Wonderful new papers refine the black hole complementarity and show that the black hole interior operators are included in the CFT and other descriptions of the bulk while locality holds more exactly than previously thought (by most experts)



Kyriakos Papadodimas and Suvrat Raju, two careful and bright researchers with a refined Harvard pedigree, wrote their first paper about the black hole information puzzle in November 2012.







Yesterday, they released two new papers that make the incorporation of the infalling observer's observations into a description of quantum gravity – especially the AdS/CFT correspondence – clearer than ever before. But before I will discuss their new insights, let me look at a fresh hype by Clara Moskowitz in Scientific American,



the strong subadditivity puzzle by Mathur and by AMPS

the \([E,\tilde B]

eq 0\) paradox

the non-existence of a left inverse paradox by AMPS

the Marolf-Polchinski \(N_a

eq 0\) paradox

the objections against unitarization of the Hawking radiation by small corrections

the frozen vacuum criticism by Bousso

which seems extremely unfortunate to me. My memory isn't too bad but I really don't remember the last article in Scientific American about theoretical physics, climatology, or sociology of science that didn't look painful to me. The basic premise of Moskowitz's article is that a significant contradiction was found by Joe Polchinski et al. in quantum gravity, the firewall paradox, and most of the insights that were claimed to have been settled became unsettled again. While Scientific American would promote the "consensus" in other situations, now the fact that a majority of the AMPS followups say that there is no firewall paradox is not only ignored but it is being pretended that the papers don't exist at all.Moskowitz quotes several physicists who say extreme things. Those things may be divided to two opposite extreme camps – extremely excited ones and extremely disgusted ones – but every reader who can read in between the lines understands that these two camps really want the reader to make the very same conclusion: something is seriously wrong with the field.Raphael Bousso says that the firewall arguments are "by far the most shocking and surprising things of his career". Different people clearly think very differently because they surely don't make it to my top 1,000 list. Joe Polchinski says that he's uncertain about the firewalls half of his life but no one has found a flaw in their arguments – which, as far as I can say, is a lie, in fact a collection of about 5 lies packaged into one package. Several independent serious enough flaws in the AMPS arguments (enough to invalidate them) are known.Donald Marolf does admit that many people do say that their pro-firewall arguments are flawed but he dismisses all these papers that disagree with AMPS and MP as "red herrings". And Brian Greene says that this whole ludicrous firewall fad (my words) is "what we live for". Not exactly the measured wording that I used to praise Brian for.On the other hand, Moskowitz quotes Matt Strassler who indefensibly claims that "quantum gravity is stuck". It even prints sentences by a hardcore crackpot, a teaching assistant at Columbia University, about "people lulled themselves to sleep" and now "shaken out of their dogmatic slumber" while Donald Marolf is said to "agree" with those insane propositions. Make no doubts about it: sleeping are those who haven't noticed how wonderfully consistent the previously accumulated wisdom has been shown by the research of quantum gravity in the recent 2 decades or so.While Bousso & Greene and others are presented as "folks excited about the developments", it must be very clear that in reality, they play the role of something that Joseph Stalin would call "useful idiots" for the basic propositions of demagogues like Strassler and the teaching assistant at Columbia University that quantum gravity sucks.All these people are wrong and, when it comes to their more general proclamations, a more accurate assessment is that they are all deluded. It is sort of sad to look at several chaps whom I used to value so highly as they are joining this decadent "everything is stuck and, at the same moment, in the state of permanent revolution" movement. I emphasize that this comment is mine and shouldn't be automatically associated with other folks who think that there aren't valid arguments showing that firewalls exist.Fine, that was the negative part of this blog post. Now the positive one. I had the pleasure to see Kyriakos Papadodimas' and Suvrat Raju's new papers in advance; they appeared yesterday in the morning. Their titles areThe short paper is a summary of the long one but both of them are excellent. Suvrat and Kyriakos demonstrate that the AdS/CFT-based (and probably other) descriptions of quantum gravity do contain sufficient degrees of freedom to account for all the infalling observer's observations while the unitarity is preserved and all the paradoxes in the literature are resolved.The two features of their description that contradict some of the AMPS assumptions (and assumptions of other firewall advocates) are the usual notion of complementarity – namely that the degrees of freedom inside the black hole are a reshuffled collection of observables that are in principle already included in the observations outside; and that the definition of the black hole interior operators is state-dependent Well, perhaps one should use a less provocative adjective than "state-dependent", perhaps "environment-dependent", to emphasize that there is a sense in which the change of the black hole interior operators is "small" if the state upon which the operators depend is changed "a little" (by an action of a few operators). This is the reason why the operators are still "large enough matrices" with many matrix elements. We're effectively not fixing a ket vector exactly; we're choosing a subspace of the Hilbert space that contains states that are "similar" to this ket vector – where the similarity means "obtainable by a limited number of actions of local operators".With these disclaimers or generalized assumptions – which are perfectly compatible with all the postulates of quantum mechanics and all existing knowledge of string/M-theory or AdS/CFT, they explicitly show how all the paradoxes in the literature known to Suvrat and Kyriakos are resolved, including:and several others.When unnecessary complicated things from the pro-firewall arguments are stripped off, their basic claim may be formulated in a very simple way: The pro-firewall folks always claim that the CFT in AdS/CFT or any consistent, unitary theory of quantum gravity cannot contain enough degrees of freedom to define the operators inside black holes which means that the perceptions of the infalling observers just can't be predicted from the CFT. It follows that the babes who fall into a black hole must have a "universal perception" – namely a death caused by their contact with the black hole event horizon where a deadly "firewall" should consequently reside.Papadodimas and Raju show that this claim against the completeness of the AdS/CFT correspondence (and probably other descriptions) is invalid by explicitly constructing the black hole interior operators that have all the desired properties and obey all the consistency conditions. More precisely, they carefully summarize what these conditions are and they prove that the conditions required from the black hole interior operators have solutions. In their first paper , the black hole interior operators depended on the separation of the degrees of freedom into fine-grained and coarse-grained. This dependence looked puzzling to me (and probably others) and it was eliminated in the new papers. Instead, the potential non-uniqueness of the resulting operators was extended by finding all solutions for the conditions that the set of black hole interior operators have to obey.The different constructions don't substantially differ and it's likely that an infalling observer doesn't have enough time (before she's killed in the singularity) to figure out which of the possible sets of operators is realized in her actual universe.OK, what are the basic objects and the key conditions? The basic reason why the operators inside the black hole are included in the description of the AdS physics by the CFT is that for a particular state \(\ket{\Psi}\) which is pure but effectively indistinguishable from a thermal one (and for the similar states obtained by an action of a few natural/local operators on \(\ket{\Psi}\)), the set of local operators may be doubled.In other words, one may define the so-called "mirror operators" \(\tilde A_p\) that satisfy\[\eq{\tilde A_p \ket{\Psi} &= \exp(-\beta H / 2) A^\dagger_p \exp(+\beta H/2) \ket{\Psi}\\\tilde A_p A_m \ket{\Psi} &= A_m \tilde A_p \ket{\Psi}.\] So the tilded operator to an annihilation operator is conjugate to the corresponding Hermitian conjugate by the evolution by \(\exp(\beta H /2)\), the operator shifting you by one-half of the thermal circle (that drives you to the other side of the cigar in the Euclideanized black hole solution), at least when it acts on \(\ket{\Psi}\).The second condition is that the tilded operators "seem to commute" with the untilded ones when they act on \(\ket{\Psi}\). This is enough for the commutator to "effectively vanish". This effective vanishing means that if you calculate the commutator's matrix elements – or, more generally, the matrix elements of this commutator multiplied by a limited number of other operators from both sides – in the state \(\ket{\Psi}\) and/or a "small enough excitation" of \(\ket{\Psi}\) (which may be constructed by a polynomial action on \(\ket{\Psi}\)), these matrix elements vanish.Those two conditions reproduced as eqn (3.8) on the longer paper's page 12 represent the (almost?) only displayed \(\rm\LaTeX\) equation in this blog post because I believe that by these conditions, Papadodimas and Raju really got to the essence of the problem of the black hole interior and found a much more accurate formalization of the black hole complementarity than one that we have vaguely believed for two decades.What do I mean?Since the early 1990s, people who took complementarity for granted (including your humble correspondent who was arguably affected by my ex-adviser Tom Banks who claims to have learned these things directly from Lenny Susskind) would usually say that the commutator of the interior and exterior operators "is not exactly zero" although "it is effectively zero for all measurable purposes". Such a comment seemed to directly follow from the assumption that the black hole interior operators are "redundant" in the sense that they're already encoded in the physics that is generated by the black hole exterior operators.Papadodimas and Raju explain why the commutator is "effectively zero" in a completely new, more satisfactory, more constraining, more well-defined way. They actually say that the commutator of the interior and exterior operators vanishes exactly as long as it acts on the state \(\ket{\Psi}\) for which the interior operators were defined – or its low-excitation siblings.The fact that this "effective vanishing" isn't "completely vanishing" and ultimately breaks down if you insert the product of too many operators in front of the ket vector (or if you try to make too many measurements, operationally speaking) is the underlying reason why many of the paradoxes mentioned in the literature are resolved.Kyriakos and Suvrat show that their conditions for the mirror (and black hole interior) operators have a solution by counting dimensions of the available space and the number of constraints. But they also identify the right operators in various numerical ways (I got a very transparent toy model Mathematica code doing it for the spin chains) and even analytic ways – even in cases that aren't the simplest ones.As I said, there are over 50 papers that use various constructions and observations to argue that there aren't any firewalls. These 50+ papers aren't exactly equivalent to each other. Do they agree? I believe that the new Papadodimas-Raju paper defines the most general framework for addressing the problem.What do I mean by this generality? Well, I believe that any picture that solves the problem arising from the infalling observer's observations does have to claim that the black hole interior operators exist in some sense and they may be expressed as functionals of some operators that exist in a theory that doesn't need to talk about the black hole interior at all – the interior operators are effectively encoded in the exterior ones but in a complicated way.Any satisfactory solution to the black hole interior problems should probably obey the Raju-Papadodimas conjugation-and-commutation consistency conditions, at least approximately. But because they show that the conditions may be required exactly and we don't get an overdetermined system, it really seems that a good solution obeys their conditions exactly, in the form they have stated. At most, you have the freedom to choose one particular solution for the interior operators from the Papadodimas-Raju set of solutions.So for these reasons, I believe that even Maldacena-Susskind's ER-EPR correspondence should be viewed as a special solution or Ansatz to the new Papadodimas-Raju rules of the game – although we might be forced to resolve the problems for the operators inside the Einstein-Rosen bridges rather than inside ordinary black holes.But I believe that even though it hasn't been written in the literature yet, the Papadodimas-Raju way of thinking implies a rather simple way to prove that the ER-EPR correspondence is true. How do we prove it? Well, we just prove that if we have the Hilbert space of states with two black holes, it is possible to find the "Einstein-Rosen-bridge interior operator" that obey all the conjugation-and-commutation conditions that are needed for the locality and that connect to the two black holes smoothly. So we may literally show that the two black holes' horizons may be connected by a non-traversable wormhole by defining the operators in this wormhole that smoothly connect to the black hole exterior operators at the two horizons, that obey all the locality etc. conditions we expect, at least when restricted to the neighborhood of a state \(\ket{\Psi}\), and that only use the Hilbert space of the two (seemingly disconnected) black holes we started with.I find it almost obvious that this will work and the paper with all the details may be written down. ;-) If it doesn't work for some reason I can't foresee now, I think that the Raju-Papadodimas' methodology is general enough to allow you to disprove the ER-EPR correspondence.There are other ideas that these papers led me to and I wrote some of them to Kyriakos and Suvrat. They will surely have lots of their own new ideas. At any rate, I think that you have seen the text that demonstrates that all the claims that the firewalls are supported by solid arguments and no flaws in these arguments have been known are simply untrue. There exist papers that are much more careful, constructive, and explicit than papers by Marolf, Polchinski, their collaborators, and their followers, and it's these papers that deserve to be read because they really show how the things work.The research in quantum gravity isn't stuck and the frameworks allowing black holes to be incorporated in unitary quantum theories have been around for 2 decades or so. The provocation by AMPS has arguably led to these more explicit proofs that all the apparent paradoxes one might invent are illusions due to the subtly coherent internal structure of the theory. But it's important to say that these paradoxes were never there and many quantum gravity folks always "knew" the reasons although only Kyriakos and Suvrat (and perhaps others) were able to disprove the existence of the paradoxes this clearly. Yes, I realize that these comments of mine are completely analogous to what I said about the discovery of quantum mechanics and various would-be paradoxes that some people starting from EPR (incorrectly) "saw" inside quantum mechanics.Incidentally, a month ago, there was a Google+ Hangout featuring Bousso, Maldacena, Polchinski, and Susskind – and a host, Bruce Lieberman. It's fun but I think that Juan was by far the wisest guy in this 53-minute video. He would compare the AMPS-like paradoxes to the "many" paradoxes that people would be "finding" in statistical physics as a theory of thermodynamics – such as Maxwell's Demon. When one looks carefully, no paradoxes are actually there. For example, we must carefully impose the laws of thermodynamics and/or statistical physics to Maxwell's Demon himself and when we do so, his miraculous abilities to create a paradox evaporate.It's just an analogy, he stressed, but a damn good one, I would add, because the geometry in general relativity is a similar "emergent" structure in a theory of quantum gravity as the thermodynamic variables and the coarse-grained descriptions are "emergent" features of a system in statistical physics. Well, I had the feeling that the other three guys' faces indicated that Juan's comments looked like a form of heresy to them. It's not a heresy, it's almost certainly the truth. And by the way, the analogy isn't insulting. Maxwell's demon was coined by a guy called Maxwell who wasn't exactly a loser. He had found many true important things and sometimes added an aether or a demon on top of them. ;-)But to be sure that I am not recommending you wear pink glasses either, Maxwell was probably getting senile when he began with the demon in 1873 although he was just 42 then. He had found the Maxwell-Boltzmann distribution in 1857 and completed Maxwell's equations by 1865, years before the demon.