This text adds a few more comments about the proposed new solution of the black hole information puzzle by Hawking and two collaborators (HPS).
Jacques Distler's blog in Austin woke up after half a year and it was enough for an
To simplify things a bit, I think that their setup isn't a viable approach to settle the qualitative features of the information carried by black holes and the mysteries that this information provokes. And it seems that most experts share my viewpoint. If you wanted to define the key question that ultimately divides the folks, it's the following:
Is it possible to describe the propagation of information in black hole spacetimes in the language of local quantum field theory on a curved spacetime manifold?I think that decades of work make it clear that the answer is "No" while HPS basically say "Yes". The answer "Yes" is extremely bizarre because the language of the local field theory was and still is basically sufficient (for Hawking and followers) to derive the conclusion that "the information is lost" when the black hole evaporates. Because they don't change anything conceptual about their basic framework (BMS is nice business but just a technicality from this viewpoint), they're bound to end up with the same conclusion again. The information is lost.
Except that we know for sure – from all the controllable descriptions of quantum gravity that we have – that the information isn't lost. So the framework of local quantum field theory simply must be inadequate to describe these issues!
This is the most "big-picture-based" description of the problem. If she wants to avoid paradoxes depending on black holes, one simply can't assume a locality derived from a classical spacetime geometry. The locality is violated in some way – one may interpret the violation in different ways but it must be there. The causal structure must be allowed to be a bit uncertain because the metric tensor is dynamical; or tunneling must be allowed because the Hawking radiation behaves acausally just for a while; or completely nonlocal degrees of freedom must be embraced and allowed to play a role; or the whole smooth spacetime with its local field operators must be constructed just as a "realization" of the pre-existing exact Hilbert space of microstates (Raju-Papadodimas), and so on.
Jacques Distler has pointed out that the required nonlocality of quantum gravity affects not only observations at distances much longer than the Planck scale (e.g. comparable to the black hole radius) but even extremely long time scales, like the Page time (because the Page time in the "middle" of the long evaporation is when the entanglement between the early and late radiation begins to drop again).
However, the discussion about HPS obviously has many more detailed, "non-big-picture-based" aspects. One of them is the calculation of the black hole entropy. HPS claim to explain the black hole entropy up to a numerical factor, by the soft hair. I wrote that before Strominger-Vafa, the literature was full of such claims which never contained anything that could ever lead to a controllable framework. I had one particular researcher in mind, Steve Carlip, but didn't mention his name.
In the Distler blog discussion, Emil Martinec did so. He said that HPS looks highly analogous to the Carlip attempts to calculate the entropy. They also seem to reduce the black hole entropy to "something like the volumes of the group of diffeomorphisms" or another structure that appears in ordinary general relativity. But even Carlip has already admitted that he could get any result he wanted – largely because the specific "good" results depended on a seemingly arbitrary isolation of a subalgebra in the whole group of diffeomorphisms. I couldn't agree more. More generally, HPS basically seems to be a paper in the non-stringy school that implicitly assumes that all the important wisdom about quantum gravity is hidden in some kind of "smart but ordinary quantization" of Einstein's equations. I believe that this view has been thoroughly debunked by the recent 20 years of research. To pick this paradigm as the primary working hypothesis means to seriously misunderstand the broad lessons that these two decades of research have brought us, something I wouldn't have expected to write about Andy just a month ago.
Most of the discussion is about much more technical, detailed issues of the paper. HPS not only claim that the information (or at least its part comparable to 50% or another fixed percentage) is hiding in the soft hair at the event horizon. My previous texts discussed why it's inconceivable that some very preferred behavior may be strictly localized at the event horizon – because locally, it's simply not a preferred place of the spacetime at all. HPS say that some hair (soft photon degrees of freedom) are excited when a charged particle falls in; and the state of this soft hair calculably affects the later radiation and other things.
Even if I forget about all the big-picture-like criticisms above, this claim still sounds implausible because the mechanisms by which the black holes manipulate with the information must be very efficient and complicated. Black holes are fast scramblers. They quickly mix all the information in unreadable ways that probably depend on the finest details of the Planckian quantum physics. The idea that one could extract a big portion of the microscopic information just by playing some relatively straightforward games that conceptually take place within classical GR sounds unrealistic.
Aside from Jacques Distler, the experts who discuss these calculations of the effect of the soft hair include Marcus Spradlin (who has co-written several papers with Andy), Steve Avery, and Emil Martinec (the Carlip comment above), while Frank Saueressig tried to play the role of the main defender of the HPS program (Saueressig wrote numerous papers of the type "GR should be enough for quantum gravity") but he largely decoupled after the discussion switched from some "key" (?) sentence about some technicality involving powers of the Weyl tensor to the discussion of local and global symmetries and conservation laws.
What I largely understood was a discussion ignited by Steve Avery and revolving around their reconstruction of the data from the hair. There are some new conservation laws for the BMS charges – for each point on an \(S^2\) embedded in the 4D spacetime, there is a new charge. (I still haven't been convinced that they should be understood as new conservation laws in the quantum gravity theory on par with the total mass-energy or the total charge; it seems right to expect that the BMS symmetries are just "low-energy illusions" that don't apply to the full quantum theory.) And those are claimed to be enough to reconstruct some physics of the soft hair. I think that the debaters have uncovered several likely problems with the calculation and argumentation:
- HPS treat some diffeomorphisms at the horizon as global (and not local, gauged) symmetries which is why they can produce some new physical degrees of freedom that we would normally consider unphysical.
- The integrals of the important quantities over the spacelike hypersurface \(S\) – which would be normally understood as the "most important if not only" part of the spacetime calculation if the black hole additions were absent – are assumed to be negligible.
- It's apparently assumed that the new BMS conservation laws may be "doubled" and divided to pairs of conservation laws holding for "soft" and "hard" components separately. But this separation almost certainly doesn't hold. The soft and hard degrees of freedom are almost certainly converted to each other. In other words, they are not decoupled. If one of these two sets of degrees of freedom were completely decoupled, it would really mean that it is unphysical.
- Some formulae depend on gauge choices (gauge symmetries are the reason why it is not a problem that a certain quantity \(\varepsilon\) isn't unique) and it seems almost certain that for the gauge choice where some properties they need hold, the contribution of the surface \(S\) just cannot be negligible.
Their decision to neglect the surface \(S\) in the calculation is pretty much equivalent to neglecting the scrambling because with the gauge choices indicated by their other properties, it's the normal surface \(S\) where all the complicated stuff takes place. Once you admit that some difficult terms and processes linked to the surface \(S\) exist, you will also agree that it's impossible to get any significant information about the microscopic setup of the black hole from intrinsically classical GR calculations such as those of the "BMS soft hair". In reality, all the initial and final data are mixed to an irreducible set of basically unsolvable equations.
HPS only claim that all the difficult nonlocality and scrambling of GR may be "solved out" because they basically neglect it and the neglecting is logically inconsistent with the other assumptions they make. The fast scrambling inside the black hole isn't a feature that you may freely turn off. After all, it's linked to the ability of the black hole to "empty the trash bin" quickly (by absorbing all the matter in the volume in the singularity). In this sense, the complexity of the "black hole quantum microstate calculations" directly follows from the simplest properties of the spacetime in classical GR.
Even if I look at the discussion from a sociological viewpoint, I find it rather obvious that the physicists have basically concluded that they saw no way to read and organize the ideas in the HPS paper that would make complete sense to them and that could change their opinions or be incorporated in their future results. So they have basically decided that HPS isn't right and lost the interest about it at some moment. The discussion was intense for a few days but got silent rather quickly.
Physicists are never quite sure "forever". Some new papers with new arguments may hypothetically be published that will revive this line of reasoning and strengthen the opinion that some classical GR calculations are enough to trace lots of the information. But that's not the situation in which the proposals find themselves now. And one simply shouldn't confuse a wishful thinking with facts. HPS simply doesn't look fixable at this moment although the people have tried hard to fix the "holes". And quite sensibly, people won't spend a huge amount of time by efforts to fix the bugs of HPS if they currently believe that the bugs are probably unfixable. Hawking, Perry, Strominger are prominent physicists but physics doesn't worship "prophets" and if all the scrutiny makes it very probable that HPS is wrong, then another physicist simply has to conclude that the three men are probably wrong. They were not careful about some points that are important and they have overlooked some lessons that make it rather clear that those points are important.
I made these detailed comments about the researchers' discussions – and the likely events taking place in their brain – because I am afraid that almost no one (not even the typical person who claims to follow physics as an interested layman) has realistic ideas about what kind of thinking the actual physicists actually apply when they decide about the fate of other physicists' papers; and how these papers should influence and do influence their own future work.
It's rather important that no one in physics may be considered "infallible" and that physicists simply cannot elaborate on arguments and methods that look flawed to them. HPS does look flawed. The inability of real physics researchers to build on "nothing else than the authorities" or "on reasoning that looks sloppy or defective" are two important features by which physics differs from various other disciplines that only pretend to be hard sciences but they are not.
In many other, softer disciplines, statements by the researcher B are often "used" in researcher A's papers even if A thinks that B's claims don't quite add up; and some people's prophet status often beats all the actual detailed evidence concerning the question whether the prophet's claims add up. Perhaps, you could defend this methodology of soft sciences in the evaluation of HPS which is about soft hair, after all. ;-) However, I am confident that most active QG experts will keep on thinking that virtually all the microscopic black hole information is carried by hard degrees of freedom (those going beyond low-energy field theory) and should be studied by hard sciences. ;-)