasov. However, the relation to the twistor formulation is unclear, at least for me.

One thing that worries me is whether all of this means anything. There’s the quote from the article that John Baez pointed out:

So how do we know that you can’t find a way to string all these calculational techniques together in a Rube Goldberg way to come up with any result you want? In this case, the fact that they’ve come up with the Page curve isn’t all that meaningful.

Stringing together lots of calculational techniques makes sense when the rules of the game are clearly laid out – for example, this is how people proved that 8 and 9 are the only two powers of positive natural numbers that differ by 1. It’s a lot more risky when one is doing physics calculations that aren’t based on a well-defined underlying theory. Then one is in real danger if there isn’t a solid intuition grounding one’s work. It’s interesting that nobody in the

Quantaarticle claims to understand what’s really going on here – exactly how the information gets out of the black hole. I suspect people will be arguing about this for many years.Personally I’d be quite happy with information loss.

Replica wormholes do not depend on AdS and, as is now understood, arise for a good reason. They can be derived solely from the goal of approximating certain information theoretic quantities of a subsystem of a larger system in a more sophisticated way than just replacing your reduced state on the subsystem with a thermal density matrix (but while still not actually using more fine-grained information than equilibriation).

This was recently shown here: https://arxiv.org/abs/2008.01089

In this controlled approximation, certain matrix elements arise, and these matrix elements will in a gravity system be calculated exactly by these wormholes. Analogous objects would arise in other many-body systems.

Shouldn’t quantum gravity really stem from quantum geometry, since gravity is after all the consequence of the dynamical geometry of manifolds? In the regime where gravity is strong, shouldn’t one consider that the evolution of one spacetime slice to another takes place via all possible interpolating manifolds, to be summed over in a path-integral formulation? I believe that is what one is doing in JT gravity, but extending that to 4d is not trivial at all. For one thing, the theory of 4-manifolds is in a state of flux, so shouldn’t one hold all theories of 4d quantum gravity in abeyance until that has settled down? And all this is over and above the problem of doing a path-integral quantization, where one is faced with the usual problem of defining the path-integral unambiguously. Not to speak of the issues of non-renormalizability plaguing such a formulation.

Somdatta,

The problem with just saying quantum gravity is a “sum over geometries” is that there’s a huge variety of very different ways of specifying what a “geometry” is, and once you have done that, another huge variety of ways to try and put a measure on the space. You need a much more substantive idea to say anything useful about this, I have no idea whether this recent work has one or not.

Whenever I try and read about this to understand better what is going on, I get put off by a wall of claims about “wormholes”, then decide that my time is better spent thinking about other things.

Peter,

You’re right, but what I wanted to point out was that even if you figured out how to solve those problems, most of the work on 4-manifolds concentrates on the simply connected ones, with claims in the literature saying that the non-simply connected case is intractable. So one might be thwarted for a very long time to come if not forever, from even defining the space of interpolating manifolds in the sum over geometries, let alone a measure over it. Wonder what LQG has to say on all this.

After having a discussion with Sabine Hossenfelder on her blog, I am beginning to see the problem. Physicists have always treated mathematics sloppily and non-rigorously (e.g. Dirac delta functions, the replica method, Feynman path integrals, AdS-CFT applied to condensed matter). And they have gotten some amazing results this way. But they’ve always had experiment to tell them when their calculations gave the right answer or were completely off-base.

With the black hole information paradox and quantum gravity, they no longer have experiment to guide them. I think what they have to do is go back, look at what they think they’ve shown, and treat everything much more carefully (if not completely rigorously). But I suspect that most physicists find it inconceivable that this has become necessary.

If I recall the history of mathematics correctly, there are several times that mathematicians have needed to do this (one being the treatment of set theory that Cantor et al. put back on the right track).

@PeterShor:

It is said that the

https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry

started having annual conferences around the turn of the twentieth century, in order meet and vote on the theorems.

@Jack Morava:

Wow! That’s an amazing story, even just reading the short version in Wikipedia. I knew there were problems with making probability theory rigorous in the early 20th century, but I foolishly assumed that applied mathematicians were to blame, and that pure mathematicians had figured out how to do things better before then.

Peter Shor wrote:

I disagree. I think most physicists realize that more careful thought is required to understand quantum gravity. Theoretical physicists are used to floundering around, writing papers that try different things until the truth finally becomes clear. They aren’t like mathematicians or mathematical physicists, who start with clear assumptions and deduce consequences. They’re doing something much harder, where the rules of the game only become clear near the end. So most of their papers are wrong, but that’s okay – that’s how it works.

Another thing worth pointing out that appeared in the Quanta article.

“When researchers set out to analyze how black holes evaporate in AdS/CFT, they first had to overcome a slight problem: In AdS/CFT, black holes do not, in fact, evaporate. Radiation fills the confined volume like steam in a pressure cooker, and whatever the hole emits it eventually reabsorbs. “The system will reach a steady state,” said Jorge Varelas da Rocha, a theoretical physicist at the University Institute of Lisbon.

To deal with that, Almheiri and his colleagues adopted a suggestion of Rocha’s to put the equivalent of a steam valve on the boundary to bleed off the radiation and prevent it from falling back in. “It sucks the radiation out,” said Netta Engelhardt of the Massachusetts Institute of Technology, one of Almheiri’s co-authors. The researchers plopped a black hole at the center of the bulk space, began bleeding off radiation, and watched what happened.”

The point is, this artificial way of bleeding off the radiation doesn’t take place naturally, so all analyses based on such a thing are artificial, and may not apply to nature. One might say AdS black holes themselves are unnatural, but then that becomes the point. One is applying unnatural assumptions to unnatural black holes and then making the claim that they apply to the real world. Why would such a thing be believable?

@Jack Morava Can you cite a source for your statement?

John Baez,

I can’t find the source, but one of my favorite John Baez quotes I recall as comparing doing theoretical physics without either mathematical rigor or connection to experiment as “playing tennis without a net”.

There’s a good argument for people trying whatever they can, if it ultimately leads to rules of the game getting clarified and the truth becoming clear. The problem is that sometimes that doesn’t happen, and people keep doing the same thing endlessly, telling everyone what great tennis players they are (cf. string theory).

I’m very wary of saying much about this latest work because I don’t understand it. But looking at many decades of similar claims about “solving the information paradox”, and seeing what people claim to now have done convinces me that my time is better spent on other things. There’s no way this kind of thing can connect with experiment, what would more likely make it interesting is having a well-defined solution to a well-defined problem of some kind. If a problem is hard, maybe all people can do is flail around and do wrong things, hoping to learn something that will help. Nothing wrong with that, but then there’s no reason for articles in Quanta magazine or elsewhere.

@jsm : It’s a joke; ask your friendly neighborhood algebraic geometry grad student. I think I first heard it at Columbia in the 60s, perhaps from Spencer Bloch or George Kempf.

My father was one of the last members of the Italian school of algebraic geometry before its collapse, being a student of J. G. Semple, and publishing on the subject in 1947, 1950 and 1955. The abstract of the last contains the phrase “no great degree of rigour can be claimed” and refers to “experimental” justification (his inverted commas). That about says it all, I fear.

John Baez:

I’d be happy with that, too. (I remember watching a lecture by Bill Unruh during the heyday of the firewall back-and-forth where he suggested that information might just be “gone —

pfft!” ) I’ve also played around with a toy model where a black hole is described by a mixed state all the way from formation through evaporation, so the intuitions based on (as Page says) “forming the black hole from a pure state of radiation in a box” simply aren’t applicable.Peter Shor wrote:

No fair using John Baez quotes against me! I’m compelled to agree.

Hawking’s original work on black hole radiation had no connection to experiment but it could be, and was, made mathematically rigorous – in a “semiclassical” approach where the geometry of spacetime was described classically and the radiation was described using quantum field theory (a free quantum field, describing noninteracting photons).

So, the rigor was obtained by avoiding use of the nonexistent theory of quantum gravity and hoping that in some circumstances the semiclassical approach was a good enough approximation to the unknown reality to be worth thinking about.

The thermal nature of the radiation emitted led to a puzzle, mistakenly called the “black hole information paradox” because it only becomes a paradox if you put enough constraints on the solution that there’s… no solution.

One way to push the puzzle toward the jaws of paradox is to adopt the AdS/CFT philosophy, which roughly says that everything about the universe can be observed from arbitrarily far away, on a “sphere at infinity”, where it’s described by a quantum field theory. This philosophy is not based on experiment: on the contrary, our universe is nothing like anti-de Sitter spacetime. It’s also not mathematically rigorous. And the idea that everything about he universe can be observed from arbitrarily far away tends to conflict with the idea that once something falls into a black hole you can’t observe it. So it should come as no surprise that with this approach the information loss puzzle became closer to a paradox, and researchers began to contemplate something very strange: that anyone falling into a black hole would be burnt to a crisp by a “firewall” lurking right beneath the horizon.

Me too. All my best work came after I gave up working on quantum gravity. The “firewall” stuff happened after that, so I’ve never studied it carefully: I just listen to what people say, shake my head bemusedly, and shrug. I still hope that theoretical physicists can make progress on the black hole information puzzle by clear thinking, and I guess you caught me on an optimistic day. But the jury is still out on that.

If pop-sci magazines could manage to present the current flailings in fundamental physics in a way that made it really clear they were really just flailings, it would be okay. But somehow they feel the need to present each development as if were a wonderful burst of progress.

John Baez:

I’ve sometimes wondered whether the AdS-CFT correspondence might not be an exact correspondence, but only a good approximation. In this case, it leaves enough wiggle room that you can speculate that information could be lost.

The few times I’ve asked somebody who works in the area, they say “no, the AdS-CFT correspondence is exact, and physics is reversible because CFTs are reversible” without ever giving me a good justification for this statement. Of course, if they did have a good justification, I wouldn’t be able to understand it. But I’ve suspected for some time that they don’t. And when they assume that AdS-CFT exact, they often end up postulating something else, like locality in GR is violated, and locality is something that we do have a great deal of experimental evidence for.

I’d much rather assume that AdS-CFT is a very good approximate correspondence.

Peter Shor wrote:

Yeah, I don’t think it’s been proved, not even in the physics sense of “proved”, except in some baby cases like 2+1-dimensional gravity which have no local degrees of freedom, which makes it far less surprising that you can reconstruct solutions from data observable at infinity. (If nothing interesting is happening in any bounded region of space, it’s not shocking that you can figure out what’s happening by only doing measurements very far away.)

It’s also probably worth reminding nonexperts (like me) that the most famous case of AdS/CFT doesn’t apply to a four-dimensional universe governed by general relativity, like our own. It applies to superstring theory on a 10-dimensional spacetime that’s the product of 5-dimensional anti-de Sitter space and a large 5-sphere. So there is unbroken supersymmetry, not seen in our universe, and also a spacetime quite different from ours.

There are also other cases of AdS/CFT, but if anyone makes strong claims for the relevance of AdS/CFT to our universe you can have fun pressing them for details about which case they’re talking about.