There is a KITP rapid response 10-day workshop on the black hole information puzzle in Santa Barbara: Complementarity, Fuzz, Or Fire?
Red fire or fuzz? asks a mad professor before she connects the wires and fires some red fuzz.
The speakers (click for all the talks in various formats!) include a great part of the most well-known researchers in the area plus some folks who are close enough to them: Marolf, Bousso, Polchinski; van Raamsdonk, Susskind, Maldacena, Sanford; Mathur, Turton, Bena; Harlow, Aaronson (intelligent outsider); Preskill, Oppenheim; Hawking (remotely), Unruh, Wald, Jacobson; Papadodimas, Raju, Nomura, Verlinde, Verlinde; Lowe, Silverstein; Giddings, Banks. It was easier to retype the full list of speakers instead of thinking how to pick, how to order the picked ones, and how to justify the choices. ;-)
Juan Maldacena's talk is the only one that I have watched in its entirety so far. He makes lots of jokes – like the comment that the more mathematically precise parts of their work with Lenny were already explained by Susskind (the audience explodes in laughter because Juan is among the most rigorous folks in the field while Susskind is one of the most representative hand-wavers of a sort, but this is not meant as a criticism!).
At the beginning, Juan says that paradoxes are normally resolved by realizing that we have been thinking incorrectly about some principles. For example, Loschmidt's paradox (the surprise that reversible fundamental laws are compatible with the irreversible emergent laws in thermodynamics) has been resolved because the irreversibility enters once we consider statistical propositions (Juan says the same thing about these arrow-of-time matters as your humble correspondent). Similarly, strange aspects of dualities were not resolved by abandoning dualities; instead, we figured out how to understand them better. Juan clearly means the usual principles of quantum gravity as well as AdS/CFT that isn't inaccurate or incomplete – as Joe Polchinski is trying to suggest.
Juan also dedicated lots of time to tensor networks, a formalism that has been somewhat hot in condensed-matter physics since 2009 (Sachdev's review). These are methods to rewrite the wave function of a ground state as a trace of the product of many tensors with many indices and legs (very useful for systems with a mass gap). Juan's pictures de facto generalize Penrose's graphical notation for tensors, I would say. Tensors with 5 indices are good to describe the ground state in \(AdS_3\); the network covers this hyperbolic spacetime nicely but the choice of the tensor covering isn't unique and it's discretized which means that it is only appropriate at distances (much) longer than the \(AdS\) radius. This discretization is one of the ways to see that his picture is so far just qualitative, not an exact alternative formalism for quantum gravity. Time evolution isn't comprehensible in the picture, either. There are other reasons to say that lots of work has to be done on this paradigm.
It's clear that the participants were debating and will be debating some subtle issues and possible errors and loopholes in the work by many of them. It would be good if everyone understood everything that is known at the end and abandoned everything that is known to be wrong but I wouldn't bet that this will be the outcome.
A semi-intelligent discussion about this topic between outsiders and semi-insiders (the URL needs a manual fix) was surprisingly allowed at Woit's global HEP crackpot headquarters, Not Even Wrong. You may see that the participants form a mixed bags. The quantum information folks – especially Scott Aaronson and partially Peter Shor – are offering some sensible voices about the unitarity and other universal properties of quantum mechanics.
Meanwhile, folks like Lee Smolin are flooding the discussion with tons of rubbish. For example, Smolin screams that unitarity should be abandoned. It will solve all the problems – blah blah blah: there isn't the tiniest evidence that this could solve any problems without introducing obvious, much more serious problems – and instead, we should be talking about all kinds of nonsense such as baby universes born in black holes etc. (Baby universes have clearly nothing to do with the AMPS paradox: once you abandon unitarity, baby universes aren't needed to resolve anything because you have already previously denied an assumption of the AMPS "paradox", namely the unitarity, anyway.) Smolin is like a cell of mold that or who wants to solve the mystery of Mona Lisa's smile by inviting others to become cells of mold as well, by devouring and destroying the painting, and by replacing Leonardo's precious lines with lots of random "urine" from their bodies that have nothing to do with the original painting. After some "work" of this sort, there won't be any smile left that could puzzle us. You may only "solve" the mystery by completely destroying the fabric of the painting – or science – and everything that is valuable, true, and functional about it. Mold doesn't belong to Mona Lisa paintings and stupid unconstructive scumbags such as infected mosquitos that annoy researchers or such as Lee Smolin shouldn't be mixed up with science.
Unitarity has very good reasons. It's not only compatible with everything we know; to a large extent, it's a logically inevitable part of the description that seems to work at the fundamental level – the quantum mechanical description. Unitarity is nothing else than the claim that the calculable "total probability of all alternative, mutually excluding futures" is equal to 100% regardless of the initial state (assuming that the evolution transforms the ket vectors linearly which is required because of related arguments). You can't just throw it away without a replacement. If you throw it away, you must also present your full alternative to all derivations and calculations that depend on it – which means, in this case, your alternative to all of modern physics. If you don't do it and you promote your rubbish anyway, you're like the cell of mold above.
Some people at Woit's blog, like Chris Cesare, clarify misconceptions by some deluded participants, like Igor Khavkine, about the unitarity. Cesare correctly says that the Lindblad equation isn't unitary but that's because it's not fundamental. Instead it's an effective equation obtained e.g. by tracing over the environmental degrees of freedom in various ways. There's no reason to think that we can't reach the fundamental equations in which all the sources of non-unitarity are eliminated.
Scott Aaronson gave a surprisingly concise explanation of the AMPS firewall paradoxical arguments at Woit's blog:
As I understand it, the issue is actually pretty simple. Do you agree thatObviously, (1) i.e. unitarity is correct. All the empirical evidence supports (1) and (1) seems mathematically necessary to formulate a quantum mechanical theory. This inevitability of (1) is made even more paramount in several formalisms of string theory such as the AdS/CFT correspondence and Matrix theory. Due to these and other developments and solved puzzles, fuzzball and complementarity advocates have taken (1) for granted for almost 20 years. Firewall champions such as Polchinski agree with (1), too.
- the Hawking evaporation process should be unitary, and
- the laws of physics should describe the experiences of an infalling observer, not just those of an observer who stays outside the horizon? If so, then you seem forced to accept
- the interior degrees of freedom should just be some sort of scrambled re-encoding of the exterior degrees, rather than living in a separate subfactor of Hilbert space (since otherwise we’d violate unitary). But then we get
- by applying some suitable unitary transformation to the Hawking radiation of an old enough black hole before you jump into it, you ought to be able, in principle, to completely modify what you experience when you do jump in—an apparent gross violation of locality.
You have to be a Smolin of a sort to propose a violation of (1) and because you would need to rebuild the whole modern physics, as I said, I will consider the option to abandon (1) to be a crackpots' scenario that doesn't really solve anything and has nothing to do with the problem.
I am somewhat open-minded about (2) i.e. "physics describes the black hole interior as well" because the AdS/CFT, as Polchinski and others rightfully point out (but I would add "AdS/CFT in its current understanding"!), says nothing about the interior at all. However, I think that the laws of physics are quasi-local and because the black hole interior locally looks like some places outside any black hole (even the curvature may be arranged to agree in a neighborhood etc.), physics probably has clear rules to predict what will happen. The infalling observers have a finite life expectancy so they can't perform arbitrarily accurate experiments, however. In my opinion, this inability of theirs makes it harder, not easier, to isolate a sharp paradox.
However, even though I think it's much more likely that (2) holds, i.e. physics describes the black hole interior (and it may in principle be extracted from AdS/CFT as well if we treat the correspondence appropriately!), it's important to mention that what physics actually predicts for the black hole interior isn't 100% known. The Einstein-Rosen bridges that may be arranged by a proper entanglement are examples of the "surprising predictions" that physics may be making even though we haven't known about these predictions for decades. So one must remember that (2) does not mean that the black hole interior must behave exactly in the ways you suspected.
The main statement in the point (3) – complementarity in the normal sense – is also correct, at least morally. The black hole interior degrees of freedom are invisible in AdS/CFT, for example, which is a unitary theory, anyway. It means that the unitarity must be allowed to proceed without anything added to the strict interior. In other words, the interior degrees of freedom can't be quite independent from the exterior ones.
However, the precise nature of their functional relationships and unavoidable entanglement may be subtle and isn't precisely known (see the "slogan" in the fresh paper by Nomura et al.). For example, Juan Maldacena was emphasizing that the ER-EPR correspondence doesn't say that the radiation "is" the interior. Instead, they say that the radiation "is" the left exterior (after some encoding). I actually think that Nomura et al. as well as Papadodimas-Raju are saying the same thing. It would be great if all of these guys finally settled the picture and agreed with Maldacena using some pet-formalism-independent words – instead of spending too much time with debates about totally different pictures of this physics such as Polchinski's.
It seems conceivable but unlikely to me that the experience of the infalling observer is "entirely subjective" and there are infinitely many very different ways to choose the logical framework and observables that may be perceived by her. Some kind of Heisenberg equations should still hold for any degrees of freedom that seem localized in a spacetime and the consistency of histories in the Gell-Mann-Hartle sense should still determine "practical" sets of questions almost uniquely.
An entirely different question is whether the interior degrees of freedom form a nice tensor factor of the full Hilbert space, as written in the point (3). I don't think so. It's a flawed intuition imported from strictly local quantum field theory – one that doesn't generalize to quantum gravity. The interior is correlated/entangled with the exterior by the condition that the black hole horizon (the boundary between the two subregions) has the predetermined location and shape even though the location, size, and shape of the horizon is actually given by the amount of matter in the spacetime (spacetime is dynamical and obeys Einstein's equations of a generalized sort). So if we consider an ensemble of microstates that "contain" a particular classical black hole, it's clear that we are restricting the full Hilbert space of string theory (or a superselection sector) which may or may not contain arbitrarily black holes of arbitrary size by a condition that doesn't respect the tensor factor decomposition to the interior and the exterior!
The assumption that this tensor decomposition may always be done is one of the technical yet very naive errors that AMPS and other firewall advocates are repeatedly committing. But the most illogical part of their wrong reasoning is summarized by Scott's point (4) which finally claims that the previous points lead to a "paradox". Alice transforms the early Hawking radiation by a complicated unitary transformation and because the state of the radiation also knows about the interior, she may modify her experiences once she falls in. AMPS think that this is a paradox.
But this is no paradox at all. In fact, it is not a violation of locality, either. Alice, as long as she is a localized object, is moving along timelike trajectories in the spacetime and the observation (4) only says that if you do something now, it may influence your future fate or observations. What a surprise! On Alice's trajectory, we only modify the future by the past along timelike trajectories which is just OK. Of course, if she performs a complicated, fine-tuned, large-size, "unlikely" operation with the Hawking radiation, she may change her future "greatly". Common sense. And even if you protested that Alice's actions influence the "background spacetime" in the interior rather than the state of herself, it's still OK because you may still view the interior spacetime to be in the causal future of the early radiation once you add the Einstein-Rosen bridges (or de facto equivalent relationships between the operators that were described in the pre-ER-EPR literature).
In some sense, the black hole interior is partly connected in the future that comes "after" Scri-plus. This extended visualization of the causal structures creates no closed time-like curves (because the black hole interior is a dead end, due to the final singularity, anyway!) so it's OK. Of course that the presence of the black hole brings us some causal relationships that differ from – and would be forbidden in – the flat Minkowski space. But I think we've known it for quite some time. It seems utterly silly to be surprised by such things. The locality in the Minkowski space holds if and when and because all different inertial observers must be allowed to use the same description of physics. But this Lorentz invariance is spontaneously broken by large curvature, e.g. one near the black hole event horizon, so the consequences of this Lorentz invariance may also be modified – slight nonlocality sending information over distances comparable to (or longer than?) the curvature radius (the scale at which the Lorentz invariance is spontaneously broken most strongly) is just OK because special relativity isn't applicable in this regime.
At any rate, if Alice prepares some initial state of "all" the degrees of freedom in some state \(\ket\psi\), she may quantum mechanically predict the probabilities of observing any eigenvalue \(\ell\) of any observable \(L\), i.e. \(L=\ell\), once she falls into the black hole. Those are given by the totally standard rules of quantum mechanics (\(L\) is a functional of the operators that Alice knew in the initial state; the form of this functional is de facto given by the Heisenberg equations of motion). There can't possibly be any paradox about these matters. What irritates me about AMPS is that there's no paradox even if you agree to commit 2-3 errors from the list of mistakes done by AMPS. Even with 2-3 errors (errors making the situation look more paradoxical than it is), it's still true that there is no paradox. It's hard to debate here because they're simultaneously making mistakes at too many steps. They keep on making numerous not-really-established-and-probably-wrong assumptions (regions in quantum gravity's description of a classical black hole spacetime are tensor factors of the Hilbert space; Alice shouldn't be held responsible for her acts in the past; the occupation numbers inside a black hole microstate are guaranteed [wrong], and not just likely, to be zero, and so on, and so on) in order to falsify some assumptions that are pretty much rock-solid.
I also think that this line of thinking can't lead to any deeper understanding of anything; flawed arguments purporting to show a genuine paradox only lead to chaos. So I am interested in the clarifications of the actual relationships between various operators and reasons behind these relationships. But to deny that one may just continue space – even for practical, medium-size observers – in regions where it's nearly flat seems to be out of the credible physics. It's a super-unnatural assumption postulating the end of the world at a rather random place.