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.

## snail feedback (38) :

"They keep on making numerous not-really-established-and-probably-wrong assumptions"

Figuring out which ones actually _are_ wrong and how that happens would be useful, no?

Yup. There may be assumptions we can't even crisply describe.

But I believe that among those that have been described in explicit words, I can say which are right and which are wrong.

For example, one may focus the discussion on the tensor product decomposition. I think that I can pretty much rigorously prove that the black hole interior states of a black hole of a given size and other macroscopic parameters can't form a tensor factor of the subspace of the Hilbert space that agrees with this black hole.

Why would people like Bousso join the amps bandwaggon? After all, he wrote a largely correct anti-firewall paper, before making a u-turn. Did he honestly manage to deceive himself, or did he decide that loyalty to polchinski et al is more valuable to his career than correct papers?

Either way, in my judgement, that makes him unfit for the position he has. I'd like for honest *and* qualified physicists, like lubos, to get such jobs. Instead lubos was booted out for political reasons. It's a sad reality we are faced with. :-\

Tx for your implicit support ;-) but I wouldn't search for evil conspiracy theories here. Raphael must have thought about it and (especially?) interacted with Joe and others and he (Raphael) simply got converted to the idea that there has to be a firewall. One may change his mind, I guess, even though sometimes it's a change in the wrong direction.

I told you a few years ago. In the interior the "arrow of time reverses". As Alice falls at velocity c towards the zero entropy singularity, she is causally disconnect from the maximal entropy horizon. From her perspective the singularity looks like a big bang and she can no more affect things towards the singularity than you can affect your birth. To understand the interior one must consider the horizon from the black holes birth to its evaporation. After all the exterior lifetime is an interior distance.

Dear Lubos, would you write a detailed paper on how interior and exterior of a black hole are connected or not connected. I think many of us would like to understand this point. Thanks.

I think that I wouldn't introduce a clearer understanding for everyone than some fine papers that are already around - and most insights that would have to be written in the paper to satisfy your order would be things first clearly formulated (only) by someone else.

Hi Lubos,

I am just watching the lecture of Ted Jacobson. I think it is very good and might mark the end point of the confusion.

Interesting, I thought he was at the beginning of the confusion ;-) but I haven't watched this talk yet.

OK, I'm happy to abandon any kind of conspiracy theory, if that is what I suggested. Especially if you say so... ;-)

But let me explain my point of view. I got a PhD in theoretical physics but did not stay in academia, because -- in my own judgement and without a grudge -- others were more capable of original fundamental research than me. Have been very happy and quite successful since. :-)

But I was a very serious and decent student (and a TA) and I learned these things very properly. I was never (i.e. as a graduate student) confused about fundamental issues such as QM being non-realist and probabilistic, the emergence of the arrow of time, and many other things you explain here so correctly and lucidly. Often I feel I could not have explained it as well as you did but I certainly did not need your explanation to *know* the right answer *for sure*. Cause I studied it, stupid. ;-)

Now I see the rising young stars in academia like Bousso or Carroll who can't even figure out basic fundamentals even *with* the benefit of your explanation (and others). Is it really a conspiracy theory to ask how this is possible and if other motivations might be in play?

Come on, you have debunked AMPS in a dozen different ways, it's just completely compelling and not even very difficult to understand. (Coming up with these arguments might have been a lot harder than understanding them, mind you.)

Think of your simple and completely unambiguous arguments like the refusal of the projection operator onto the horizon-subspace to commute with the occupation number operator in the infalling frame. Any graduate student should get this within 5 minutes, no?! Somebody like Polchinski should see this by himself, but it should be entirely trivial for him when presented with the reasoning. Yet...

Do you understand my point? The Hilbert space at any interior time slice has to somehow? be related to the time evolution of the Hilbert Space in the exterior. For the entire lifetime of the black hole.

"All the empirical evidence supports [that the Hawking evaporation process should be unitary]". It should be, but could you please give me a link to the empirical evidence?

I meant all the empitical evidence supporting quantum mechanics, starting from the spectrum of atoms and double slit experiments.

I actually meant a review paper.Some of us are too old and too lazy to make a major effort to try to understand the original papers!!! But we would like to understand the controversy little bit more analytically. Is there a review or summary paper written by someone else? Or a detailed blog?Thanks.

From an essentially primal theory based position of overview/outlook&opinion on this phenomenon (i.e. of strangely 'straying' physicists):

These people are likely to be responding in a roundabout way to some sufficiently similar predicaments early in their lives. Am not sure if it is a long and drawn-out birth or a dearth of touch thereafter, or both, but I think that for some such people (they are at least formerly formidable theoretical physicists) being faced with scientifically solidifying (growing increasingly theoretically tight and immutable) logic about these aspects of fundamental physical reality can cause their still present in relevant "conditioned-in" neural form predicaments to have a subliminal misconception-forming effect on how they think about these things - an effect that may very well be impossible to avoid or remedy by the use of theoretical physics type logic.

It's slightly more complicated than that. Along the radial timelike direction in a black hole, causal information flows (from a Cauchy surface in the past of the external spacetime before the collapse of the black hole) go radially inwards for infalling observers/matter, have a very complex interaction with the singularity that apparently thermalizes them and diffuses them along the entire (locally spacelike) extent of the singularity, and then propagte/tunnel radially *outwards* again to the event horizon where they participate in Hawking radiation production to produce the observed Harking radiation. So in the interior of the black hole, there are causal contraflows radially both inwards and outwards. All the q-bits that ever fell into the black hole get mixed together (mostly at the singularity), and they all come out gain in the black hole evaporation. This isn't quantum cloning, it's just reflection -- you can measure the same q-buts twice, if you measure them (or anything entangled with them) before they fall in, you fully centangle your self with the corresponding data about what has/will Hawking radiate out. This doesn't allow you to construct semiclassical paradoxes because the singularity scrambles everything so thoroughly, and of course at the quantum level there are no paradoxes because the sum-over-histories only includes self-consistent histories.

I may be a bit confused but maybe it's just me: microcausality, as far as I know, but correct me if I am wrong, should be valid even when Lorentz symmetry is "broken" by the curved spacetime. Now, as I think, causality and locality are related. What do you mean by weak non-locality on strongly curved space-times? How comes to even a "weak" violation of locality? I probably am confused right now...

I know I am wrong but I would want to understand how... any papers?

Dear and, right but one must be very careful what "microcausality" may mean quantum mechanically, especially in quantum gravity where the spacetime is dynamical.

Classically, things are easy: you only influence things along null or timelike geodesics in the future. Quantum mechanically, particles are inevitably delocalized by the uncertainty principle. Low enough energy particles may be forced to have wave functions spread over the curvature radius. Too high energy particles are modifying the position of the horizon so you can't assume that they respect the "pre-existing" causal structure derived from the geometry, because of the backreaction. So only some intermediate energy scales respect causality and only microscopically. The energy quanta comparable to the Hawking temperature in energy may be expected to maximally violate the naive causality.

The issue that you implicitly overlook in between the lines is that the geometry is a dynamical quantum mechanical variable, too. So to say that "two points" in the spacetime are spacelike separated may be a very subtle thing and with usual definitions, quantum mechanics doesn't guarantee that this may be satisfied with 100% probability. There's always some probability amplitude that the horizon is actually much further from the expected location etc. Consequently, there's always some probability that the points may exchange information.

Very interesting as always – I appreciate theses are thought experiments to understand the interior of the event horizon, however if we use persons as observers surely the model should still remain realistic. If no particles can escape from within the event horizon because nothing can move agains the strength of gravity and therfore no blood can move from Alice’s heart to her brain and she’ll be long dead before she gets spagetified

I certainly agree but even when the spacetime geometry is a dynamical variable and one has to incorporate it as well when "quantizing" the theory, microcausality just changes its form (deforms somehow becoming more general). Why should we assume, in the place of a modified (quantum) form of the causality a "breaking" of it? The combination of extremely curved and dynamical (quantum) spacetime geometry may result in a modified expression for locality that looks to us as "nonlocal" but, in fact, may be very local and causal nevertheless, but maybe following another interpretation... just speculating, of course...

ok, maybe I am not so clear so here, maybe a better idea about what I try to say: consider you want to "glue" together the local solutions of the quantization problem and obtain a sort of geniune deformation of the algebra of the observables in such a way that you consider the non-classicality of the geometry implicitly and obtain a complete formulation with a modified (deformed) expression that keeps being local and causal but in a "deformed" way. I am mainly trying to bring to your attention that deformation quantization and sheaf cohomology may be of some use in this problem... but I admit I am pretty vague here and now...

Hi Lubos, in your argument for why (4) is not paradoxical, you seem to overlook one point. Namely, it doesn't have to be Alice herself who applies the unitary to the Hawking radiation. Indeed, if we imagine a sphere of photodetectors surrounding the black hole and routing the Hawking radiation to a quantum computer, and Alice well in the interior of the sphere, then the decision about what Alice should experience when she falls through could be made in a region distant from Alice (unless you want to argue that Alice's backreaction would always screw things up, but I guess that argument would need to be made separately). So in particular, Alice could experience a "firewall" (or not) when she falls through, depending on decisions far away from her. So, this could be considered "superluminal signalling," except that you have to want the superluminal message *really* badly -- badly enough to jump into the black hole to get it, and then not be able to tell anyone outside the hole! (This implication is made explicit by Maldacena and Susskind, in the ER=EPR paper that you've said so many positive things about.)

Dear and,

quantizing a "classical law forbidding some process" *does* mean to say that the process is quantum mechanically allowed, it's just unlikely. This *is* how quantum mechanics always works.

Some classical "forbidding laws", like the conservation laws, have to remain exact in the quantum theory. Others, like the impenetrability of a classically inaccessible potential wall - and similarly the wall separating the black hole exterior from the interior "causally" - are deformed so that they approximately (and practically) work but strictly speaking, they don't.

Such classical assertions are "broken" by quantum mechanics because there's no fundamental principle that would imply that they should remain perfectly valid. That's what quantum mechanics routinely does: certain conclusions derived from classical physics are just wrong in general!

LM

After having read your comment twice, I still don't understand what you find paradoxical about it.

In the ER-EPR correspondence, the reason is obvious: the Hawking radiation isn't quite "faraway" from the black hole interior - they are actually very close to each other if you go through the Einstein-Rosen bridges. So if you assume the right topology and geometry of the spacetime, this action not only refuses to violate locality badly: it doesn't violate it at all. It only violates the locality that one would deduce from a different, wrong spacetime topology.

The unitary transformation performed on the early Hawking radiation has to be extremely convoluted to achieve their "clear and readable" for the black hole interior. But if it's done, it's done.

Dear Lubos,

I am happy we don't "really" have any subject we could disagree upon: as far as I see the quantum nature manifests itself in the way we calculate probabilities. This being said, quantum mechanics implies the calculation of probabilities while considering all the amplitudes that are possible to happen. But please note that the wavefunction (or the amplitudes) are not physically "real". Many people do make this mistake and I hope you don't do it as well... Now, my statements (which may be as well wrong): when performing a set of experiments and obtaining a statistics one obtains a glimpse on the "global" structure of the experiment, namely on its topological structure (see the Bohm Aharonov effect but also the EPR effect etc.). These effects do not violate "locality" or "causality"... they just redefine our understanding about locality in other terms, beyond simply Lorentz symmetry (although Lorentz symmetry is perfectly valid in these cases when space-time is flat ;) ). Note that topological effects are not restricted by distance... actually you do not need a metric space to define a topological space, but this is just a parenthesis... Gravitational fields redefine again what we understand under "locality" and we gain new ideas about how to understand it. It is, as far as I see, a main idea of the EPR=ER duality that one cannot gain "in reality" any information in a non-local way. I definitely agree that in order to do some computations you have to take into account some sort of "topological" or "global" results about space-time but that means you are violating locality only at the level of your calculations, in a "non-observable" way. What I want to say is that one can extend the concept of locality such that one incorporates these "non-observable" effects. Quantum mechanics *is* a local theory (how much I like to underline words with stars ;) ). The "non-local" effects are simply extensions that allow us to do some calculations taking in some way or another into account global effects when obtaining observables. They do not appear in physical measurements at all. I have no problem in allowing specific paths in a path integral do strange things close to a black hole etc. as long as these effects add up into something that corresponds with the observable reality and observable quantities. Note, that I do *NOT* refer myself to "classical" physics. Classical physics is not correct physics. It is just considering one single path, which obviously is wrong. I refer myself to measurability. Measurability does *NOT* imply classicality and this is, I hope, clear from arguments about the double slit experiment and so many others. Fact is, we do not measure one path in the path integral. We measure one outcome. Global effects do seem sometimes "non-local" but they appear only after calculating the probabilities and obtaining a statistics. They in fact are *not* non-local simply because we do not measure anything that is non-local (this is of course no good argument). Whatever *seems* non-local is, after a better understanding, incapable to produce any measurable non-local effect. What happens if one "jumps" into a black hole and tries in this way to violate locality is for me unclear, although I tend to agree with the EP=EPR conjecture. This being said I think the black hole problems will re-formulate our intuition about locality rather than abolish it at all... but this opinion has only a historical justification.

A

Dear and, I am partly happy, partly unhappy. There are statements in your comment I agree with, statements I disagree with, and the purpose of this mixture isn't quite crystalized in my eyes. What do you want to say?

Wave functions aren't observable waves, indeed.

Quantum mechanics is compatible with locality but it's not true that quantum mechanics is inevitably local. There are local quantum theories, like QFT; there are non-local quantum theories, like undergraduate textbook non-relativistic quantum mechanics that is non-local because its potentials act at a distance. This non-locality has nothing to do with the explanation of the entanglement because the interactions are pretty much turned off once the subsystems are entangled. But it's still true that the interactions make this theory (non-relativistic QM) non-local.

It's wrong to mix locality with QM which are two independent classes of constraints. In particular, the locality in black hole backgrounds is subtle and subtly violate. This does *not* contradict quantum mechanics in any way. It only contradicts special relativity - and its naive application within general relativity (that may be accurate classically but is not accurate quantum mechanically).

I must admit I invest much passion in this discussion as I am willing to learn more about the subject. I nevertheless feel that the example on undergrad quantum mechanics and non-local potentials is rather unfortunate simply because nobody expects that kind of potentials to be anything else than approximations. Of course quantum mechanics can work with non-local potentials and you can construct some effective theories that are very nonlocal and some people do that in order to construct an "image" about some deeper purely quantum effects they ignored while going at lower energies. Is that the correct description of reality? Certainly, up to a given level, but beyond that you should work with "proper" quantum mechanics and the apparently non-local effects become local in the quantum interpretation. Let me try again to be clear: after one single measurement of one single photon going through a double slit aparatus you obtain one single outcome. This one is very local. After measuring many photons you obtain a staristics and some answers that are also very local although you need to "bend" some notions about locality to arrive at them... non-locality in the entanglement is actually no non-locality at all (sorry, I try to follow the official terms but sometimes they get mixed up). I tend to see it as the effect of the inclusion of the global "situation" in the calculation of probabilities. This kind of "fake" non-locality in the case of black holes is not really surprizing for me. What comes as a "surprise" is the statement that the same topological properties encoded in the quantum mechanics close to a black hole generate some "real" non-localities like those obtained in undergrad quantum mechanics or effective theories. How can you say these are "real"? Could they just be a result of our lack of information about an underlying local theory? I think it is hard to go beyond a naive combination of general relativity and quantum mechanics and indeed most of the discussions about this subject are speculations... Please, whenever you find some time, tell me all aspects that you consider wrong in what I say. I would appreciate that and try to improve.

Thanks a lot!

A

sorry, I hope you do not consider I over-write on your blog, but I think I can say it clearer: quantum mechanics takes into account topological information which is generally not "local" so, considering this yes, quantum mechanics doesn't "demand" locality when doing calculations before calculating any observable results. Nevertheless, after calculating probabilities we do get local observable results. Allowing for the geometry to be incorporated in the quantization procedure does by all means make perfect sense to me but this will also be "before" one starts deriving results of actual measurements. Why should the procedure for obtaining predictions of observable phenomena be non-local in the generalized relativity sense and through what technique does one arrive at this?

Dear and, your contributions are totally fine.

Non-relativistic QM with its action-at-a-distance potentials is an approximation to a local theory, quantum field theory, indeed. But quantum field theory is just an approximation to a more complete theory of the real Universe, quantum gravity or string theory, which is surely non-local again, at least in some sense and at least in principle (the effects on these non-localities for practically measurable physics are probably exponentially small), and to clarify what the sense is and what it's not is subtle and requires more than just words.

I am not completely ignorant in more abstract symbolic constructions. I would enjoy reading some articles about that if you could recommend me a few.

Thanks a lot

A

Hi, this is not a subject that has been fully settled so there are no authoritative reviews with the final indisputable answers to everything.

Instead, there are research papers that contain work in progress and I have indicated over the years which of them are good, crisp, and important papers. They include Raju-Papadodimas, Maldacena-Susskind, and others that have been linked to. There exist no other, miraculously "more authoritative" papers or reviews of a sort.

Well, there exist older reviews in which some of the newest objections are ignored because they hadn't been raised yet. Those older reviews are sometimes more sensible than many papers written in the recent year - but despite this overall advantage, these reviews are still insufficient to address any of the last-year questions in any detail.

One of the elements used by AMPS in their firewall paradox argument, to convert the paradox from one excited quantum to an entire firewall, is mining black hole Hawking quanta via lowering a box on a string. In http://arxiv.org/pdf/1207.3342v1.pdf Adam R. Brown has shown some new limits on the rate at which this can be done, derived from the averaged null energy condition applied to the box and string (and if your equipment can violate the averaged null energy condition, you can trivially violate causality and clone quanta the Alcubiere way), which drastically reduce the rate at which quanta can be mined out of the black hole to one per black-hole light crossing time per string supporting your quantum mining apparatus. I'm uncertain what this does to AMPSs' proposed firewall, but I strongly suspect it will drastically reduce its intensity, possibly to down to one qbit per qbit of correlation that Alice carries in.

Dear Lubos,

I think the main problem with black hole interiors and quantum mechanics is that there exits no time variable which can provide global time slices which are valid both inside and outside the black hole.

Dear Mikael, no, for the Schwarzschild black hole in 4D (non-evaporating), for example, such slices do exist. It's not really *the* problem, you just were guessing and the guess wasn't right.

I see, Lubos. Quite surprised to hear. I assume then though that these time slices are not very well behaved, eg. they are no Cauchy surfaces.

I know nothing about anything relevant to this debate, but I really like the Mona Lisa analogy - in fact it's so good I have to ask if you took it from somewhere or is it originally yours?

Thanks, it's mine, at least I am not aware of anything similar sketched by someone else.

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