Thursday, May 11, 2017

A Philosopher Tries to Understand the Black Hole Information Paradox

Is the black hole information loss paradox really a paradox? Tim Maudlin, a philosopher from NYU and occasional reader of this blog, doesn’t think so. Today, he has a paper on the arXiv in which he complains that the so-called paradox isn’t and physicists don’t understand what they are talking about.
So is the paradox a paradox? If you mean whether black holes break mathematics, then the answer is clearly no. The problem with black holes is that nobody knows how to combine them with quantum field theory. It should really better be called a problem than a paradox, but nomenclature rarely follows logical argumentation.

Here is the problem. The dynamics of quantum field theories is always reversible. It also preserves probabilities which, taken together (assuming linearity), means the time-evolution is unitary. That quantum field theories are unitary depends on certain assumptions about space-time, notably that space-like hypersurfaces – a generalized version of moments of ‘equal time’ – are complete. Space-like hypersurfaces after the entire evaporation of black holes violate this assumption. They are, as the terminology has it, not complete Cauchy surfaces. Hence, there is no reason for time-evolution to be unitary in a space-time that contains a black hole. What’s the paradox then, Maudlin asks.

First, let me point out that this is hardly news. As Maudlin himself notes, this is an old story, though I admit it’s often not spelled out very clearly in the literature. In particular the Susskind-Thorlacius paper that Maudlin picks on is wrong in more ways than I can possibly get into here. Everyone in the field who has their marbles together knows that time-evolution is unitary on “nice slices”– which are complete Cauchy-hypersurfaces – at all finite times. The non-unitarity comes from eventually cutting these slices. The slices that Maudlin uses aren’t quite as nice because they’re discontinuous, but they essentially tell the same story.

What Maudlin does not spell out however is that knowing where the non-unitarity comes from doesn’t help much to explain why we observe it to be respected. Physicists are using quantum field theory here on planet Earth to describe, for example, what happens in LHC collisions. For all these Earthlings know, there are lots of black holes throughout the universe and their current hypersurface hence isn’t complete. Worse still, in principle black holes can be created and subsequently annihilated in any particle collision as virtual particles. This would mean then, according to Maudlin’s argument, we’d have no reason to even expect a unitary evolution because the mathematical requirements for the necessary proof aren’t fulfilled. But we do.

So that’s what irks physicists: If black holes would violate unitarity all over the place how come we don’t notice? This issue is usually phrased in terms of the scattering-matrix which asks a concrete question: If I could create a black hole in a scattering process how come that we never see any violation of unitarity.

Maybe we do, you might say, or maybe it’s just too small an effect. Yes, people have tried that argument, which is the whole discussion about whether unitarity maybe just is violated etc. That’s the place where Hawking came from all these years ago. Does Maudlin want us to go back to the 1980s?

In his paper, he also points out correctly that – from a strictly logical point of view – there’s nothing to worry about because the information that fell into a black hole can be kept in the black hole forever without any contradictions. I am not sure why he doesn’t mention this isn’t a new insight either – it’s what goes in the literature as a remnant solution. Now, physicists normally assume that inside of remnants there is no singularity because nobody really believes the singularity is physical, whereas Maudlin keeps the singularity, but from the outside perspective that’s entirely irrelevant.

It is also correct, as Maudlin writes, that remnant solutions have been discarded on spurious grounds with the result that research on the black hole information loss problem has grown into a huge bubble of nonsense. The most commonly named objection to remnants – the pair production problem – has no justification because – as Maudlin writes – it presumes that the volume inside the remnant is small for which there is no reason. This too is hardly news. Lee and I pointed this out, for example, in our 2009 paper. You can find more details in a recent review by Chen et al.

The other objection against remnants is that this solution would imply that the Bekenstein-Hawking entropy doesn’t count microstates of the black hole. This idea is very unpopular with string theorists who believe that they have shown the Bekenstein-Hawking entropy counts microstates. (Fyi, I think it’s a circular argument because it assumes a bulk-boundary correspondence ab initio.)

Either way, none of this is really new. Maudlin’s paper is just reiterating all the options that physicists have been chewing on forever: Accept unitarity violation, store information in remnants, or finally get it out.

The real problem with black hole information is that nobody knows what happens with it. As time passes, you inevitably come into a regime where quantum effects of gravity are strong and nobody can calculate what happens then. The main argument we are seeing in the literature is whether quantum gravitational effects become noticeable before the black hole has shrunk to a tiny size.

So what’s new about Maudlin’s paper? The condescending tone by which he attempts public ridicule strikes me as bad news for the – already conflict-laden – relation between physicists and philosophers.

1,706 comments:

  1. Is there an underlying philosophical difference here, that is helping confuse matters.

    In the "mathematical" point of view, I have a mathematical model that describes a dynamic spacetime and dynamical stuff within it, and it just so happens that a particular asymptotic spacetime geometry and boundary conditions make calculations tractable, but the mathematics remains the same in all cases.

    In the "physical" point of view, the different geometry of spacetime and the different boundary conditions make the various choices into different physical situations, even different physical theories.



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  2. Physphil

    Please look at your last post to me. Then think for a minute. Then retract it. It is so manifestly nonsense that I won't bother to point out why. If you really, really cannot see why, then I will be explicit, but of you really, really cannot see why then you should retire from comment forever.

    And yes, I mean in AdS.

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  3. Bee,

    " Do we agree that Hawking's calculation shows the microcanonical interpretation of the BH entropy is violated without the need to know what's going on in the Planckian regime? If you want to hold onto it you need some way to deviate from that calculation (that being the usual conundrum). The only ways I know how to do that are nonlocal (or acausal, but I don't think the distinction matters). So where do you get these deviations from?"

    I agree that if you trust the approximations Hawking is using, which in particular includes locality at the black hole scale, then indeed it appears that info is lost, the microcanonical interpretation of BH entropy breaks down, etc. So it appears that you need some sort of nonlocality or "new physics" at the horizon scale to get around this conclusion. On the other, the domain of validity of Hawking's computation is not clear, since it's not appearing as a systematic approximation to some specific theory of QG, and locality etc. has never been tested in the situation of interest. So a natural thing to do in such a situation is to actually take a well defined non-perturbative theory of QG and analyze the problem there. Assuming this theory reproduces known physics in the regimes where it has been tested, if it turns out that "nonlocal" effects do in fact arise at the horizon scale of the black hole, then this shows that Hawking's approximations can break down, undermining his conclusion. This is precisely what I have been proposing. How exactly these "nonlocalities" arise is only vaguely understood, but it seems likely that it's connected to the fact that string theory contains all sort of branes and other extended objects that might appear in the presence of a black hole due to the infinite redshift. This is pretty handwavy at this stage, I fully admit, but the point is that there is a well defined theory in which to try to answer such questions. In the theory based on the CFT, it seems pretty inevitable that such "nonlocalities" must arise one way or the other, since it seems clear (Tim disagrees) that the info comes out in the radiation in this theory. The details are hard to extract, due to the very fact that they arising behind the horizon.


    Don't get me wrong: I personally still regard black hole evaporation as paradoxical, since both Hawking's approximations and the AdS/CFT argument seem pretty believable yet they lead to different conclusions. I am sure we are still missing some significant pieces of the puzzle. But the great thing about AdS/CFT is that you can actually attack this problem systematically, rather than engaging in all the pointless wild speculation that occurs when there is no underlying theory of QG to base one's conclusions on.


    Are we any nearer towards agreement now?

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  4. Tim,

    What you write about the recurrence time is incorrect: the recurrence time is typically set by the entropy. e^{e^S} is a typical estimate one sees. You seem to think there is some contradiction between this and my statement that your question (2) cannot be answered, but of course there is no contradiction. I'll let you figure that out for yourself.

    As it stands, the recurrence argument kills your proposal since it requires a breakdown of the Penrose diagram, and says that all entanglement with the disconnected region goes away an infinite number of times in the future, in contradiction to your claims. You need to address this if you want to raise your proposal from the dead.

    You still need to answer the homework questions I asked you. Shankar of course follows standard QM, and so he computes probabilities according to the usual rules, in particular probabilities are computed from inner products of states in the Hilbert space, whereas you flagrantly violate this rule. This issue of delta functions is totally beside the point as you surely know: let's just restrict to finite norm position wavepackets and ask the question there. Can you find any reference where one needs to go outside the Hilbert space to compute probabilities in such a case? You're also wrong about the time dependent Schrodinger equation in asymptotically flat space. Since the boundary Hamiltonian is nonzero, there is a well defined equation H\psi = i d\psi /dt, where t is the boundary time. Anyway, you agree this is the case for AdS, but I claim you will not be able to find any ref. where imposing this equation plays a part in defining the Hilbert space.

    As for refs on "physical Hilbert space", I pointed you to Dirac because that's where this is all explained in detail. He may not use the precise words "physical Hilbert space"; is that your only complaint? Yeesh. Why do you think it's called "Dirac quantization"? If you look in pretty much any paper on canonical gravity they will take the physical Hilbert space to be just what I (or rather Dirac) state it to be. The Smolin ref just happened to come up on google as a place where this is stated in one bite sized chunk, and I passed this on because I thought it would be helpful to you. Now you attack me for this. I am done with trying to be helpful if this is what I get back.

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  5. physphill,

    "We are discussing black holes in AdS. For a black hole in AdS, the recurrence time goes to zero as the mass goes to zero (all else fixed). That invalidates your entire argument."

    I suggested that you stop and think. You are not taking the suggestion. I will give you one last chance to reflect on what you just wrote, and everything else you have said about recurrence times in AdS. Think about what a recurrence time is. Picture in your mind what must occur for recurrence to happen. Ask yourself how that depends on the radius of the AdS space, and on the mass of the black hole.

    If you understand, you will come back and retract pretty much everything you have said on this topic. An apology would be in order. If you still can't work this out for yourself then I will school you. But I don't think that is a good result you for.

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  6. BHG

    If you want to go down with physphil on recurrence times, that's your business, I guess. I have been trying to find some way to get the two of you to come to your senses, but it is evidently no good. This is just beyond belief at this point.

    So you think that the recurrence time for a black hole in AdS is of the order e^(e^(S))where S is the entropy of the black hole? The very same entropy that goes into the Bekenstein equation for the entropy of a black hole? Let's just get absolutely, 100% clear on this. Is that really what you are maintaining? And the the recurrence time for a small black hole can be made as small as I like by reducing it's entropy sufficiently? Is that really, honestly your view? !00% sure? Either sign on to that or explain that that is not at all what you think. What you have written reads that way, and I just want to be sure you are not expressing yourself in some obscure way.

    As for the "physical Hilbert space" well yes, if someone tells me that there is a standard definition of a "physical Hilbert space" and that what, e.g. Shankar explicitly defines as the "physical Hilbert space" is non-standard, and I ask for a citation for a proper definition, I do expect that the citation should actually contain the words "physical Hilbert space". How in the world one is to determine what the "standard definition" of a "physical Hilbert space" is from a text that never uses that phrase is beyond my wildest powers of imagining. And for someone who said that the definition if commonplace, and can be found in any old introductory text not to be able to provide such a text, but to have to google to get a result is simply being disingenuous. I can google it—in fact I did google it long ago and got that hit!—but what is the point of that: I actually found an explicit definition in Shankar just to be told that that explicit definition is a very well known book is wrong, and the only example you can find of this supposedly proper usage is in a not-widely-known paper that you have never even read. If this passes for scholarship and informed commentary in physics then there is probably no hope for the entire field.

    Just come clean. You have gone on and on about the "physical Hilbert space" and when I called your bluff on it you folded. You could not find that term defined or used in all these places you claimed it was because it isn't there. You were reduced to Googling for it. And now you are all in a huff. Well tell you what: the next time you claim that some concept is standard and widely used and everybody in the field knows it, be able to back up your claim and we won't have to go through this.

    Now how about just either accepting the precise claim above about the recurrence times in AdS or correcting the claim to the one you believe. If you correct it, please be sure that e^(e^S) appears somewhere in the claim. To repeat: is the S in that formula the same thing that is usually referred to as "the black hole entropy", and that goes into the Bekenstein formula? Yes or no?

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  7. The proof of classical Poincare recurrence requires the phase space "volume" occupied by the system to be preserved during time evolution. I don't know or understand the quantum version of classical Poincare recurrence, but on the face of it, it would seem that some kind of "quantum phase space volume" must be preserved during time evolution for recurrence to occur.

    IF this preservation of "quantum phase space volume" is equivalent to unitarity, then it seems that we have a circular argument here, because recurrence assumes unitarity, and then we're saying recurrence proves unitarity (of the black hole in AdS).

    My thanks in advance to Bee, Tim, BHG who may set me straight.

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  8. Tim,

    As physphil and I have been patiently explaining to you, the recurrence time goes to zero as the energy of the system goes to zero, everything as being held fixed. If you don't understand this, you need to go through the derivation of the recurrence time, ask questions, and stop wasting everyone's time with this silliness. Yes, e^e^s is a typical estimate for the recurrence time, where S is the microcanonical entropy at the specified energy; in general the result obviously depends on details of the particular system. The other statements you write were never uttered by me, and just indicate how confused you are.


    Now, as I said before, this recurrence argument has killed your scenario unless you can come up with some counterargument, which seems unlikely given that you just keep trying to confuse everyone. Your proposal has been killed twice now, and I am afraid that's all the lives it has.

    I pointed you to the original source for Dirac quantization which lays out the construction of the Hilbert space, and also gave you an explicit reference where the word "physical Hilbert space" is used (of course just summarizing what is in Dirac). What else do you want? How much hand-holding do you need? I find it bizarre that keep on citing Shankar, who is obviously not talking about gauge theories here.

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  9. Physics of recurrences is this. BHs larger than AdS radius R are dominant phase of thermal ensemble. When BH is smaller than AdS radius, thermal gas is the dominant phase. Classical Poincare recurrence time is exp S (exp(exp S) is quantum recurrence time).

    If all energy is in one BH with mass M at time t and M is taken small (all else fixed), BH will evaporate because it is not dominant phase, making thermal gas of entropy S. S is small if M was small. Then, all states recur in time t = R exp S. This includes BH.

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  10. Tim,

    I think you might as well spell out the catastrophic error that you think Physphill and BHG are committing, about recurrence times. I don't see the problem, and it seems that they don't either.

    Carl

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  11. Time maybe doesn't really go to zero, depends on how recurrence is defined. Maybe better to say it goes to some characteristic time, like inverse gap between ground state and first excited state. For AdS that would be AdS radius R.

    Arun,

    yes, quantum version of recurrence theorem relies on unitarity. This discussion is about whether Tim's idea is consistent with AdS/CFT. AdS/CFT says quantum gravity in AdS = unitary evolution in CFT. Unitary evolution in CFT means quantum recurrences. Quantum recurrences are not compatible with Tim's idea. Therefore, Tim's idea is not compatible with AdS/CFT. What is circular?

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  12. BHG & Physphil & Carl

    OK, but I am almost embarrassed to do this. You all claim—taking a result of Poincaré for classical mechanics and completely mindlessly plugging in a value of S for the black hole, that the recurrence time will be e^(e^S). And I asked specifically whether this is he same S in the Bekenstein formula. You seem to think it is. Well, let's look at some simple facts.

    Start with one black hole in Minkowski. Let it evaporate. What is the recurrence time? Well, it will obviously never recur. Ever. The Hawking radiation goes out and never comes back. Period.

    Ok, now in AdS. The radiation goes out and ...? What? If you put absorbing boundary conditions at the boundary....it will never recur. So to even have a chance, you need reflecting boundary conditions. But what is the physics of that? What is making things reflect?

    Now suppose I even grant you that. Still, the radiation must get to the boundary and back many, many, many, many times. Which means that the recurrence time is a function of the radius. But you formula does not mention the radius at all.

    Now: let's take the recurrence time for a given radius alpha and increase the radius. the recurrence time goes up. so by your formula, the entropy goes up. So by Bekenstein the horizon area goes up. But of course the horizon area goes not go up.

    You have taken a formula from classical theory and just thrown some numbers into it from a completely different context, and derived nonsense.

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  13. Also, systems with recurrence times don't obey the second law of thermodynamics (on timescales of the recurrence time). Never bet against the second law of thermodynamics :)

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  14. Also, a conceptual question, thanks in advance to whomever sets me straight - how do I define the S-matrix in a system that Poincare-recurs?

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  15. BHG and physphil,

    So lets recap a couple of claims you to made, and made, and made, even having been warned to stop and think.

    BHG: "As physphil and I have been patiently explaining to you, the recurrence time goes to zero as the energy of the system goes to zero, everything as being held fixed. If you don't understand this, you need to go through the derivation of the recurrence time, ask questions, and stop wasting everyone's time with this silliness."

    physphil: "We are discussing black holes in AdS. For a black hole in AdS, the recurrence time goes to zero as the mass goes to zero (all else fixed). That invalidates your entire argument.

    Either you do not understand this basic fact or you are throwing dust as usual."

    OK gents, let's examine these claim from both a mathematical and a physical point of view.

    Mathematically, what is the limit of Re^(e^S) as S —> 0? Well, it sure isn't 0, as both of you so confidently assert! Of course it doesn't go to zero. How could it?

    Let's think about this physically. Some Hawking radiation is released from an event horizon. How long must the recurrence time be? Well, the light must get out to the boundary and back., probably many many times How long is each of those trips? Well, that raises the question of what the relevant t even is. But no matter how that is answered, the recurrence time cannot be less than that. So the idea that one can drive the recurrence time below that makes no physical sense.

    In short, both of you signed on to saying that a claim that is both mathematically and physically completely nonsensical is not merely true, but anyone who disputes it must be confused. This is revelatory of what absence of both mathematical rigor and plain physical understanding you both have. You grab some formula and insist on it despite all mathematical and physical principle.

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  16. bhg,

    I do indeed largely agree on what you write. Maybe it would have been better to start that way. As you say,

    "it appears that you need some sort of nonlocality or "new physics" at the horizon scale to get around this conclusion"

    What I was trying to get across earlier is that it doesn't make sense to use the argument that the physics in asymptotic AdS and Minkowski is locally the same to justify carrying over non-local effects which, as you note, are necessary to keep your scenario consistent.

    "locality etc. has never been tested in the situation of interest"

    If by "situation of interest" you are referring to curvature regimes, it has been tested in the sense that the curvature at the horizon could be arbitrarily small. If "situation of interest" means nearby the horizon, you are already assuming non-locality by stating that the local information in the curvature isn't sufficient.

    Having said that, let me be clear that I have no particular problem with the approach in general. It's all well and fine by me that you do a calculation in AdS and hope it tells you something about asymptotic Minkowski (or de Sitter). I merely think that the locality-based argument for why it's plausible the AdS results should apply in asympt Minkowski doesn't make sense.

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  17. Tim,

    (quantum) recurrence time is not exactly e^(e^S). It scales that way with S, but prefactor depends on details and definitions. When S gets small the recurrence time gets small. When S goes to zero recurrence time might be zero or might be characteristic time of system (inverse gap), depending on precise definition. These are all trivialities.

    Also, it does not matter what the recurrence time is to invalidate your idea, as long as it is not infinite.

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  18. Tim,

    Everything you write is wrong from start to finish. First, I specifically said that the recurrence time is typically set by the microcanonical entropy of the system at the given energy. For a small black hole in AdS that is obviously not the BH entropy, but rather the entropy of a thermal gas at that energy, so that renders almost all of your post completely irrelevant right off the bat. Physphil already explained this to you, by the way.

    Next, I see you still haven't grasped that standard AdS boundary conditions cause light rays to reflect. Oh dear.

    Finally, you still don't get that the recurrence time goes to zero as the energy goes to zero. First, you can prove this in two lines just assuming a finite gap in energy between the ground state and first excited state, which is of course true for the CFTs under considerations. Your counterargument, must therefore have an obvious flaw, and indeed it does. As the energy goes to zero the states in AdS consist of a few low energy quanta delocalized throughout the space, and so there is no need for signals to bounce off the boundary. Any state involving a localized black hole has an energy above some threshold, simply due to the fact that localization is space requires superimposing eigenstates over a significant range of energies. Also, I said that e^e^S is a "typical estimate". It should have been obvious that you shouldn't take it literally when S->0, but even if you do you get an O(1) number, which is not incorrect at the level of this discussion.

    In any case, all this is totally irrelevant. What matters is that the recurrence time is finite, since that is enough to drive a stake through your argument. You just continue to ignore that inconvenient fact and instead turn the fog machine on to 11.

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  19. Bee,

    Good -- I don't think we have any major disagreements then, even if we may differ in what approach we find most promising to pursue. When I say that locality has never been tested in the regime of interest, i.e. inside a black hole, I totally agree that there is good reason to expect it to be valid there and this is what makes Hawking's computation so hard to mess with. Still, let us be honest and admit that black holes are exotic objects and keep an open mind, given the lack of any direct evidence. Given that AdS is a nonperturbative theory of QG that is known (by explicit computation, not assumption) to reproduce local Minkowski space physics in the regime where it has been directly tested, to me it seems of clear interest to ask what it says about how black holes evaporate. If AdS/CFT manages to produce local physics everywhere except inside black holes, that would be quite a neat trick.

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  20. BHG and physphil

    Well, you are both willing to go down in flames. Fine by me.

    Just to remind you, since you don't seem to keep your mind on the actual problem before us, the question is about the recurrence time of a black hole that forms and evaporates, not for a "thermal gas at that entropy". You guys are so far from actually doing physics that you somehow think that it is just fine to replace an evaporating black hole with a thermal gas because...well...because you have been caught out talking complete nonsense and want to double down on it. Now I know why you insist on posting under pseudonyms. Neither of you are vaguely serious.

    Yes, I can see how the recurrence time of a thermal gas could go to zero as the entropy goes to zero, i.e. as it goes to the vacuum state which, since it is stationary, has a zero recurrence time. But that wasn't the question. The question was the recurrence time for a black hole which has to evaporate and then, somehow, has to re-form to recur. Or maybe I have to explain that the recurrence time is the time it takes for a given state to actually recur? That both of you would have the chutzpah to say that that goes to zero can only be explained by the fact that no one can figure out who you really are.

    The question before us was the recurrence time of a specific state. Not of any microcanonical ensemble, or indeed any kind of ensemble. Of a specific state that has to recur. And I gave a clear and unanswerable argument that the recurrence time 1) does not go to zero and 2) is a function of the AdS radius. Further, I specifically asked you whether the entropy you were taking about was the BH entropy. I specifically asked that and you did not deny it. Only now, when you see what a wooden-headed answer you gave do you sudden decide to deny it.

    Basically, you are taking some equations derived for a classical system in a box and, without a moment of thought or physical understanding, assuming you can somehow apply them the a black hole in AdS. And all you have proved is that you can't.

    I gave an argument about the recurrence time for an evaporating black hole. Your response to that argument was to replace the actual system at issue with a completely different system. Well I guess by that method you can prove anything you want. Let's see if ether of you can actually address the question at hand. Explain how the black hole, which was formed by injection of high-energy particles carefully aimed toward the same space-time point and then turned by the evaporation into a thermal bath largely of photons, manages to recur in zero time. This should be good.

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  21. physphil,

    I'll start with the fact that AdS/CFT is not proven, therefore one must be able to rule out on independent grounds any phenomena in AdS that cannot be described by the CFT. An argument by quantum recurrence is not a good argument.


    To one circularity: Read carefully section 3.3 of David Wallace's paper. No reference to CFT (e.g., " another (York 1986) is just to impose reflecting boundary conditions on the black hole at a radius less than 1.5 × the Schwarzschild radius")

    https://dornsife.usc.edu/assets/sites/1045/docs/informationloss.pdf

    The argument is that a discrete energy spectrum and unitarity apply, which is what enables one to write equation 5. The argument following Equation 5 is simply a generalization of the idea that a Fourier series can give periodic functions only, one needs a Fourier transform to get non-periodicity. In this case, equation 5 says there must be quasi-periodicity, and hence the correlation function in equation 5 cannot decay exponentially forever. Therefore we must choose between black hole statistical mechanics and QFT. ("So if black hole statistical mechanics is true....All this is of course in flat contradiction with the QFT prediction of permanent exponential decay.")

    Recurrence is a result of an assumption of unitarity and discrete spectrum, and points to the limits of what a system in a box can describe about the world. Note that everything recurs, not just black holes, but everything from the radioactive decay and reconstitution of a uranium atom to your birth and death.

    The same is true of finite N in the CFT (N which everyone conveniently elides over).
    "Finite N and the failure of bulk locality: Black holes in AdS/CFT" https://arxiv.org/pdf/1405.6394.pdf. I assume going to infinite N will cure the non-exponential decay of the correlation function in David Wallace's argument, the non-locality in the just-mentioned paper, and send the quantum recurrence time for anything to infinity. E.g., if there are ~N states of energy E, and a system must visit each one of them before recurrence can occur, then the recurrence time goes to infinity.

    Even if my assumption is wrong, we need to be suspicious of any phenomenon that relies on the recurrence.










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  22. BHG,
    you wrote:

    "Your counterargument, must therefore have an obvious flaw, and indeed it does. As the energy goes to zero the states in AdS consist of a few low energy quanta delocalized throughout the space, and so there is no need for signals to bounce off the boundary. Any state involving a localized black hole has an energy above some threshold, simply due to the fact that localization is space requires superimposing eigenstates over a significant range of energies."

    If this is what you had in mind all along, then I think it would have been more helpful to say, not that the recurrence time *of black holes in AdS* goes to zero as their energy goes to zero (as you and Physphill both did), but rather that the recurrence time *of systems in general in AdS* goes to zero. It's no good taking Tim to task for criticizing a assertion you made, but now claim you didn't actually mean to make. (And notice that it was clear all along that Tim was talking about recurrence times *for black holes*, and in addition he asked you and Physphill to confirm that you were talking about *the black hole entropy (Beckenstein's)*, not some other entropy.)

    Physphill did mention at some point that the recurrence time "maybe" doesn't go to exactly zero, but rather to some fixed characteristic time, which he said would be related to R in AdS. But Tim's argument from physical grounds shows that this can't be right either, by your lights: if Physphill was talking about systems in general (and not, as context made super-clear, black holes), then you disagree with him, because you now say that for systems in general the recurrence time does go to zero as energy (entropy) goes to zero. Moreover, Physphill can't be right even if he was talking about black holes. The minimum recurrence time should indeed depend on R, but it should also depend on the minimum S required to have a black hole in the first place (now that you're telling us that there is indeed a minimum entropy for black holes in AdS).

    I understand that, in the pissing contest that this discussion has become, one doesn't want to concede anything to the opponent, ever. (And this applies to all sides.) But if progress is to ever be made, it will come a lot faster if everyone is willing to occasionally say "Oh, right, sorry, I didn't mean to say exactly that, ..." or "OK, you are right about X, but I still want to maintain that Y ..."

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  23. Arun,

    before, you said argument was circular. Now, you say "I'll start with the fact that AdS/CFT is not proven".

    OK, then you are considering a different argument than rest of us. We are discussing whether AdS/CFT is compatible with Tim's idea. We can take AdS/CFT as given, then try to derive a consequence from it that is incompatible with Tim. If we succeed we have proven AdS/CFT is not compatible with Tim. We did succeed. Obviously this does not prove AdS/CFT is right and Tim is wrong.

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  24. Tim,

    "Just to remind you, since you don't seem to keep your mind on the actual problem before us, the question is about the recurrence time of a black hole that forms and evaporates, not for a "thermal gas at that entropy". You guys are so far from actually doing physics that you somehow think that it is just fine to replace an evaporating black hole with a thermal gas because...well...because you have been caught out talking complete nonsense and want to double down on it. Now I know why you insist on posting under pseudonyms. Neither of you are vaguely serious."

    This shows 1) you do not understand thermodynamics in AdS, 2) you have not read our posts explaining it.

    Also, discussion about what time is, is more throwing dust. Any time except infinity is incompatible with you ("drives a stake through your argument", that is 100% apt). Will you keep ignoring that?

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  25. The circularity is that you can't assume unitarity and discrete spectrum to obtain quantum recurrence, and then point to a postulated quantum recurrence as proof that unitarity can't be violated.

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  26. Tim,

    It's all very simple, and I am not sure why you are getting yourself so confused. If the system has energy E (expectation value) let S(E) be the microcanonical entropy for that given energy. Every state of energy E will recur in some finite time, and for S>>1 a reasonable estimate for the time is e^e^S. So if the state in question is a small black hole, the recurrence time is set by the entropy of the thermal gas at that same energy, since the latter is the most entropic configuration and hence tells us the microcanonical entropy at that energy. So we are indeed talking about the recurrence time for a small black hole, but what sets the timescale for that is the entropy of the thermal gas. It's this point that you are apparently missing. Also, you obviously can't even talk about black holes once their mass get to be about the Planck mass or lower, so the minimal recurrence time for a black hole is some O(1) number (measured in units of AdS time) whose value depends on various details and definitions. The recurrence time indeed goes to zero as the energy of the system goes to zero, but the relevant states in the extreme low energy tail are not black holes but rather a few delocalized quanta in AdS. So it all fits together perfectly.

    Now that you (I hope) understand these basics, do you see why your proposal is dead?

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  27. bhg,

    This is getting more ridiculous by the post. First, I mentioned how insanely long any recurrence time would be, if the state recurs at all. So long that there in no conceivable way to rely on claims about what would happen over such a period of time. Any calculations ever made about the AdS gravity theory would not be reliable: too many idealizations and approximations are made. Then, in order to get around this objection, physphil and you state that the recurrence time for a black hole could be made arbitrarily small by making the black hole arbitrarily small. That claim was so bizarre and obviously wrong that I could not believe either of you would make it, but you made it and stuck with it. Instead of just pointing out how incorrect it was, I tried to get both you and physphil to see for yourselves, but apparently you are so blinded by some sort of misunderstandings that you can't follow out a three step proof. And now you are doubling and tripling down on it. As I said, it's your funeral. Since I apparently need to walk you through this step-by-step, I will.

    Let's start with the basics, shall we? Our question was this: what is the recurrence time for a black hole in AdS? My original observation is that it is so astronomically long, if it exists at all, that is cannot possibly be of any significance for our problem. In response, you are physphil asserted that the recurrence time can be made as small as one likes—limiting to zero time!—by making the black hole sufficiently small. Start with a black hole such that the region exterior to the event horizon is a vacuum, or nearly so. The black hole will evaporate via the release of Hawking radiation—largely photons—over a rather extended period of time. They will propagate out to the boundary and be reflected. So to begin with, no recurrence can possibly occur in less time that the return time for the light, which can be made arbitrarily long by increasing the radius of the AdS. This observation holds independently of the mass of the black hole. So much for the claim that the recurrence time can be made arbitrarily small, tending to zero. That is flat false. Period.

    Now let's go a bit further. Note that in order to get our black hole reconstituted, we have to not only get individual photons back to the same place, we have to get *all* of the photos back to the same place *at the same time*. Now since the Hawking radiation has been emitted essentially continuously over a period of time, if the photons all take the same time to reflect off the boundary and return, then it certainly it will take many, many, man, many, refections to get them all back together. In fact, one might rightly wonder whether the black hole will *ever* recur. It hard to see that it ever will.

    What about your doubly exponential recurrence time? It is absolutely completely totally worthless. We have already seen that it cannot possibly be right. So what's wrong? Simple: what you have got your hands on (Googling?) is an *average* recurrence time for a state with a given energy. But of all the states with a given energy, the state in which it all is locked up in a single black hole is extremely atypical. The *average* recurrence time has nothing to do with the recurrence of such an atypical state.That's why you were making the irrelevant comments about gasses.

    In fact, I see no reason at all to suppose that the black hole state will ever recur. Does that contradict AdS/CFT? All the worse for AdS/CFT. In fact, you have already admitted that the calculated results that supposedly confirm AdS/CFT are perturbations off the vacuum, and that black holes are not perturbations off the vacuum. If the recurrence times in the CFT all follow the doubly exponential rule without exception, then we have just refuted AdS/CFT. And if individual states in the CFT do not recur, then the argument you have been trying to make evaporates.

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  28. Tim,

    I have no idea why you are discussing recurrence times to begin with (I side with Arun - the argument presumes unitarity, so you can't possibly use it to prove unitarity). But I don't think you have to get each individual photon back to the same place to get the same state because the photons are interchangeable.

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  29. Sabine,

    I posited that the region exterior to the black hole is a vacuum. If so, you need to get every last photon back to reconstitute a black hole with the same mass.

    I don't know why we are talking about recurrence times either: ask bhg and physphil. But beside introducing the topic, they have gone on to make absurd claims about it.

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  30. I posted reply to Tim, but it never appeared. Anyway bhg has said what I said.

    Arun, Tim says that his idea is compatible with AdS/CFT. CFT is unitary so by AdS/CFT both sides must have recurrences. This is not very complicated and there is nothing circular. Maybe it is confusing because Tim's position is not rational.

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  31. Tim,

    "But of all the states with a given energy, the state in which it all is locked up in a single black hole is extremely atypical. The *average* recurrence time has nothing to do with the recurrence of such an atypical state.That's why you were making the irrelevant comments about gasses."

    That is wrong. It shows that you do not understand the meaning of entropy, or recurrences. Anyway, it is not relevant. What is relevant is that the time is not infinite.

    "In fact, I see no reason at all to suppose that the black hole state will ever recur. Does that contradict AdS/CFT? All the worse for AdS/CFT. "

    Do you now admit that your proposal is not compatible with AdS/CFT?

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  32. physphil,

    No I do not admit that. And I am not going to respond to you again unless a) you real who you are or b) you admit that everything you have posted about recurrence times is idiotic.

    I have explained in detain, step by step what what you have claimed about the recurrence time of a black hole is 100% completely and totally wrong. Your claim that the recurrence time, in particular, got to zero as the black whole mass goes to zero is some completely incompetent that I as surprised that you are willing to show your pseudonymous face around here again, and that you would accuse be on not understanding recurrence time when I have demonstrated both that what you have claimed is impossible and why the tubers you are throwing around a irrelevant is beyond toleration. I simply will not engage with you again until you admit that. You can whine all you like.

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  33. Well, that needed a spell check! I hit the post button on that way too fast, but that's what this sort of provocation will do.

    Corrected:

    physphil,

    No I do not admit that. And I am not going to respond to you again unless a) you reveal who you are or b) you admit that everything you have posted about recurrence times is idiotic.

    I have explained in detail, step by step, that what you have claimed about the recurrence time of a black hole is 100% completely and totally wrong. Your claim that the recurrence time goes to zero as the black hole mass goes to zero is so incompetent that I am surprised that you are willing to show your pseudonymous face around here again, and that you would accuse me of not understanding recurrence times when I have demonstrated both that what you have claimed is impossible and why the numbers you are throwing around are irrelevant is beyond toleration. I simply will not engage with you again until you admit that. You can whine all you like.

    Once more, I do not concede anything at all about my solution, but I see no point in engaging with you if you refuse to fess up to either who you are or the plain mistakes you have made.

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  34. Tim,

    "And I am not going to respond to you again unless a) you reveal who you are"

    You said that before.

    "I have explained in detail, step by step, that what you have claimed about the recurrence time of a black hole is 100% completely and totally wrong. Your claim that the recurrence time goes to zero as the black hole mass goes to zero is so incompetent that I am surprised that you are willing to show your pseudonymous face around here again, and that you would accuse me of not understanding recurrence times when I have demonstrated both that what you have claimed is impossible and why the numbers you are throwing around are irrelevant is beyond toleration. I simply will not engage with you again until you admit that. You can whine all you like."

    Everything I wrote is based on mathematics. It is not very difficult to prove theorems about quantum recurrence times, and there is a large literature. Quantum recurrence times are just epsilon-almost periods of almost periodic functions. You can read them in Besicovitch from 90 years ago.

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  35. Arun and Bee,

    If you have looked at the 10^3 posts on this topic, you will see that the issue is not unitary (everyone agrees on that) but rather whether the information about the initial pure state is fully accessible at late times in the external AdS region, or is it instead entangled with some disconnected region. Tim is arguing for the latter. The recurrence argument serves as a very useful nonsense (or, insert less polite word here) detector. In AdS/CFT there are recurrences in finite time (that is a theorem, assuming only some minimal energy spacing), so if the information about the wavefunction was accessible to the external region before the black hole formed, the same will be true an infinite number of times in the future. The naive Penrose diagram that Tim assumes certainly breaks down on long timescales. So any claim that the Penrose diagram is accurate for all times is incompatible with an AdS/CFT description. Tim's counterargument is ... uh, well, ... I'm not sure. Something along the lines of "the recurrence time is very long so let's just ignore it".

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  36. Tim,

    Most of what you write concerns claims that I never made; not sure where you got these ideas from. I suggest we return to the actual argument. Assuming only a minimal energy spacing in the CFT (which is a pretty weak assumption,but I am happy to label it as such) we have the following rigorous results

    1) Every state of finite will recur in finite time

    2) The recurrence time goes to zero as -> 0

    A number of claims you make disagree with these theorems, so are false.


    You talk of a small black hole at the center of AdS, but as I have repeatedly explained such a state cannot have arbitrarily low energy both because the whole notion of a black hole is only sensible for M > M_Planck, and because it takes energy M >> 1/L_AdS to localize a state in AdS. Now, apart from the rigorous result (2) noted above, there are no universal results on the precise recurrence time of a given state. The typical estimate is e^e^S, and there is no reason to doubt this estimate for a black hole state in AdS, for the reasons I noted, and where one has to be aware (as I have repeatedly stated) that S refers to the microcanonical entropy of the system at energy E (which has nothing to do with the area law formula for a small black hole). It might be somewhat longer or shorter; it's hard to say in general, but we know for sure that it is finite due to theorem (1), which is the main point. The theorem (2) is also in perfect accord with AdS physics, since the E->0 states are those of a few low energy quanta in AdS, and it's clear that the recurrence time for such states goes to zero in the limit. So it all fits together perfectly, as is well known.


    Your position seems to be that since the recurrence time is long we can ignore it based on some "approximations" breaking down over such a long period. No, the CFT is perfectly well defined for all times, so this is not a good argument. You should try to come to terms with the fact that the Penrose diagram necessarily breaks down over long time periods, and the entanglement with the would-be disconnected region goes to zero an infinite number of times in the future. You might find this more satisfying and productive than composing lengthy messages where you invent positions to assign to your debate foes and then argue against them, complete with insults and childish name calling.

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  37. bhg,

    You are not defining your terms. Indeed you are not completing your sentences. Let's do these one by one. You claim:

    "1) Every state of finite will recur in finite time"

    First question: of finite what? Of finite energy, restricting the claim to energy eigenstates? Or of finite expected energy, extending it to all states? And what to you mean by "recur"? I assume you do not mean literally that the state will recur. So you have a definite state space with a metric. Can you please explain, on the AdS side, exactly what this is? Can you also explain what you mean by the state "recurring" given that the actual state will not literally recur.

    Now about your assumption of a "minimal energy spacing in the CFT". Do you make this assumption for the CFT that is the limit as N goes to infinity? Why? That is not very plausible on its face. What if it is exactly that CFT that is dual to the gravity theory in AdS?

    Next: The reason we got into all this was that the recurrence time—which, once more, you failed to mention at all in the first 10^3 posts but suddenly seized on as the key to everything *after reading David Wallace's paper*—for a black hole would have to be so long as to be irrelevant to rtes question before us. It is also a much longer time period than that presumed by the thought experiments you have proposed. Like the ones about somehow doing quantum tomography on an infinite ensemble of identically prepared black hole states. (By the way: do you have any proof that that it is even possible, granting all the impossibilities? Like can you prove that the observables associated with the regions far from the black hole are dense in the space of operators?) And in response to that observation about the recurrence times, physphil decided that he could make the recurrence time for a black hole arbitrarily small by making the black hole arbitrarily small. Now if I understand your present position, you do not think the is possible: a black hole cannot be made arbitrarily small because below a certain energy the geometry is not well-enough defined to even say there is a black hole state. OK, if that's true why didn't you take a moment to correct physphil? Why is it my job to point out his errors—just because he's "on your side" it doesn't matter to you what nonsense he posts? Anyway, you can first of all agree (or not) that what he said about making the recurrence time of a black hole as small as you like is indeed nonsense. And you can also bear in mind that talk of black holes below a certain energy is nonsense.

    Now if I am tracking all this, your present position is that at low enough energies the entire conceptual apparatus that supports the notion of a black hole breaks down. Perhaps you can say some more about this. Since the calculations that have actually been done, as I understand it, are perturbations off the vacuum, what grounds to you have to think that the vacuum state even has a recognizable geometry?

    And finally, about your "nonsense detector". It sounds to me that you would have endorsed the recurrence objection to Boltzmann. That is, you would have rejected Boltzmann's claim to have explained the Second Law because of the recurrence objection. Let's take that as an analog to objecting to my solution to the information loss problem on the basis of recurrence. Now if that analogy is good, you are on the wrong side here: Boltzmann did explain the the Second Law FAPP. So I take it you object to the analogy. What is your objection?

    That is not all the questions I have about your claims. But let's start with these.

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  38. Tim,

    An html issue caused the formatting to get lost. Let [E] denote "expectation value of E". Then the theorems are

    1) Every state of finite [E] will recur in finite time

    2) The recurrence time goes to zero as [E]-> 0


    The definition of recurrence is the following. Given a positive delta, the state \psi(t) is said to have "recurred" to \psi(0) if |\psi(t)-\psi(0)| < delta, where |...| is the standard Hilbert space norm. If the theory has a spectrum with some minimal energy spacing, then theorems (1) and (2) hold. More precisely for (2: for any positive delta, there exists an epsilon such that if \psi obeys [E] < \epsilon, then |\psi(t)-\psi(0)|<\delta for all finite t. This is elementary to show, and implies that the recurrence time is zero for sufficiently small \epsilon, for any choice of delta.


    The AdS theory is, by definition, equivalent to the CFT theory in terms of its spectrum and inner products, so the above holds in AdS.


    The CFT is defined at large but finite N. Recall that Newton's constant in the bulk is proportional to 1/N, so we don't want to actually set N=\infinity as that would turn off gravity. When people talk about the large N limit what they mean is that one computes quantities in a 1/N expansion, just like in quantum gravity you would compute in an expansion in powers of Newton's constant. The claim then, is that the spectrum is discrete for any finite N corresponding in the bulk to some finite value of Newton's constant.


    I have been thinking about recurrence related issues for well over a decade. Wallace's argument is old hat, but I brought up his paper because he is a philosopher, and so I thought you might be more receptive to him, since he is presumably not an ignorant philistine like us physicists.


    I don't actually recall physphil saying that the recurrence time for a black hole could be made arbitrarily short, but I am sure I never said any such thing, and I was careful to to speak of black holes of mass, say 10 M_pl. I definitely stand by everything I have written, but am not going to vouch for everything others have said, although I will say that physphil's comments seem on target in general. Anyway, I think everyone would agree that it's senseless to talk of black hole of mass M_pl or below. Below this mass the compton wavelength is larger than the horizon radius, so quantum uncertainty blurs out any notion of causal structure at this scale. There are many tests of AdS/CFT beyond perturbation theory, and in particular excellent evidence that the CFT reproduces the semicalssical bulk physics of black holes.


    No, I wouldn't object to Boltzmann's explanation of the microcopic basis of the 2nd law of thermo. What I would object to is the use of some fluid dynamical description of an ideal gas over arbitrarily long time scales. At the longest time scales it is important that the gas is composed of discrete entities and the total entropy is finite and the spectrum is discrete. In the fluid approximation the spectrum is continuous and the recurrence time is infinite. Similarly, in AdS/CFT what makes the recurrence time finite is the finiteness of N. At finite N you see the "graininess" of spacetime if you wait long enough, just like in the gas case. As I see it, you are effectively defending the validity of the fluid approximation in a regime where it must break down.


    Now, I have said right from the beginning that the recurrence argument is quite weak in that it only establishes information preservation over a much longer timescale than the evaporation time. Nonetheless, it shows clearly that the Penrose diagram must break down over *some* time scale, and once you go down this path you naturally start to realize that it can break down at earlier times as well.

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  39. bhg, Tim,

    In the hope of advancing the case, let me try to summarize the recurrence time issue.

    For all I can tell bhg is saying that if you have a CFT dual (at finite N) then any state must be able to recur at finite time. Meaning that if you start with a state that doesn't have information parked in a disconnected part of spacetime, you must be able to go back to such a state. He concludes that Tim's scenario isn't compatible with this. I agree. Either you reconnect the disconnected regions or you agree the scenario has no CFT dual.

    Tim, in response, says that the reference to recurrence is irrelevant because the time is much longer than the evaporation time of black holes. It follows a long exchange about the limit m \to 0 which remains inconclusive (or in any case, I seem to be missing some information here). Everyone accuses everyone else of being wrong about everything. Let us just assume for a moment we are dealing with a black hole for which the recurrence time is much longer than the evaporation time, then it seems Tim would have to argue that his scenario is compatible with the AdS/CFT time-evolution on evaporation-time-scales but no longer on recurrence-time-scales.

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  40. Sabine,

    Correct. And I have not given any time—nor do I see any point in it—in even thinking about what might happen over such hyper-astronomical time scales. physphill tried to argue that the time scales could be brought down to whatever you liked for a black hole recurrence, and I take it that you, I and bhg all agree that he is wrong about that. Getting back to near the original state (and of course we only mean near) over these unimaginable time scales is not what anyone ever had in mind by solving the Information Loss problem. They meant: shortly after the black hole evaporates, is the information about what fell in contained in the region connected to the AdS boundary. I say "no". bhg says "yes". What happens over unimaginably longer time scales is neither here nor there.

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  41. Sabine

    Sorry, I missed the "I seem to be missing information here" bit. The recurrence time for the formation of the black hole, starting from a state that is vacuum outside the event horizon, is trivially bounded below by the time it takes for light to reflect off the boundary are return, and actually (due to the long evaporation time) to many, many orders of magnitude more than that. So it can't go to zero in the limit *of smaller and smaller black holes*. What the limit is for states that don't contain any black holes is neither here nor there. Why is this not sufficient information?

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  42. Tim,

    I understand what you say but I can't follow bhg & physphill's response. They are right of course that the limit m -> 0 stops making sense once you are below the Planck mass. In that case also the whole penrose diagram doesn't make sense, so I don't know why even talk about it. On the other hand, I don't think your image is the same as the ones they use. You are thinking of forming a black hole surrounded by vacuum. I believe they see the black hole as a fluctuation in a thermal gas. So I'm not even sure you want to 'recur' the same state to begin with. Or in any case, maybe I missed something here. I am not very familiar with thermodynamics in AdS.

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  43. I get confused by statements like this (re: AdS/CFT)

    "In gravity, the phase transition is on S3. Normally it is not possible to have a phase
    transition in finite volume – with a finite number of degrees of freedom, the free energy is an analytic function of β, and we get sharp phase transitions only in the thermo-dynamic limit. However this is possible in gravity because of the large-N limit"

    (from 16.2 http://www.hartmanhep.net/topics2015/16-hawkingpage.pdf via http://www.hartmanhep.net/topics2015/ )

    So what effects are artifacts of being in a box, of being at finite N, etc., not clear to me.

    Anyway, Note 14 at http://www.hartmanhep.net/topics2015/ has a textbook-precise statement of AdS/CFT.



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  44. The invocation of quantum recurrence does settle one thing: the uniqueness of the CFT ground state is irrelevant to the issue of blackhole evaporation.

    I had written some days ago:

    I am told AdS is gravity in a box. How do I withdraw energy from gravity in a box while remaining consistent with gravity? If the AdS has a black hole and hence is not in a ground state, how can it relax to the ground state? It never does, not if it is in a box. From this point of view the uniqueness of the CFT ground state is irrelevant. The only way the AdS can relax to the ground state is if energy escapes past the boundary at infinity - which it never does.

    The picture of an ever-diluting gas of evaporated Hawking photons "after" the black hole evaporates, bringing the AdS bulk and hence the CFT arbitrarily close to the ground state is not consistent with quantum recurrence. The idea of such a state is a intuition smuggled in from asympotically-Minkowski-space intuitions. (Yes, perhaps you can recover this picture in the limit of a very large AdS space, or conversely, in the limit of an infinite quantum recurrence time; but then the argument from quantum recurrence should not be invoked.)



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  45. Couldn't one (at least as a thought experiment) reduce the recurrence time for a micro-blackhole by (artificially) creating it inside a box with reflective inner surfaces? I had thought this was what BHG and pp had in mind in saying that the recurrence time could be made realistically small.

    However, the idea of blackholes continuously forming, evaporating, and thus bleeding information from a universe into sequestered remnants (and recurring and bleeding more information) has its attractions. There might be a good science-fiction story with that premise. (I write this sincerely and as a big fan of good s-f.) (S-f has its flaws but so does most, probably all, imaginative writing.)

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  46. Tim,


    Yes, the recurrence time is long, but the evaporation time for a solar mass black hole is already vastly, vastly, longer than the age of the universe, so we're talking about points of principle here, not of actual observation. The CFT makes perfect mathematical sense for all times, so we can analyze it with confidence.


    But more important is that as soon as you realize that the Penrose diagram must break down on the recurrence timescale (I gather that you don't really dispute this) it sets you down a path to realizing that it will break down at much earlier timescales as well. The common feature is the discreteness of the energy spectrum.

    I return to the analogy of a fluid description of a gas in a box. The die hard fluid dynamicist, if confronted with the existences of recurrences, would be forced to admit that the actual theory has a discrete spectrum. And as soon as you realize that, it becomes clear that this discreteness will manifest itself on time scales vastly shorter than the recurrence timescales, namely through correlation functions. Similarly for the black hole case. The discreteness has implications for black holes at the time scale of the inverse temperature, and so the Penrose diagram will break down on these time scales as well. This was all nicely explained in Maldacena's paper that brought up the recurrence issue.

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  47. jimV,

    Yes, if you put a small black hole in a small reflecting cavity I would expect the recurrence time to be "small". However, it would be hard to argue for this via AdS/CFT, since it's not clear how to implement a reflecting cavity in the CFT description. This would involve various assumptions, which I prefer to avoid.

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  48. bhg,

    "Yes, the recurrence time is long...." Thank you. That is the point that I was making from the beginning. In fact, the recurrence time for a solar sized black hole is so mind-boggling long *compared to the evaporation time* that there is no conceivable way that any considerations about recurrence can have any bearing whatever on the observations in my paper. That has been my point all along, as you can verify by going back to my original reaction. And nothing you or physphil have said is responsive to the point I made originally. So let me say it again, and we can bring this particular pointless deflection to an end.

    First, in a physically realistic scenario—asymptotically flat or dS—the recurrence time is not just long, there is no recurrence time at all. We agree about that, which was one point I was trying to get physphil to see on his own, so it would actually stick. If there is no recurrence time in a physically realistic situation, then appeal to recurrence in a physically unrealistic situation like AdS is not going to be any help for our question, which is about actual black holes, not imaginary ones.

    Second, even in an imaginary AdS situation, the recurrence time for a solar mass black hole is so absurdly, unfathomably much longer than the evaporation time that again appeal to the recurrence time, even if it provably exists at all, cannot have any bearing on our problem. That is why I could not take, and still cannot take, any appeal to recurrence as remotely relevant, and regard bringing up recurrence as a mark of being hopelessly confused. Let me state again, with complete clarity, why.

    Our problem was this: does the information about what originally fell in to form the black hole come out in the Hawking radiation or not. My contention from the beginning has been that it does not. Before we waste another second on this debate about recurrence, please in a clear and comprehensible way respond to this question: even if the black hole state will recur in some time period that is incomprehensibly longer than the evaporation time, what relevance could that have for the question before us, namely whether the information comes out in the Hawking radiation emitted during the evaporation? That was my original point, and it has been obscured or forgotten or deflected from in this exchange. Neither you nor physphil has even attempted to answer it as far as I can tell. Let's not go another step without a clear answer.

    What happened instead? Well, physphil tried to respond that the recurrence time for a black hole can be made as short as you like—limiting to zero!—by making the black hole sufficiently small. This claim was so manifestly absurd that I kept asking him, and you, whether you really meant to claim it. Neither of you recanted. I take it that at least you now acknowledge that the claim is absurd, and that no one competent would make it who it thinking clearly and not just grasping at straws.

    Con't

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  49. Now you have introduced yet another distraction from my point. You want to say that the recurrence time that you "calculate" isn't even the point: the point is that if there is a recurrence time, no matter how long, then the Penrose diagram a) must fail for such long periods of time and b) must (by some as yet unarticulated argument) fail even much earlier. But before entering in on this new obscure argument, let's ask: even if I grant you every last claim you make, *what in the world does this have to do with our question*? Answer: nothing. In no circumstance, will there be any recurrence until an unutterably longer time than the evaporation time. In no circumstances will this line of argument show the the Penrose diagram I advert to is unreliable over the evaporation time, which is all that matters. Even if that diagram in not reliable for time scales much much much much much much shorter than the recurrence time, it is still the case that the time scales are much, much, much, much, much, much longer than the evaporation time, which is the time scale of interest. We want to know what happens over the evaporation time: does the information come out in the Hawking radiation or not? I say not. Please restrict any arguments or comment to that question, not to that happens over hyper-astronomially longer periods.

    Finally, you are now on about the question of whether the Penrose diagram "breaks down" eventually, eventually meaning over the recurrence time or even some much shorter time. Again: I could not care less if it does. Nothing in my argument says anything one way or another about that question, and I won't waste any more of my time on it unless some direct bearing on our actual question can be established.

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  50. In a "physically realistic scenario" you can't measure if black hole evaporation is unitary, so why are you having this discussion to begin with? It's not a entirely rhetorical question.

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  51. Not to add to the distractions, but the lectures say that to have anything like semiclassical gravity in the bulk AdS with little impact from the stringy infinite tower of states, the CFT must be strongly coupled.

    What is the calculational meaning of "strongly coupled CFT"? I seem to miss the "strong coupling" in the discussions of CFT operator product expansions. Admittedly, I'm an easily confused person.

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  52. In light of Tim's last posts, I would like to raise again a question I raised earlier: If a state of an object in AdS recurs (within epsilon) after some enormous amount of time, is that because "the information" about that state was somehow carried along over time, encoded in the intervening states (most of which look like a thermal gas), and somehow the dynamics forces that information to make itself manifest again eventually? Or is it instead because, if you wait around long enough, every state (or something epsilon-close to it) is bound to occur, over and over? The latter reason, which I called the monkeys-on-typewriters scenario, obviously would not imply that the information had to escape from behind the event horizon.

    Looked at from the CFT side, I guess you'd want to say that since the evolution is deterministic, the reason is the former and not the latter (monkeys). But I'm not familiar enough with the recurrence theorems to be sure. BHG, which is it?

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  53. Arun,

    Maybe I misunderstand the question, but I suppose the coupling constant is >>1.

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  54. Tim,

    I think you are missing the point here. Go back to the ideal gas. Suppose the gas fills an infinite volume. Then the recurrence time is infinite, even though the physical issue of interest, the discrete nature of the constituents, is still present. To expose this, we put the gas in a finite box, and then the recurrence time is finite. From this we learn about the underlying discreteness, and we can use this information to make predictions about correlation functions, which will display deviations from the fluid approximation at earlier times.

    Same with the black hole: we put it in a box (AdS) to expose the discreteness. You are assuming that the naive spacetime picture is valid, and drawing the associated Penrose diagram. We have now proven that your assumptions are false, and the Penrose diagram breaks down. Your complaint about the long time scale is irrelevant as I keep telling you, because the CFT is valid for all time scales. We are talking about points of principle, so complaining that the time is "unutterably long" is just a dodge. So until you modify your proposal, it is ruled out by recurrence.


    To drive this home, we could follow up on jimV's suggestion, and place a small black hole (say M=10 M_Pl) inside a small reflecting cavity, (say two or three times the size of the horizon). Then the recurrence time would be a reasonable time scale. How would you explain this?

    The key point that gives rise to recurrence is the discrete spectrum, and this disallows your disconnected Cauchy surface scenario, if you follow the standard rules of QG. Namely, disconnected Cauchy surfaces imply a degeneracy of the spectrum, as I have explained again and again, so this is incompatible with the CFT, and hence ruled out (unless you modify the rules of QM).

    So the situation is quite clear: recurrence clearly exposes the discrete nature of the spectrum, and once this is established it rules out the disconnected surface scenario, and the only possibility left standing is that information comes out with the radiation. So far the only counterarguments you have presented are (not actual quotes here) "the recurrence time is very long so lets' ignore it", and "let's drastically modify the rules of QM to avoid a degenerate spectrum, since anyway QM has no rules so I can make them up as I please".

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  55. Carl3,

    In QM the state evolves unitarily, so the information about some initial state is always "there" at some later time. The point of contention is: if the information about a state at one time is contained in an AdS region, is that always true at later times, or is the AdS state entangled with some disconnected surface, rendering the full information inaccessible to an AdS observer. To make this quantitative we can consider the von Neumann entropy of the density matrix for the the AdS state. If S_vN is large, then some information is inaccessible. Now, recurrence tells us that if you wait long enough the state will come back arbitrarily close to its starting point. Hence if S_vN =0 at t=0, we know there is some later time when S_vN will be as close to zero as we want. At that time we can extract essentially all the information about the state by making measurements in AdS. This rules out Tim's scenario, because he assumes the standard Penrose diagram, and this implies that the information contained in the disconnected region is inaccessible forever. If he wants to save his proposal he needs to modify it to make it compatible with this fact. He will need the disconnected region to reconnect somehow, but once you start down this path the entire foundation of his proposal will begin to crumble. Eventually he will realize this.

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  56. Bee,

    Yes, strongly coupled likely means coupling constant(s) >> 1. But where is this manifest? It occurs only qualitatitively to my limited view, in that the CFT is somehow "confining" and may have a "deconfining" phase transition.

    While I'm at it, here are some more questions :)

    1. We are postulating a pure state (pure in the AdS, pure in the CFT) that collapses to a blackhole, and that evaporates into a pure state. Then, since the necessary conditions for quantum recurrence hold good, given enough time, after some huge orbit through quantum state space, the system will return arbitrarily close to the blackhole state. Question -- does this orbit through quantum state space pass through the CFT vacuum state?

    2. Can the AdS have a scalar field with a Mexican hat potential, and thus dynamically broken or rather unmanifest symmetry? If yes, how does that show up in the CFT, where the CFT vacuum is unique? Or is the idea that the AdS/CFT dictionary maps the AdS vacuum maps to the CFT vacuum in need of refinement? Or is the answer, No!

    3. If the AdS bulk can have matter fields with broken symmetries, can we say that we understand the all the possible vacuum phases of a CFT?

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  57. Sabine,

    This entire discussion is taking place under the assumption that the evolution of the wavefunction (quantum state) is information-preserving, i.e. deterministic in both time directions. It is also assumed that it is unitary because that is a fundamental axiom of typical quantum-mechanical theories. If you deny this—i.e. if you adopt a physical collapse postulate—then information is lost all the time, and there is no obvious paradox at all. Some collapse theorists (e.g. Daniel Sudarsky) take exactly this line: they have no paradox because they never signed on for deterministic, unitary evolution in the first place. I think that is exactly correct. So I think that the terms of the debate are just whether unitary evolution can be reconciled with evaporation via Hawking radiation.

    I agree with you completely about the pointlessness of appealing to empirical results here. Unitarity will never be, and can never be, verified empirically. I have no idea why bhg keeps going on about that.

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  58. Arun,

    "Strongly coupled" indeed means that the effective coupling constant of the gauge theory (the 't Hooft coupling) >> 1.

    When the gauge theory is at weak coupling there are many light single-particle states with spin > 2 in the spectrum. Any gravitational theory one might want to call a "bulk dual" to a weakly-coupled CFT must have the same spectrum of higher-spin particles, so it must be very different from ordinary gravity, which only has particles with spin up to 2.

    When the gauge theory is taken to strong coupling the higher-spin single-particle states become very massive and are effectively irrelevant at low energies. In terms of the CFT data this manifests as the higher-spin single-trace operators acquiring large anomalous dimensions. In the bulk we are effectively left with only the spin-2 graviton (plus whatever matter fields).

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  59. Tim,

    This has nothing to do with collapse. I am saying if you were concerned with what's "physically realistic" you wouldn't be discussing black hole evaporation to begin with. Or are you trying to tell me you will catch a black hole, put it in a box and patiently wait 100 billion years while you count every last quanta that comes out? Your sudden insistence on physical realism when it comes to the recurrence time strikes me as insincere.

    I also cannot fathom why you are still discussing the matter. Your scenario isn't compatible with the microcanonical BH entropy, so it's not compatible with AdS/CFT. What is there even to discuss? Wasn't your whole point that you don't need to change anything about the usual Hawking-evaporation business?

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  60. Tim,

    "We want to know what happens over the evaporation time: does the information come out in the Hawking radiation or not? I say not. Please restrict any arguments or comment to that question, not to that happens over hyper-astronomially longer periods."

    Second question is connected to the first. If you have recurrences (of the type in CFT) all information must come out. You say all energy comes out early as normal Hawking radiation. Now you are saying, but information comes out much later. How can information come out without any energy?

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  61. The implication that AdS/CFT quantum recurrence renders the usual Penrose diagram of blackhole formation and evaporation invalid is interesting.

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  62. Bee,

    you wrote "I also cannot fathom why you are still discussing the matter. Your scenario isn't compatible with the microcanonical BH entropy, so it's not compatible with AdS/CFT. What is there even to discuss?"

    You are correct, but 90% of this conversation has been Tim denying this point.

    I am not sure AdS/CFT is correct. Even if correct as duality, I am not sure it describes quantum gravity in our world. But, I am very sure it is not compatible with Tim's proposal.

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  63. Sabine

    I really cannot parse your first concern here. I have never, from beginning to end of this entire discussion, invoked any laboratory procedure. In fact, I have suggested that BHG's attempts to operationalize certain issues—e.g. whether the quantum state of the external region after the evaporation is pure or an improper mixture—was both pointless and fruitless. You don't try to describe some idealized experimental process to determine that: you just look at what the theory says. Indeed, since the only interesting question here is about the universal quantum state, the idea of operationalizing *anything* is silly. But that's BHG, not me.

    If by "physical realism" you mean operationalism then 1) you have chosen precisely the wrong terminology and 2) I never have been, in your sense, a "physical realist".

    As to why we are discussing it, I am still interested in finding out whether there really is anything in AdS/CFT that contradicts the basic point I am making. (I am also a bit interested whether there is anything in AdS/CFT full stop.) BHG has not been talking in any direct way about the microcanonical BH entropy. If you would like to state clearly this killer observation you have that shows my approach to be inconsistent with AdS/CFT I would be happy to discuss it. I will warn you that I have fairly developed views about the whole literature on BH entropy and BH thermodynamics and (surprise!) they are not sympathetic to most of that literature, so don't expect that you can take the "standard" account of BH thermodynamics in general and BH entropy in particular for granted. But I would welcome a new discussion, since I think all this talk of recurrence has been pointless from the get-go.

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  64. Tim,

    I was commenting on your statement

    "First, in a physically realistic scenario—asymptotically flat or dS—the recurrence time is not just long, there is no recurrence time at all. We agree about that, which was one point I was trying to get physphil to see on his own, so it would actually stick. If there is no recurrence time in a physically realistic situation, then appeal to recurrence in a physically unrealistic situation like AdS is not going to be any help for our question, which is about actual black holes, not imaginary ones."

    Quite possibly "physical realism" is not the technically correct noun, but "physically realistic scenarioism" didn't sound healthy and I was assuming you'd recall what you said.

    My "killer observation" is that (for all I recall) your point was to say there isn't any paradox. Black hole evaporates a-la Hawking and nothing's wrong with that, information stays in the black hole and that's that. In that case the BH entropy doesn't count microstates, so it's incompatible with AdS/CFT.

    Now you could of course insist that you can lump AdS/CFT-induced non-locality on top of your proposal and stuff information into the Hawking-radiation, but in that case I don't understand what's the point of your idea to begin with.

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  65. Sabine,

    Ah, OK. I understand about "physical realism". That's fine. Leave that all aside.

    What you are bringing up is the point that the BH entropy á la Bekenstein does not "count microstates" *of the black hole interior*. Right, of course it doesn't. There was never any reason to think it did. What the BH entropy "counts microstates" of is the region near the horizon. And that trivially goes to zero as the horizon goes to zero and disappears when the horizon disappears, and is trivially proportional to the horizon area. It is confusion about this that led to all this nonsense about the "Holographic Hypothesis" and blah, blah, blah.

    But that's a completely different question than the one we have been discussing, and has nothing to do with recurrence times or anything like that. I was wondering if anyone was ever going to bring it up, because I've been ready for that one for months. But you are the first person to even mention it.

    Once you sort out that confusion, there is still the whole AdS/CFT duality to worry about, which is what I have been trying to get a grip on. But the BH entropy argument is easy. Can you find anything wrong with what I just wrote?

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  66. Tim,

    There isn't anything wrong with what you wrote, I am saying it's not compatible with AdS/CFT.

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  67. Tim,

    you wrote "It is confusion about this that led to all this nonsense about the "Holographic Hypothesis"...Once you sort out that confusion, there is still the whole AdS/CFT duality to worry about, which is what I have been trying to get a grip on."

    Are you aware that AdS/CFT is example of holography, so shows that "Holographic Hypothesis" was very far from "nonsense"? Just a question.

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  68. Sabine,

    So this is just a matter of semantics. The whole "Black hole entropy á la Bekenstein counts microstates" fallacy could be used—if it were correct!—to shoot down my proposal without any reference to AdS. If that were correct, then the proposal is dead even in asymptotically flat or dS spacetimes, and you would not have to wheel in AdS/CFT at all. As I said, I was expecting someone to bring up that argument long ago, but no one did. And since you also seem to think that the argument is nonsense, I guess no one here will try to defend it. I will put some commentary about that mistake in the final version of the paper. It is actually thinking about how confused physicists are about entropy that inspired me to put together our summer school on entropy. The foundations of statistical mechanics and thermodynamics are in as bad a shape as the foundations of quantum mechanics, but don't get 1% of the attention.

    So I have just been ignoring all that. Maybe the Holographic Hypothesis inspired the AdS/CFT conjecture, and inspired the construction of the CFT in the first place, but that is neither here nor there. There is still the question of what the supposed AdS/CFT duality is supposed to be and whether the conjecture is even plausible. If bhg wants to start talking about Bekenstein entropy and the errors concerning it, I'm game. But so far he has not committed that fallacy, as far as I can see.

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  69. Tim,

    You apparently missed that Bee's argument (which is a standard one) is basically equivalent to the one I have been making all along, and by the same token immediately shows why your scenario is incompatible with AdS/CFT. This can be put most cleanly as follows. Suppose the information does not come out with the radiation. Then as evaporation proceeds, the von Neumann entropy of the emitted radiation increases and the black hole shrinks. If the full state is pure the von Neumann entropy of the black hole must equal that of the emitted radiation. Hence, we have an object of low mass (the black hole near the end of its life) that can support an arbitrarily large von Neumann entropy (because the starting black hole could have been arbitrarily large). Obviously, this is incompatible with the spectrum of the theory having some minimal energy spacing, so it is impossible in AdS/CFT. Once again, information loss leads you inexorably to the existence of arbitrarily many states of arbitrarily low energy, which is inevitable since these states are precisely the repository for the lost information.

    Since two clear disproofs of your scenario were insufficient, it seems unlikely that three will do the trick...

    You write

    " all this nonsense about the "Holographic Hypothesis" and blah, blah, blah."

    Witten's original paper on AdS/CFT is titled "AdS space and holography". If you arrive the conclusion that the subject of one of Edward Witten's papers is "nonsense" and "blah, blah, blah", I suggest that this is because you are incapable of understanding it. When you make such comments, it becomes very clear what the true source of the "nonsense" and "blah, blah, blah" is.

    Also, FYI, in string theory the area law counts the full entropy of the black hole, as was shown by Strominger and Vafa and since verified in countless other situations. There is at present no other theory of QG where such a computation can be done without massive handwaving and essentially putting in the answer by hand.

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  70. Tim,

    No, it's not a matter of semantics. You are asking if your proposal is compatible with AdS/CFT. The answer is no, for the reasons I have given you above.

    You can of course say, well, who cares, I'll just throw out the strong interpretation of the BH entropy (read this if you aren't sure what "strong" refers to). You have done that already. As I explained a long time ago, your scenario is a remnant scenario - these are all incompatible with AdS/CFT (which is why string theorists don't like them).

    That I personally think they are the most plausible scenario (see 2009 paper with Lee) is besides the point for the issue I thought you were discussing, namely whether your scenario is compatible with the AdS/CFT approach.

    As bhg says in his recent comment, it's a standard argument, and it's the same one that bhg has been making in somewhat different ways (as with the number of states and so on).

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  71. bhg,

    It doesn't have direct relevance for your exchange with Tim, but is it well-understood "where" the degrees of freedom of a black hole in the AdS bulk are? Does the question even make sense?

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  72. Sabine and bhg,

    Okay, both of you seem to think there is something in this entropy argument. I repeat that there is nothing in it. Zero. The thermodynamic arguments for the "entropy of the black hole" scaling with the horizon area are empty: as I said, they are arguments that the entropy *of the horizon* scales with its area, which is hardly a surprise. Since that entropy does *not* "count" (or measure) microstates of the interior, the fact that it goes to zero says nothing about the number of degrees of freedom of the interior.

    How many microstates or degrees of freedom are available in the interior? Well this is pretty simple: you just have to think about how the whole shrinkage and eventual disappearance of the horizon is accounted for. As the horizon shrinks, the ADM mass of the black hole goes down. But where does the mass inside the horizon "go"? Answer: nowhere! The positive mass that fell in starts to get combined with negative energy modes (as judged from the AdS boundary) of anti-Hawking radiation. As more negative energy modes become available, the number of interior degrees of freedom (and hence interior microstates) goes *up* not *down*. The von Neumann entropy of the interior (because the universal state is pure and entangled) goes *up* as it should. The von Neumann entropy of the exterior, entangled region goes *up* in synch with the interior, as it must. And the entropy associated with the horizon itself goes *down* as it should. Easy-Peasy.

    Somehow, you have all forgotten about the source of the Hawking radiation in the first place: the change in definition of positive vs. negative energy modes that is induced by the space-time curvature. Take that into account, and everything falls into place.

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  73. Tim,

    You are summarizing the classical remnant arguments. As I told you above, there is nothing a priori inconsistent about that scenario, it's just not compatible with AdS/CFT. Your scenario: Number of interior dofs goes up, no information in radiation. AdS/CFT: Number of interior dofs goes down, information is in radiation.

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  74. Sabine,

    So I just don't understand why what you claim follows from AdS/CFT, but that's because I have yet to get a clear statement of what AdS/CFT even says. Everybody says that somehow or other (nobody can say how) the states of the interior of the AdS are "encoded" in some unspeakable non-local way in the CFT. That's common ground. So if the state in the interior of the black hole can be encoded *before* the evaporation, why can't it be encoded *after* the evaporation? Why does AdS/CFT imply that the black hole interior DoFs go down once you adopt the (correct) Weak view? It is that claim that *forces* the information to come out in the Hawking radiation. But since no one can tell us how the interior DoFs (both "interior of the AdS space-time" and "interior of the event horizon") are encoded in the CFT, what is the argument that the DoFs in the interior of the event horizon go down?

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  75. Tim,

    First, I don't know why you say the states are ""encoded" in some unspeakable non-local way in the CFT." I think it's actually pretty well understood how this works. In case you were referring to my earlier question to bhg, I was asking about the bulk-state, not about the CFT.

    "if the state in the interior of the black hole can be encoded *before* the evaporation, why can't it be encoded *after* the evaporation?"

    Well they can be encoded after the evaporation, just not in the black hole.

    " Why does AdS/CFT imply that the black hole interior DoFs go down once you adopt the (correct) Weak view?"

    I am telling you that "adopting" this view is incompatible with AdS/CFT. Black hole microstates (all of them, inside too) are counted by the BH entropy. If the BH entropy goes to zero, the black hole microstates go to zero.

    "But since no one can tell us how the interior DoFs (both "interior of the AdS space-time" and "interior of the event horizon") are encoded in the CFT, what is the argument that the DoFs in the interior of the event horizon go down?"

    Again I don't know why you are saying that. Look, the whole reason string theorists are so proud of AdS/CFT is that if you count the bulk-microstates of a black hole in AdS, you get the BH entropy. It follows from that that if you have a smaller black hole, it has fewer microstates. That is not the case in your scenario. It's not compatible.

    I am also not sure why you want it to be compatible to begin with, seeing that you seem to think the whole approach is "nonsense".

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  76. Sabine,

    So either we are talking past each other or what I have read is wrong. Suppose I want to know something about the interior of the AdS (e.g. whether there is a binary star system), and all I have to hand is the dual state in the CFT. My understanding is that at this point I am just out of luck: nobody has built a "dictionary" that will translate the question asked about the bulk into a question about the CFT state. Is that incorrect? Let's just start with that one question and go step by step. I thought that was why bhg told me long ago that AdS/CFT is a "work in progress".

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  77. Tim,

    The AdS-side of the AdS/CFT duality is gravity in AdS-space with certain source fields that may or may not be gauged, but usually are. In the cases that are well-understood the sources are not anything like standard-model matter. I cannot at this point recall in which context bhg may have been saying something like that, but if you ask a string theorist to put a binary star - nuclear matter and neutrinos and all - into AdS and tell you what the CFT is, they don't know if it even exists. (Especially QCD, as with being asymptotically free.) It is indeed a "work in progress."

    But to get back to the issue at hand, here's a simple way to see the contradiction. What's the entropy of a black hole of solar mass? In AdS/CFT, it's given by the BH entropy. In your scenario, it could be something else. Best,

    B.

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  78. Sabine,

    Looking back at the last couple of posts, I think there is this confusion: when I was talking about "encoding" I meant "encoding the bulk state in the CFT" not "encoding the information in the bulk state". I think you were misunderstanding my point.

    I follow this: I am committed to the Weak understanding, which I think can be easily defended. And many string theorists are committed to the Strong understanding. But what I don't see is why AdS/CFT—if it is just a claim about the existence of some isomorphism between the AdS and the CFT—would be committed, as such, to either understanding. How do you get from the isomorphism to the doctrine about BH entropy?

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  79. Tim,

    "How do you get from the isomorphism to the doctrine about BH entropy?"

    You calculate it.

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  80. "You calculate it."?

    Look, if you just calculate the number of microstates in the bulk by reference to AdS, then what's the point of bringing up CFT at all? And if you can't pin down the mapping from the CFT degrees of freedom to the AdS degrees in the bulk (which is what I gather), then having the CFT won't help. So what work is AdS/CFT doing?

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  81. Tim,

    I get the impression you have very little idea of how the whole AdS/CFT business works to begin with; it's not remotely as philosophical as you seem to think. I don't feel like I am the right person to break this down for you, but I'll give it a try and hope bhg will check that it's not grossly wrong.

    Given a state on the boundary (in the CFT), you calculate the state in the bulk (in the AdS) by expanding around the boundary. You also of course need an initial condition on a space-like hypersurface. All you do then is, essentially, solving an initial value problem. There are various subtleties in this procedure that I am glossing over (eg, you may need additional consistency conditions in the bulk), but the only relevant point for your purposes is that the boundary state determines the bulk state (given the initial conditions). So, any field in the bulk has a corresponding field on the boundary.

    Now, what do you need the CFT for? Well, since the CFT is strongly coupled when the gravitational theory isn't, usually you do it the other way round - you use the gravitational theory to learn something about the CFT. But as I said earlier, not all bulk states can be expanded around the boundary. The AdS/CFT duality *defines* what you mean by the gravitational theory, but there are states that are asymptotically AdS that cannot have a boundary equivalent. An obvious example is adding an entirely disconnected part of space (that doesn't have an asymptotic region) to the AdS. The boundary can't know anything about it, hence the CFT can't distinguish the states. This already should have told you that adding a point to a causal diagram isn't something you can accommodate in the duality.

    Having said that, a thermal state in the boundary CFT corresponds to a black hole of the same temperature in AdS. But for this black hole you can calculate the number of microstates. The result is that it matches the number expected from the BH entropy.

    Now the point I am making is simply that your scenario is not compatible with that. According to your prescription, a black hole of temperature T does not correspond to any specific number of microstates. If you insist that your scenario is compatible with AdS/CFT you are basically denying that there even is a correspondence. Best,

    B.

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  82. This is confusing, too (the following is from Tom Hartmann's lectures, previous mentioned)

    The basic starting point is that thermal states in CFT are dual to black holes in quantum gravity.

    Thermal state in my mind is the mostest opposite of a pure state, and that confuses the heck out of me.

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  83. Bee,

    "It doesn't have direct relevance for your exchange with Tim, but is it well-understood "where" the degrees of freedom of a black hole in the AdS bulk are? Does the question even make sense?"

    This is a pretty subtle question, but I think it's fair to say that the conventional wisdom is that they are spread out over the interior of the (would be?) horizon. At our current (incomplete) level of understanding based on AdS/CFT fuzzball/firewall etc ideas, the degrees of freedom are invisible in any approximation which treats the spacetime metric as a smooth entity, and since the metric is part of what we use to specify "where" something is, it would appear to be the wrong question to ask where the dof are. Again, there is some analogy here to the fluid vs. atomic description of an ideal gas, in the sense that one could ask "which specific fluid modes are responsible for the entropy of the gas". This question is ultimately not answerable in the fluid description, since it is coarse grained.

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  84. Tim,

    "How many microstates or degrees of freedom are available in the interior? Well this is pretty simple: you just have to think about how the whole shrinkage and eventual disappearance of the horizon is accounted for. As the horizon shrinks, the ADM mass of the black hole goes down. But where does the mass inside the horizon "go"? Answer: nowhere! The positive mass that fell in starts to get combined with negative energy modes (as judged from the AdS boundary) of anti-Hawking radiation. As more negative energy modes become available, the number of interior degrees of freedom (and hence interior microstates) goes *up* not *down*. The von Neumann entropy of the interior (because the universal state is pure and entangled) goes *up* as it should. The von Neumann entropy of the exterior, entangled region goes *up* in synch with the interior, as it must. And the entropy associated with the horizon itself goes *down* as it should. Easy-Peasy. "

    You realize that you killed your own argument, right? You just argued that as the black hole mass goes to zero its von Neumann entropy gets large. So you have a low mass object with high entropy. Congratulations, you have just discovered what's known as a remnant. Unfortunately, since the CFT has a discrete spectrum it has no such low energy, high entropy states, so this scenario can't occur in AdS/CFT.

    It's also amusing that you seem to think it's a novel insight that the black hole loses mass by absorbing negative energy as part of the Hawking process.

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  85. Dear Sabine,

    Thanks so much. I am getting a clearer picture of AdS/CFT from what you wrote than I have gotten out of a year of back-and-forth with BHG, physphil, dark star, etc. And the way you are putting things makes more sense in one way, but raises puzzles in another. In particular this:

    "Given a state on the boundary (in the CFT), you calculate the state in the bulk (in the AdS) by expanding around the boundary."

    Now unless there is some unbelievably strong constraint, akin to only using holomorphic functions, I can't see how this is possible. It contradicts, for example, the gluing theorems in GR (I think), because they imply that there are always alternative solutions to the field equations that agree precisely at the boundaries. Is there a clear statement of what these constraints are? This may well hold the key to the mystery of BHG's "physical Hilbert space". If the Hilbert space is so cut down as is needed to validate this procedure, then there may be no natural way to arrive at it.

    If I am following, you take AdS/CFT not to *derive* (or *conjecture that one can derive*) the critical isomorphism between the gravity theory and the conformal field theory (each of which can be formulated in its own terms) but rather to *postulate* the isomorphism into existence: let there only be exactly as many physical states of the bulk (and operators on the bulk states?) as are required by the isomorphism. If that's the situation, then my whole understanding has been upside-down: the question is not the "conjecture" (which becomes true by definition), the question becomes why we would be entitled to regard the bulk theory as the sort of theory of gravity we are aiming for, e.g. the sort of theory of gravity that allows for the existence of black holes in the bulk at all! If that is right, it throws the whole thing into an entirely new light. The unproven assumptions are different from what I thought. Just as implausible, but different!

    Cheers,

    Tim

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  86. BHG,

    Once again we seem to arrive at this situation: you say that my theory is "killed" (as consistent with AdS/CFT only, of course) because a claim I have made is inconsistent with AdS/CFT. But then it seems that *that precise claim follows from principles that you yourself endorse, and that have nothing to do with my solution at all*! That is, you get a contradiction with AdS/CFT not via *my* theory, but via *your own* theory! You keep pointing out incoherences *within AdS/CFT*, and then trying to conclude that therefore my theory is incompatible with AdS/CFT rather than that AdS/CFT is incompatible with itself!

    In particular: you say it is trivial and well-known that the black hole horizon shrinks because more and more negative energy modes get mixed in with the positive energy modes behind the horizon. You act as if everybody know this, and it is amusing that I think it is relevant to point it out because it is so obvious. But then why is it not obvious that the number of microstates available to the system as more and more negative energy modes become available *grows* rather than *shrinks*. There are more ways to divvy up a fixed amount of energy (or really, ADM mass) among both positive and negative energy modes than there are ways to divvy it up amongst only positive modes. But then it follows: as the hole "evaporates" and the horizon shrinks, the number of microstates available to the system goes up rather than down, so the Strong interpretation of the black hole entropy is refuted. If this contradicts the CFT somehow, then it is you that are screwed, not me. Because absolutely nothing in the argument I just gave depends in any way on my solution to the information loss paradox.

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  87. You realize that you killed your own argument, right? You just argued that as the black hole mass goes to zero its von Neumann entropy gets large. So you have a low mass object with high entropy. Congratulations, you have just discovered what's known as a remnant. Unfortunately, since the CFT has a discrete spectrum it has no such low energy, high entropy states, so this scenario can't occur in AdS/CFT.

    This blackhole system in the AdS (and corresponding CFT) undergo quantum recurrence. Either the orbit through quantum state space of the quantum recurrence takes the CFT through a low energy state or else this lack of low energy high entropy states in the CFT is a red herring.

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  88. Suppose an initially pure quantum state can collapse to a black hole in AdS.

    Very soon after the collapse, and before very much Hawking radiation has been emitted, the subsystem that is the horizon and exterior of the black hole has lost almost all information about the initial state, retaining only mass, charge, angular momentum. Presumably this information is not in the environment, but has been somehow retained by the black hole.

    The CFT assures us that the information is somewhere, just cannot tell us where.

    In AdS, looking at just the black hole subsystem, it has access to some huge number of microstates. These are reflected somehow in the CFT, moreover, these these have to be tangled up in the CFT so that though "thermal states in CFT are dual to black holes in quantum gravity", this is really still a pure state in the CFT. Somehow black hole formation in the AdS corresponds to going from a pure state to a pseudo-thermal state in the CFT; pseudo- because it really is a pure state.

    Then the black hole evaporates in AdS, and in the CFT, the state in the CFT relax towards low energy where the number of available states is greatly reduced, helping rule out any kind of black hole remnant. Then quantum recurrence makes the whole thing happen all over again.

    What did I miss?

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  89. Tim,

    Well, as I said, I am not an expert, but this is my understanding of the situation. Maybe my earlier comments about analytic functions and so on now make sense?

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  90. Tim,

    The AdS/CFT cases that are well understood are the things I was referring to when you quickly and firmly declared me "confused" a week ago at the MAPS NYU pre-workshop on quantum field theory. As I was trying to say then, it's been the case that calculations of a quantity of interest were first made through a AdS/CFT duality and then later found how to do without referencing the duality. I was thinking of examples where this has been the case in condensed matter theory, e.g, where it's being used entirely as a mathematical tool.

    As a high energy physics PhD student I enjoyed listening to some philosophy of physics as a new change of pace for a while, but I haven't been sure what to make of the bizarre interaction with you, especially given the exchange here. I'd enjoy heading over to listen to some talks again sometime, but I don't want to be any trouble.

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  91. Tim,

    The AdS/CFT cases that are well understood are the things I was referring to when you quickly and firmly declared me "confused" a week ago at the MAPS NYU pre-workshop on quantum field theory. As I was trying to say then, it's been the case that calculations of a quantity of interest were first made through a AdS/CFT duality and then later found how to do without referencing the duality. I was thinking of examples where this has been the case in condensed matter theory, e.g, where it's being used entirely as a mathematical tool.

    As a high energy physics PhD student I enjoyed listening to some philosophy of physics as a new change of pace for a while, but I haven't been sure what to make of the bizarre interaction with you, especially given the exchange here. I'd enjoy heading over to listen to some talks again sometime, but I don't want to be any trouble.

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  92. Tim and Bee,

    Let me clarify a few points. First, Bee wrote "Given a state on the boundary (in the CFT), you calculate the state in the bulk (in the AdS) by expanding around the boundary." . I am not sure what is precisely meant by this. The kind of bulk state that cannot be described in the CFT is a disconnected universe; this is not a problem, since what happens is that starting from AdS such states will never be created in the first place in this theory; ie. ignoring such states is self-consistent. On the other hand, what definitely can be described is some strictly localized field excitation deep in AdS; that is, there is no requirement that a bulk scalar field at some time t must have the scalar field nonzero at the boundary in order to exist in the CFT. Furthermore, there is a fully explicit dictionary relating such bulk and boundary states, and likewise for, say, two massive particles orbiting each in AdS. This can be read about in many places, and I am not going to go through the details here. When I said that AdS/CFT is a work in progress that does not mean that we don't know a huge amount about the details, which we of course do, including the points just mentioned, and much more, both at the perturbative and non-perturbative level.


    Overall, what is clear is that the CFT reproduces expected bulk gravitational physics in those regimes where it has been tested; i.e. we recover Einstein's equations coupled to generic matter. And this is done within a well defined non-perturbative quantum mechanical framework. This is exciting because no other theory comes close. One place where the CFT seems to predict behavior that we might not have expected is inside black holes, where the naive principles seem to break down. Such a break down is of course necessary if the Hawking radiation is to encode all the information. What is remarkable is that this can be done without doing apparent violence to physics outside the horizon or in the absence of black holes -- the weirdness is confined to a regime where we have no observational evidence of what actually occurs.


    You may or may not choose to believe that this is the way our world works. If you think it isn't, you are essentially betting on the existence of some alternative theory of quantum gravity in which there is no unitary S-matrix, baby universes might be created, etc. That's all fine, but just be aware that until such a theory is formulated all you can do here is add to the thousands of essentially handwaving papers that put forth "scenarios" with no firm foundation. For example, I cannot for the life of me see what Tim has added to the story that wasn't in Hawking's original papers.


    I don't find Tim's comment about negative energy excitations inside the horizon seeming to give lots of states novel because this fact is well known in many different guises (also, the fact that black holes shrink by absorbing negative energy is obvious since otherwise they would violate Hawking's area theorem). For example, if you take a black hole of mass M, and ask, in the presence of a scalar field, say, how many states are there between energy M and M+dM you get infinity, simply because there is an infinite redshift at the horizon and so you can just pile up short wavelength quanta near the horizon in infinitely many different ways at low energy cost. On the other hand when you compute the total entropy of a black hole in string theory you get A/4 (plus additional corrections which precisely match expectations). This is another signal that naive principles break down in the presence of black holes, and a worthwhile task is to elucidate the details of this.

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  93. Gabby,

    What you said at that session is that AdS/CFT had been, in some cases, proven. That is not so. It was, and remains, a conjecture. Checking that some calculations in the AdS gravity theory give results that match some other calculations in the CFT is not a proof of any duality. Indeed, if either off the two theories was expressly constructed to be structurally similar to the other in some way, then the matching of some calculations using each is not very strong evidence for any deep isomorphism.

    As I have said, not only it is a conjecture, it has not yet been made clear even what the conjecture says. The last time I tried to get that information, I was told that the conjecture is that the Hilbert spaces and the algebra of observables of the two theories are isomorphic. I responded that the fact that the Hilbert spaces are isomorphic is trivial: all infinite-dimensional Hilbert spaces are. I then asked about a clear characterization of what the relevant algebra of operators is and was met by radio silence. If you can't even formulate a clear conjecture, then obviously there is no issue about proving it.

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  94. bhg,

    I am having a harder and harder time getting a grip of the supposed bearing of the AdS/CFT conjecture on anything, including, of course, the Information Loss Paradox. You write:

    " One place where the CFT seems to predict behavior that we might not have expected is inside black holes, where the naive principles seem to break down. Such a break down is of course necessary if the Hawking radiation is to encode all the information. What is remarkable is that this can be done without doing apparent violence to physics outside the horizon or in the absence of black holes -- the weirdness is confined to a regime where we have no observational evidence of what actually occurs."

    How about specifying which "naive principles" seem to break down? Further, why think the breakdown, whatever it is, signals information coming out in Hawking radiation? What if I wrote:

    One place where the CFT seems to predict behavior that we might not have expected is inside black holes, where the naive principles seem to break down. Such a break down is of course necessary if a baby universe is to form. What is remarkable is that this can be done without doing apparent violence to physics outside the horizon or in the absence of black holes -- the weirdness is confined to a regime where we have no observational evidence of what actually occurs.

    or

    One place where the CFT seems to predict behavior that we might not have expected is inside black holes, where the naive principles seem to break down. Such a break down is of course necessary if the maximal spacelike surfaces are to become disconnected. What is remarkable is that this can be done without doing apparent violence to physics outside the horizon or in the absence of black holes -- the weirdness is confined to a regime where we have no observational evidence of what actually occurs.

    Why don't these work as well as yours?

    As for your comment about Hawking's original papers, I don't know, after all these months, how to make this any plainer.

    Hawking:
    After the black hole evaporates, the information that was in the interior disappears since there is no place for it to exist. The evolution of the universal wavefunction fails to be unitary, so scattering must be described by a Superscattering matrix. Quantum mechanics has broken down.

    Me:
    After the black hole evaporates, the information that was in the interior still resides in the interior. The evolution of the universal wavefunction is always unitary, so quantum mechanics has not broken down. Scattering from an ingoing state to just the outgoing state associated with the piece of a Cauchy surface connected to the asymptotic boundary must be described by a Superscattering matrix. One arrives at the conclusion that information is indeed lost to the interior of the black hole, but nonetheless the evolution of universal state never contradicts QM.

    Those are quite different, yes?

    As for the negative energy states, again, how can I be clearer? If the negative energy modes can be excited, then the spectrum must be wildly degenerate when calculated for all physically possible states. But you insist that the spectra cannot be wildly degenerate. So you are in a fatal bind.

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  95. bhg,

    As to your comment about localized states, let me make the following observation. Any analytic function can be expanded around any point, in principle to arbitrarily high precision. This has nothing to do with AdS. If you postulated that we'd only deal with such functions, there'd be no black hole information loss, done. You can of course localize these functions as much as you like.

    Now in AdS/CFT you don't require functions to be analytic, but they do have to be expandable around the boundary. Imagine you have a function that is identically to zero in a region epsilon>0 around the boundary. How do you want to get the bulk state from a boundary-expansion in that case? For all I can tell, you can't, so by postulating the duality you are assuming such states don't exist. Or if I am wrong, please tell me how it's supposed to work. Best,

    B.

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  96. Tim,

    Indeed, I don't think Erdős would be pleased if I tried to sneak one of these proofs of specific cases into "the book". However, I didn't think some relatively minor friction over the sense in which I was using the word proof explained your reaction. My sense at the time was that we most probably had some totally different idea of what it would mean for AdS/CFT to be 'true' for the purposes of some particular case that you didn't wish to hash out. My sense of the discussion here is that I think this may still be the case, but I wanted to make sure I wasn't just missing a cue to buzz off before showing up again sometime at a talk.

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  97. Gabby said:
    My sense at the time was that we most probably had some totally different idea of what it would mean for AdS/CFT to be 'true' for the purposes of some particular case that you didn't wish to hash out.

    Not accusing you of missing this distinction, but I think it can't hurt to remind ourselves, frequently, that 'AdS/CFT is true' can mean at least 3 different things. (And I do think at times these get muddled up in the above 1300 or so posts.)

    1) Mathematical: Some particular string theory is equivalent to some particular conformal field theory set in a spacetime of 1 fewer dimension, under some [non-trivial] way of mapping elements of the one into the other and vice-versa.

    2) Mathematical: As a generalization, all interesting string theories with asymptotically AdS bulk spaces are equivalent to a dual conformal field theory set in a spacetime of one fewer dimension, again under some [non-trivial] way of mapping elements of the one into the other.

    3) Physical: The string theory of QG that is most-studied and most-well-understood, often simply (and misleadingly) called 'AdS', is in some sense true as a description of our actual world, even if actual spacetime is not asymptotically AdS. (The sense of 'true' intended here would have to be spelled out carefully...)

    [Side-note: 3) could be true even if 1) and 2) turned out to be false.]

    1) and 2) are still only conjectures, at this point, since (as BHG has said a number of times) the mapping or "dictionary" that would spell out the equivalence(s) has not been fully worked out. But partial results have been established, giving many physicists confidence that 1) and 2) are probably true.

    Evidence for 1) and/or 2) is NOT automatically -- or, indeed, in any sense -- evidence for 3). From what BHG has stated here, the evidence for 3) consists of the fact that one can squeeze Einstein's equations out of the theory in some appropriate sense, and the fact that various calculations done on one or another side of the duality have yielded results that either match what we think should be right, or things that have been measured in actual experiments.

    It seems to me that one of the best things that could happen to this over-long debate would be for it to turn into a discussion of the issue just mentioned: what things constitute evidence for 3), and how strong is that evidence?
    I think this would be more fruitful than continuing to try to convince one another that Tim's info loss scenario is / is not compatible with AdS/CFT.

    Carl

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  98. Bee,

    you ask "Imagine you have a function that is identically to zero in a region epsilon>0 around the boundary. How do you want to get the bulk state from a boundary-expansion in that case?"

    The answer is, you look at a nonlocal observable in CFT. Examples: entanglement entropy of a region, correlation function of local operators inserted at far separated points, Wilson loops.

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  99. Bee,

    you ask "Imagine you have a function that is identically to zero in a region epsilon>0 around the boundary. How do you want to get the bulk state from a boundary-expansion in that case?"

    The answer is, you look at a nonlocal observable in CFT. Examples: entanglement entropy of a region, correlation function of local operators inserted at far separated points, Wilson loops.

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  100. Bee,

    There is no such restriction. Let's consider this in the large N limit where we can think of a free scalar field in the bulk. The claim is that any bulk state that you would think you can write down based on your ordinary intuition has an explicit realization in the CFT. For example, suppose we have a bulk coherent state exp[\int f(x) \phi(x)]|0>, where f(x) is strictly zero outside some compact region deep in the bulk (i.e it's definite not analytic). We can map this to a CFT state as follows. The bulk field \phi is dual to some CFT operator O. There is an explicit function (the HKLL smearing function) that is used to literally express the bulk operator \phi(x) as an integral of O over the boundary weighted by the smearing function. Since phi(x) for a bulk point x can be represented as a CFT operator, the same is of course true for our coherent state.

    Comments: the smearing is over both space and time on the boundary. However, we can always use the CFT Heisenberg equations of motion to express all the CFT operators at a common time. Also, the above is for the large N limit, but one can correct this order by order in the 1/N expansion, corresponding to including bulk interactions. Of course, we expect this procedure to break down in some way at strictly finite N, since we don't expect that in non-perturbative QG it makes sense to talk about a local field operator. But the precise failure mode is not understood.

    So there is a very nice and explicit understanding of how the operator algebras on the two sides match up, at least order by order in the 1/N expansion,

    For details on all of this you can look at papers referring to the oddly named procedure of "bulk reconstruction", or the nice recent lectures on this topic by Harlow.

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  101. Tim,

    For your first question, the baby universe or disconnected scenarios imply zero energy states, and since they are not present in the CFT this cannot happen in AdS/CFT. To connect this to the recent entropy discussion, as the black hole shrinks its von Neumann entropy must go to zero since otherwise one would have a low energy but high entropy object, and the CFT simply does not have such a spectrum. Therefore we know that within AdS/CFT the information comes out with the Hawking radiation. For that to happen, there must be some novel physics going on inside the (would be?) horizon, since otherwise we are stuck with Hawking's information loss argument. I am not sure how many ways I can find to restate this...

    Same story for your negative energy modes: this argument is predicated on there being "standard physics" within the (would be?) horizon, but that is precisely what is being denied. Overall, I get the sense that you are taking as axiomatic the claim that standard physics prevails inside the horizon, and then using that to "rule out" AdS/CFT. That's fine, but this is completely different than finding an *internal* contradiction within AdS/CFT, and its also totally different from showing that AdS/CFT implies novel physics in regimes that we have direct access to.

    Your supposed summary of what Hawking claimed is not accurate. I will simply quote the man himself and leave it at that:

    "The situation changed, however, when it was realized that black holes evaporate by emitting particles with a thermal spectrum [1]. Suppose that one started from an initial pure quantum state which could be described in terms of a complete set of commuting observables on a space-like surface in the past. The same quantum state could also be described in terms of observables in the future only in this case one had to have two sets of observables, observables at infinity which described the outgoing particles and observables inside the black hole which described what fell through the event horizon. The system would still be in a pure quantum state but an observer at infinity could measure only part of the state; he could not even in principle measure what fell into the hole. Such an observer would have to describe his observation by a mixed state which was obtained by summing with equal probability over all the possible black hole states. One could still claim that the system was in a pure quantum state though this would be rather metaphysical because it could be measured only by an angel and not by a human observer. "

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  102. Carl,

    To add to your list

    4) Mathematical: "An incomplete theory of quantum gravity in AdS, such as a gravitational effective field theory (e.g. the standard model of particle physics including general relativity), defines an approximate or effective CFT. Finding a complete theory of quantum gravity, a ‘UV completion’ for any given EFT, amounts to finding an exact CFT that suitably approximates the effective CFT. Among other things, this means that we can make exact statements about quantum gravity by studying CFTs. General theorems about CFTs can be re-interpreted as theorems about all possible theories of quantum gravity in AdS."

    (source of quote: Lectures on AdS/CFT from the Bottom Up
    Jared Kaplan
    Department of Physics and Astronomy, Johns Hopkins University)

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  103. Geez. My last post was meant to be an invitation to discuss something (slightly) different, not to bring this saga to a crashing halt!
    :D

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  104. Hi All,

    Google seems to have made some changes to the comment feature, and one of the consequences is that I no longer get the comments myself. I have no idea what's going on, but that's why I haven't posted comments for some days.

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  105. bhg,

    Well, after a full year of going back and forth we have finally come to an end and I can finish my paper and submit it! Thank you for all of the time you put into this, although as Carl says it would not have taken nearly as much time if you had produced an exposition as clear as this one at the outset. Assuming that your expertise allows you to stand in as a spokesman for the HEP community here, I can think of no grounds to discuss this topic any farther. Carl has suggested some other issues, and maybe the people who have been following along can settle on one.

    Your recent post finally makes evident—which in my obtuseness I had never cottoned on to—that using the interpretive principles you advocate not only can Black Holes in AdS/CFT not think to zero size and have their event horizon disappear, they cannot shrink at all. Because the argument that black holes can shrink (which was, of course, a huge shock when Hawking announced it) depends critically on the appeal to negative energy modes (as judged from infinity) to account for the shrinkage. But you now assure us that there can be no negative energy modes in the CFT (because that would obviously lead to degeneracies in the spectrum) and since (by hypothesis) everything that happens in the AdS happens (dually) in the CFT, it follows that there are no negative energy modes (as judged from the boundary) in AdS. So if there are black holes at all in the AdS physical Hilbert space, then they just don't shrink, and I suppose they just don't emit Hawking radiation either. If one were under the impression that all black holes emit Hawing radiation, then I guess the next step is to conclude that black holes just can't form in AdS. For all I know, that is true. But what conceivable bearing that peculiar fact about AdS has on our original question—which concerned black holes that emit Hawking radiation and do shrink—I can't for the life of me imagine.

    Now it might occur to someone to argue that *since* black holes can form in AdS if it is a decent theory of gravity, and since black holes *do* always emit Hawking radiation and shrink, what this really shows is that AdS/CFT is just a load of bunkum that has been leading research in HEP astray for a few decades. In fact, it might occur to me to argue that. But you have hedged your discussion around in such a way as to be impenetrable to such criticism: when talking to you about AdS/CFT it is a condition of having the discussion that AdS/CFT be accepted as absolutely correct. So I have no interest in pursuing that question with you at all.

    (Con't)

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  106. If you want to continue discussing some relevant issues here, I can think of a few. For example, the argument you gave made a critical move that conflates the von Neumann entropy of states with their statistical mechanical or thermodynamic entropy. Now such a conflation strikes me as highly questionable. The thermodynamic and statistical mechanical entropies of systems are, for example, necessarily extensive quantities, and the von Neumann entropy most certainly and strikingly is not. Indeed, it is exactly because of illegitimate arguments involving entropy like that that I have organized a Summer School devoted to the topic of entropy. But I have no appetite for further discussions with you along these lines since I'm not convinced that you have any particular expertise in that subject.

    As for your citation from Hawking, I can't for the life of me understand why you thought that posting it made some point against my insistence that my solution to the paradox is different from Hawking's. I have a virtually identical passage from him cited in my paper and discuss its errors at great length. Perhaps it will suffice to note that if one expected unitary evolution and information preservation at all in any quantum theory, it is only for the universal state. Preferably the universal state on a Cauchy surface, but certainly only for the universal state on a maximal space-like hypersurface in a non-globally-hyperbolic space-time such as AdS. But Hawking seems to want to only accord physical significance to quantities that can actually be measured, and no such universal state can ever be measured (obviously). So Hawking's opinions on these matters seem rather straightforwardly worthless from the get-go.

    I have learned quite a lot from this exchange, and that knowledge will do me—and maybe other people working in the foundations of physics—a tremendous service. So thanks again.

    Adieu.

    Tim Maudlin
    Professor of Philosophy
    NYU

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  107. bhg,

    We're not talking about the same states. You have a set of fields in the bulk, let's call them \Phi. The \Phi's include the metric itself. These states have some values on the boundary. The boundary values are the only information I give you. My point is that if the values are identically zero in a region \epsilon > 0, you don't have sufficient information to reconstruct the full state. What you are saying is that if you have information about the bulk in the CFT states on the boundary, you can reconstruct the bulk. I have no reason to doubt that, but it's not particularly insightful.

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  108. Bee,

    reconstruction procedure bhg refers to only works if bulk satisfies correct equations (in large N limit, classical gravity+fields or classical string theory). Boundary will not reproduce unphysical bulk. That is feature not bug. All fields zero outside some region might be OK as initial condition, but probably will not remain true for all time if equations are satisfied.

    Also, there are non-local operators in CFT, like Wilson loops, that measure bulk far from boundary.

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  109. Tim,

    many things are confused and wrong in your post. Take this "The thermodynamic and statistical mechanical entropies of systems are, for example, necessarily extensive quantities, and the von Neumann entropy most certainly and strikingly is not."

    This is nonsense. Von Neumann entropy of thermal ensemble is extensive and is same thing as statistical mechanical entropy. It is the definition of statistical mechanical entropy.

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  110. Bee,

    It's not clear what you are asking. The fields \phi are quantum operators. It makes no sense to say that these operators "vanish" near the boundary. Maybe you mean their expectation values? If yes, the point is that the information in the state is contained in the full set of correlations of the quantum fields near the boundary. The 1-point functions are only a tiny bit of this information, and of course they are insufficient to determine the state -- that's obvious, but also irrelevant. The point is that the full state can definitely be reconstructed from knowledge of all the boundary correlators, which is the data that maps onto the CFT.

    Anyway, if you restate your question in a more precise fashion I will answer it, if I haven't already.

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  111. Tim,

    I am glad that you now accept that your scenario is incompatible with AdS/CFT, although it is unfortunate that you are drawing the wrong lessons from this. Overall, I think this exchange provides a fairly effective case study of why philosophers have not made any important contributions to physics and are unlikely to do so. In reading your post I am reminded of lines from Steven Weinberg's essay "Against Philosophy", for example, "The insights of philosophers have occasionally benefited physicists, but generally in a negative fashion—by protecting them from the preconceptions of other philosophers." In the present case, you are quick to label AdS/CFT as vague nonsense because it does not fit with your preconceptions, but since you are not familiar with the technical guts of quantum gravity, your preconceptions are leading you astray, much like someone in the early 20th century might have insisted on being able to simultaneously determine position and momentum. It really is important to understand technical details to make progress in theoretical physics -- a vague word level understanding just will not do.

    An example of this is your statement "The thermodynamic and statistical mechanical entropies of systems are, for example, necessarily extensive quantities, and the von Neumann entropy most certainly and strikingly is not.". I am afraid you are misinformed about the basics of entropy. First, statistical mechanical entropies are not necessarily extensive; i.e. microcanonical entropy in general contains not just volume terms but also subleading terms, so for a small system this entropy is in no sense extensive. And for the case at hand, namely the radiation as computed by Hawking, the von Neumann entropy is extensive, contrary to what you say, since its density matrix is thermal, according to Hawking, and it fills a large volume.

    The Hawking quote I provided nicely characterizes his position but flatly contradicts your summary of what he supposedly claims. Again, I cannot for the life of me see what you have added to the story. Hawking clearly states that there is unitary evolution for the system as a whole, but not for the part of state that is accessible to an external observer. Since the part of the state that disappears behind the horizon is fundamentally inaccessible to an external observer, this represents a loss of information of a sort not present in prior physics (e.g. in the absence of black holes one can always work in a perfectly sealed lab so that the full state remains accessible.

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  112. bhg,

    I primarily had in mind the metric which, so my understanding, is classical in the limit under consideration. But ok, so let me phrase this question more precisely (or at least attempt to do so). Suppose I give you all n-point functions for the bulk fields, evaluated at the boundary. You can use these to reconstruct bulk states, fine. How do you know that these are all bulk states that can come about from all possible initial conditions (that being initial conditions on a spacelike bulk slice plus boundary values)? The correspondence itself simply postulates that this is the case, it doesn't prove it.

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  113. Physphill,

    Could you clarify what you mean by "correct equations" and "unphysical"?

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  114. Bee,

    I mean not every set of bulk equations will agree with given specific boundary CFT. Some bulk equations will not agree with any boundary CFT. Free equations in bulk will not match general interacting CFT. Interactions of one determine the other. Also QFT without quantum gravity in bulk will not match any CFT.

    If you say something like metric is interesting inside, but exactly AdS outside, and stays like that for all time, it is probably not a solution to Einstein's equations or string theory equations and is not dual to any CFT.

    " How do you know that these are all bulk states that can come about from all possible initial conditions (that being initial conditions on a spacelike bulk slice plus boundary values)? The correspondence itself simply postulates that this is the case, it doesn't prove it."

    Correspondence itself is a conjecture, it is not proven. Something like what you ask is impossible to prove I think because there it requires non-perturbative bulk theory of quantum gravity that does not exist.

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  115. Bee,

    I agree that it it's an assumption, but I would emphasize that it's a self-consistent assumption. If some independently defined bulk QG theory includes states that are not in the CFT Hilbert space, then indeed AdS/CFT will not describe this theory in full detail. But AdS/CFT manifestly describes a consistent theory of QG (or perhaps a "sector" thereof) in which includes, for example, all of the "expected" states arising from a scalar field weakly interacting with gravity, with no "analyticity" requirements or anything of that sort.

    I would make an analogy with S-matrix theory in flat spacetime. This is built on the "assumption" (in the above sense) that the space of scattering states is complete, but you could imagine a theory that contains states that are neither created from nor decay into scattering states. Of course, no such theory is known.

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  116. Tim Maudlin wrote:
    The thermodynamic and statistical mechanical entropies of systems are, for example, necessarily extensive quantities, and the von Neumann entropy most certainly and strikingly is not.

    Let me see if I understand.

    I assume thermodynamic entropy is the Carnot/Clausius one.

    Von Neumann entropy is that computed from the quantum density matrix; and has the property that the entropy of a system can be less than the entropies of subsystems because of entanglement (which is how in a pure CFT state and hence pure AdS state, a black hole can nonetheless have non-zero entropy). So it is not extensive.

    Statistical mechanical entropy is I assume the one computed from occupation numbers of micro-states? It is then extensive.

    Is the above right?

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  117. bhg,

    Once again I find myself agreeing with you... Funny, in some sense, how we seem to draw different conclusions from the facts.

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  118. Physphill,

    "If you say something like metric is interesting inside, but exactly AdS outside, and stays like that for all time, it is probably not a solution to Einstein's equations or string theory equations and is not dual to any CFT."

    I don't know about string theory but about Einstein's equations I don't see what would prohibit it. (See Tim's earlier remarks about gluing etc.) Depends of course what you allow as sources. In any case, as I said before, I have little doubt you can self-consistently formulate this duality. But if you constrain the states in the AdS bulk so that they have a boundary CFT dual qua assumption I don't see how that's relevant to asymptotically Minkowski space (see earlier exchange). Best,

    B.

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  119. Bee,

    I would like to better understand your position. Let me pose the question this way. Do you think there is some concrete measurable phenomenon, in asymptotically AdS or Minkowski, for which AdS/CFT would either a) give the wrong answer or b) is incapable of providing an answer? If so, the question is of course why you think this, beyond simply having a hunch that this is so.

    I would like to focus on some measurable phenomenon here that have a concrete experimental implementation, not on questions like "why are the laws of physics the way that they are". Also, let us grant ourselves arbitrarily strong computational power, as well as the ability to engineer CFTs that have, say, the particle spectrum of the Standard Model.

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  120. BHG,

    It's pretty unwise to take such a dismissive attitude towards philosophy. Every scientist comes to the table with philosophic dispositions. Anyone who thinks that they don't almost surely has terrible philosophic dispositions because they've never taken the time to criticize them.

    It's unfortunate that more people with technical skill don't think about supposedly philosophical problems. The measurement problem in quantum mechanics is the most serious problem in all of physics, and hardly any physicist can be bothered to think about it, even though they could probably make great progress in it if they would just listen to the first steps that the philosophers have taken.

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  121. Arun,

    Yes, that's it exactly. The place to be careful is in the statistical mechanical part. There, there are two approaches: Boltzmann and Gibbs. For Boltzmann, the entropy is an individualistic quantity: a single system has an entropy that evolves through time. The Boltzmann entropy is a function of a partition of the phase space, and measures the log of the volume of phase space that belongs to the element of the partition that the system is in. By talking the log, the quantity becomes additive when you consider a pair of systems as a single system.

    The Gibbs entropy is a strange beast. It is a function not of the state of an individual system but of a probability measure over the phase space. So either you are dealing with an ensemble of systems, or an epistemic state, or something. The main virtue of the Gibbs entropy is that it can be easy to calculate. If you can show that the Gibbs value is within epsilon.

    Von Neumann is something else altogether and is not extensive. And Shannon yet something else again. But physicists confuse these all the time, and get into a mess.

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  122. bhg,

    The obvious example is black hole evaporation, but we already discussed this above. Of course I don't know what will happen. But, as I believe we agreed, you use AdS/CFT to force some nonlocality onto the black hole on horizon distances. This nonlocality isn't there if you simply evolve forward whatever field theory you have in semiclassical GR (to which you can add perturbative QG if you like).

    Now you can say of course that you believe the AdS/CFT result is the correct one, or maybe that you hope one day someone will figure out how to put a CFT on asymptotic infinity in the limit \Lambda \to 0, but at least presently there's a gap in this argument. This difference is measurable, at least in principle. So they can't both be right - either the evaporation does or doesn't preserve the BH entropy.

    I don't think there's anything local you can do to tell a difference.

    Having said that, upon further thought something remained unclear to me about your earlier explanation with the delta-functions. Suppose you put a delta function (or several of them) on a bulk slice, and you have those encoded in the boundary correlators. Which initial conditions are you still free to choose? Do the initial conditions on the bulk-slice fully determine those on the boundary? Somewhat confused here because I was under the impression you actually need the boundary initial values in addition to the bulk initial conditions to evolve the bulk state forward. Best,

    B.

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  123. travis,

    "It's pretty unwise to take such a dismissive attitude towards philosophy. [...] The measurement problem in quantum mechanics is the most serious problem in all of physics"

    Agreed, except that I'd say one of the best things about philosophy is that it can help physicists identify which problems really are serious problems in physics. The measurement problem / non-problem is a case in point (see e.g.).

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  124. Bee,

    In the CFT we of course need to specify the Hamiltonian and the state at time t_0, and then we get unique evolution forward in time. Note that we are allowed to vary the Hamiltonian in a time dependent fashion by adding sources, and this is part of the AdS/CFT setup. In the bulk we need to specify the bulk Hamiltonian, along with boundary conditions (which are in correspondence to the sources we might choose to add the H_CFT) and the initial state at t_0, and then we can integrate forward in time. If I interpret your question correctly, you were asking about boundary conditions in the bulk description, yes? There is usually a unique choice for these boundary conditions that preserves all the symmetries, and we choose these if we want to have a bulk theory dual to the CFT without added sources.

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  125. Travis,

    Yes, physicists have preconceptions just like everyone else, and one should of course examine these. But one also needs to understand technical details to make progress in physics, not just the general word-level concepts. Note that I quoted Steven Weinberg, easily one of the top handful of theoretical physicists alive today. He has in fact someone has spent considerable time working on foundations of QM, although I doubt that he (or most other physicists) would regard this as one of the most important problems in physics. Anyway, rather than invoking generalities, perhaps you can come up with some counterexamples: what is a case where philosophers have played an important role in solving a problem of interest to physicists? In case it isn't clear, I am not bashing philosophy, philosophers, or philosophy of science, just making the statement that philosophy and philosophers tend not to be useful to physics, and I think history supplies ample evidence for this claim (again, see Weinberg).

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  126. BHG,

    I would definitely consider Einstein a philosopher, even though he was also a physicist. John Bell, another physicist/philosopher contributed the knowledge that any single-world theory which is consistent with QM must be nonlocal, although most physicists haven't fully grappled with that yet. I agree that examples of philosophers contributing to physics is rare, but I also think we're in an unusual situation where most physicists believe Bohr and Heisenberg when they argued that there's nothing serious to worry about in QM. So I guess we're in kind of the situation Weinberg described: we need philosophers to protect us from Bohr and Heisenberg's very confused philosophy.

    You're right that most physicists don't consider the measurement problem to be one of the most important, and it's baffling to me. It's basically telling us that we don't actually have any theory of the world at a fundamental level; we only have a procedure that we can carry out to get observations which has worked so far. "Measurements" are not fundamental constituents of the universe, and it's an embarrassment that our most fundamental theory contains them. Actually finding a real physical theory of the world should be our most important goal; it's kind of the whole point of physics.

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  127. Travis,

    Since it has come up, Weinberg is a perfect example of the errors even the top physicists can fall into when they do not really understand foundational issues. In his most recent popular book, To Explain the World, Weinberg completely screws up on the issue of the physical significance of rotating coordinate systems in GR. This is something that Newton had worked out, but of course the average physicist has never read a word of Newton. Weinberg has, but he didn't understand it. He explemplifies the way physicists can fail to really grasp the basics of the theories they work with because they just solve equations without understanding the supporting theses that give the equations physical implications.

    The most philosophically acute physicists of the last century were Einstein and Bell, followed by Schrödinger. The most incompetent was certainly Bohr. You make the call about who did better.

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  128. bhg,

    Do you mean that if you have a boundary condition on a slice t_0 in the bulk, the boundary state (of the bulk fields) is entirely determined by that?

    Everyone,

    I spoke with Weinberg about the measurement problem and you can read all about that in my awesome book.

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  129. Travis,

    "I would definitely consider Einstein a philosopher, even though he was also a physicist."


    Einstein "also a physicist". Hmm, that is an unusual way to put it. I think by any reasonable definition Einstein and Bell were physicists: they certainly had the standard training of physicists, worked and collaborated with other physicists etc. Your examples here prove my point: it is precisely because they had that background that they were able to make advances in physics, some of which were also of interest to philosophers. Can you name anyone with a typical philosophy background who has made an impact in physics within the past, say, 100 years? Or any important physicist alive today whose contributions to physics have been aided by philosophers, as I have defined the term? I am not aware of any such examples.


    The most interesting work by far going on in foundations of quantum mechanics concerns quantum information theory, quantum computation, etc. This forces one to think deeply and concretely about the implications of entanglement, quantum non-locality etc, in a way that is much more penetrating than anything I have seen written by philosophers. But again, and I could be mistaken here, I am not aware of philosophers playing any significant role in these advances, even though there are non-physicists (e.g. computer scientists and mathematicians) playing such a role.


    I think you are wrong in saying that most theoretical physicists today just blindly accept the Copenhagen Interpretation of QM. Many would agree that we are missing some pieces of the puzzle. Of course, there are many basic issues in physics that we don't understand, and this is just one of them. The question is how to proceed. Perhaps you think that philosophers will play some important role here, but I am exceedingly skeptical, more or less for the reasons Weinberg explains.


    And again, I think everyone should study at least some philosophy for the intellectual thrill, just don't expect it to be helpful for doing physics!

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  130. Bee,

    "Do you mean that if you have a boundary condition on a slice t_0 in the bulk, the boundary state (of the bulk fields) is entirely determined by that? "


    I am sorry but I cannot parse this. What does "boundary state of the bulk fields" mean? Do you mean the CFT state that is dual to the bulk state? Or are you referring to some feature of the bulk state defined at the boundary of the bulk? I can't tell, and if you mean the latter I don't understand the question because the bulk state is defined over the entire bulk.

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  131. "John Bell, another physicist/philosopher contributed the knowledge that any single-world theory which is consistent with QM must be nonlocal, although most physicists haven't fully grappled with that yet."

    Physicists and philosophers would be better advised to brush up on their understanding and interpretation of [quantum] probability and grapple with the misconceptions that led Bell and still lead others to such... premature conclusions. "Bell locality" is not locality* and there is no inconsistency in QM as a local single-world theory.

    * "Hence Bell locality is violated by quantum mechanics, but this does not imply
    that “quantum mechanics is nonlocal” (as some say). Bell’s is a very specific locality
    condition [P.I. + O.I.] invented as a constraint on hidden variable theories." --Landsman.

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  132. Travis,

    Also, the S in CHSH is Shimony. Abner was a philosopher. It is not a coincidence that among the first to appreciate and contribute to the generalization of Bell's 1964 paper was a philosopher.

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  133. Travis,

    It is also an extremely difficult question how one should understand the fate of the philosopher Grete Hermann. She was the first person to correctly diagnose the fatal flaw in von Neumann's supposed no-hidden-variables proof and publish the result. It was completely ignored. How much it contributed to this that she was a philosopher and that she was a woman is impossible to tell, but if she had been appreciated, literally decades of confusion would have been avoided.

    It is more than ironic that physicists claim that philosophers have been of no help when the reason that is true is because they ignore what the philosophers have been saying.

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  134. bhg,

    I am trying to understand your sentence:

    "There is usually a unique choice for these boundary conditions that preserves all the symmetries, and we choose these if we want to have a bulk theory dual to the CFT without added sources."

    I am not sure what "these boundary conditions" refers to. When I say "boundary state of bulk fields" I mean the limit z->0 of the bulk fields, not the CFT fields. Of course the bulk state is defined over the entire bulk, I was asking for the initial conditions. What are the initial conditions for the bulk state? Best,

    B.

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  135. Paul,

    Could you let me know what P.I. and O.I. refers to?

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  136. "It is more than ironic that physicists claim that philosophers have been of no help when the reason that is true is because they ignore what the philosophers have been saying."

    Definitely. I agree with BHG that there aren't very many people with traditional philosophy backgrounds that have made an impact in physics, but it's definitely true that a lot of the people in physics who have made the biggest impact were well-versed in philosophy. The idea that philosophy won't be helpful for creating new scientific theories seems absurd to me; how can you figure out how to go beyond the current theory if you don't fully understand what the current theory is saying? I would venture to say that understanding the philosophical implications of our theories is more important than ever, just because they are more removed from everyday experience than ever before and so sloppy thinking can lead us down more blind alleys.

    I would argue that the measurement problem isn't just one of the basic issues that we don't understand. It's a fundamentally new problem (well, it's almost 100 years old now, but still) that we've never faced before in physics, which is why philosophy might be especially helpful. In all previous paradigm revolutions in physics, the old theory was replaced by a new theory which was capable of explaining everything in its own terms; it was perfectly understandable, when speaking in terms of the old theory, what was meant in terms of the new theory, and vice versa. In QM, for the first time ever, this is no longer true. We can't actually describe the outcomes of experiments without falling back on speaking in classical terms: the location of the pointer on this instrument is such and such, for instance, can't be translated into some approximation of QM. We can only describe our observations in terms of the old theory, and we merely use quantum mechanics to modify what we expect those observations to be. So we're in the weird position of not yet having a fully comprehensive new theory, but of only catching glimpses of it through modifications of the old theory, and yet getting amazing predictions nonetheless. This can be seen from the fact that we typically develop quantum theories by "quantizing" the classical theories. And then the "observables" are just plain old classical observables from the old theory.

    Paul Hayes:

    Bell's theorem combined with EPR shows that *all* single-world theories must be nonlocal, not just hidden variable theories. EPR showed that, unless there are hidden variables, QM must be nonlocal. Bell then showed that, even if there are hidden variables, QM must be nonlocal. You're right that he used a particular definition of local, but what other definition would you propose to use? In what other sense is single-world QM local?


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  137. Bee,

    Let a bulk field be \phi(x) and let the boundary be at z=0. The bulk quantum state can be thought of as a wavefunctional \Psi[\phi(x)]. The boundary conditions are that \phi(x) must fall off with some prescribed power of z as z goes to zero (the power depending on the mass of the field). For linearized scalar fields, the falloff condition is equivalent to finiteness of the usual Klein-Gordon inner product.

    If you hand me any such \Psi[\phi(x)] I can use the bulk Hamiltonian to evolve it forward in time. And (at least in some regime) we know the explicit map between such bulk states and CFT states. I.e. there is a commutative diagram involving mapping states back and forth and evolving with either the bulk or CFT Hamiltonian.

    Does that answer the question?

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  138. “Could you let me know what P.I. and O.I. refers to?”
    One can find it e.g. here (6.128). It is a notion by Jon Jarrett and Abner Shimony. Maybe Tim can tell more about it. And maybe Tim can also tell more about possible solutions to the measurement problem. I think here physics needs input from philosophy. This is a problem where we have to think really carefully, because the solution will affect all areas in physics.

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  139. Bee,

    Parameter Independence and Outcome Independence. (p 218). I think that "constraint on hidden variables", classical probabilistic, perspective can still leave you a little spooked. It's a lot less troubling from the general probabilistic, "constraint on noncommuting observables", perspective.

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  140. Paul Hayes,

    As you may or may not know, I have devoted more or less half of my career both studying and expositing Bell's work. You might want to read my book, Quantum Non-Locality and Relativity. In any case, I assert with all the conviction that you do, and more time having given it thought and discussing it with the entire foundations community, that Landsman is completely wrong here and Bell was completely right. As long as you believe that a computer that is not connected to the web or any other communication channel can replicate any local physics you like, then it is simple to prove Landsman wrong by a straightforward challenge. I hereby grant him three computers of whatever computational power he likes, and challenge him to reliably reproduce the GHZ phenomena by programming the computers however he likes. The computers are to be taken to three separate rooms where an input bit, either "X" or "Y", representing the choice to measure the particle in either the X or the Y direction will be provided. The choice is made however I decide. If there is anything in what Landsman says, then he should accept a wager. I will wager at odds of 1,000,000 to 1 that he cannot program the computers to replicate the GHZ predictions over a run of 1,000 experiments. Easy pickings if he is right. Conversely, if he refuses the challenge, and says he cannot do it, then what he says is just baloney. Deal?

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  141. Tim,

    I haven't read your book but I have read your "What Bell Did" paper and argued with you on Scott Aaronson's blog about that PBR theorem. Similarly to points made and missed there: Landsman isn't wrong. He's 'merely' making the distinction between [Einstein] locality and Bell locality (as other physicists and philosophers have), thereby avoiding being led into drawing wrong (ontic) conclusions.

    No deal. Sets of physical systems not appropriately described by probability theory as entangled can't be made, not even by clever programming, to behave as though they were. Landsman knows that and his (probable) unwillingness to accept a bet which he is certain to lose would prove nothing.

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  142. Travis,

    " The idea that philosophy won't be helpful for creating new scientific theories seems absurd to me; how can you figure out how to go beyond the current theory if you don't fully understand what the current theory is saying? "


    I agree with the second half of the sentence, but not the first. The last time theoretical physics produced a fundamentally new (and fully verified) theory was the development of the Standard Model in the late 60s early 70s. Weinberg was of course one of the central figures in this story, and his statements about philosophy are surely colored by this experience. As far as I know, philosophy/philosophers played absolutely no role in any of this. So this seems like an explicit counterexample to what you claim is absurd.


    I do hope that in say, 100 years, we will have a more satisfactory understanding of measurement in QM. But I strongly suspect that the key insights will come either from experiments, or indirectly from advances in other areas, like quantum computation, string theory, or cosmology. I doubt philosophy/philosophers will play any role -- I just don't see anything coming out of that community that is useful for physics, even though I am happy to accept that they are grappling with interesting philosophical questions, and don't mean to denigrate their efforts on those terms.

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  143. bhg,

    Thanks, yes, it answers the question. But now I'm perplexed because it sounds as if AdS is globally hyperbolic. What am I getting wrong here?

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  144. Paul,

    That is just a cop-out. A computer can simulate anything you can write down and calculate with. You want negative probabilities (as if that makes any sense!)? It's a snap for a computer to represent that. Or imaginary "probabilities" or whatever you like. If it is local physics, in the critical sense of local (I don't care to quibble about whose definition) then a computer that is not plugged into any source of information from the outside can simulate it. And conversely, if you can't simulate it, it ain't local. Landsman is just wrong, and I will put my money where my mouth is.

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  145. Bee,

    Sorry, I should have been more clear. To get unique time evolution for all time one needs to specify boundary conditions at all times. So one can, for example, demand that fields have normalizable falloff at the boundary for all times; this is the choice that preserves conformal symmetry. But one could alternatively say that for some period of time a given scalar field has some non-normalizable falloff at the boundary, and then the time evolution will be different (this is a consequence of the non-global hyperbolicity). The point is that this structure perfectly mirrors what happens in the CFT. Taking the CFT Hamiltonian to be H_CFT (with no added sources) corresponds to the normalizable falloff, while the non-normalizable falloff case is implemented by adding J(t) O_\phi(t) to the CFT Hamiltonian, where J(t) is precisely the coefficient of the non-normalizable mode in the bulk. So from the CFT point of view, the non-global hyperbolicity is just the statement that we have freedom to modify the CFT Hamiltonian by adding sources for local operators. It is quite lovely how it all fits together.

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  146. I think the word locality has two different meanings in circulation. Originally it meant “no superluminal conveyance of energy or information”, which was sometimes expressed as “no action at a distance” (with the literal physics meaning of action). This is indeed the definition one finds in many (most?) physics book, and of course quantum entanglement does not violate this kind of locality.

    In the discussions of quantum entanglement between Einstein and Bohr they never used the word locality, they talked about separability, noting that the outcomes of spatially separate observations are not separable in the sense that their wave functions can’t be factored into separate wave functions. This non-separability is what disturbed Einstein (he argued that separability is a sine qua non of science, although this may have been partly because he wasn’t clearly distinguishing it from locality), whereas Bohr embraced it.

    Then Bell came along and clarified the unavoidability of what Einstein had called non-separability, but Bell called it non-locality, and this usage then found its way into the literature, especially discussions of quantum entanglement. Bell’s choice was not accidental, because he was actually a neo-Lorentzian who explicitly stated that he believed quantum entanglement shows that “something is propagating faster than light”, and the “cheapest solution” is some kind of ether theory with absolute time, even though he acknowledged that this would conflict with Lorentz invariance. So, his use of the word “locality” to refer to what Einstein and Bohr had called (more accurately, in my opinion) separability was in line with his suspicion that quantum entanglement really did violate locality in the original physics definition of the word, i.e., superluminal conveyance of energy or information. Most people don’t endorse Bell’s neo-Lorentzianism, but many have nevertheless adopted his usage of the word “locality” - while never quite reconciling this with the original definition. This leads to a lot of confusion and arguments over definitions.

    I think it would be better to reserve the word “locality” for it’s original (and still prevelant in the physics literature) definition of “no superluminal conveyance of energy or information”, and use the word separability to refer to factorability of spacelike separated wavefunctions. With these definitions, quantum entanglement violates separability, but not locality. Others have suggested the compromise of just distinguishing between “locality” (no superluminal action) and “Bell locality” (factorability of spacelike wave functions).

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  147. Amos,

    All single-world theories must convey information faster than the speed of light, so by both definitions of local, QM is nonlocal. This doesn't mean that *we* can convey information faster than light, but it means that information of some kind must go faster than light in order to account for the outcomes of Aspect/GHZ-type experiment.

    BHG,

    Fair enough. The standard model wasn't fundamentally new though in the same sense that Newtonian Mechanics, Electromagnetism, General Relativity, and Quantum Mechanics were fundamentally new at the time they were invented. All of these theories required an entirely new conceptual way of thinking about the world; the standard model is just quantum mechanics applied to fields with certain symmetries (which isn't to say it isn't extraordinarily profound and interesting). To get to the theory that goes beyond our current understanding of quantum mechanics is likely going to require a conceptual revolution of the former type.

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  148. Tim,

    Why is it a cop-out? You want Landsman and his computers to play the GHZ game, but unlike the Wizard there you know about QT and won't let him have the 3-part correlated physical system he would need to beat you. Obviously he will refuse and equally obviously that doesn't mean that he, or anyone else, is wrong to make the locality / Bell locality distinction. It's your insistence on the conflation that's wrong (unwarranted) - like your insistence that the PBR proves more than it does. You want those of us who currently understand QM as "a generalisation of probability rather than of mechanics" to realise our error(s) and repent, but you won't achieve that by such easy means.

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  149. bhg,

    I don't understand how you have 'freedom to modify the sources' in the CFT. The CFT ought to have a unitary evolution, isn't this the whole point? How can you add information after you have already specified an initial condition at some time t_0?

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  150. Paul Hayes,

    Rather than arguing over definitions of locality, let's just ask this: do you agree that information of some kind must travel faster than light? This is what Bell's theorem shows, and it is striking regardless of what definition of locality you want to use.

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  151. Bee,

    I don't understand your objection. Yes there is unitary evolution. All I am saying is that you have the freedom to choose the Hamiltonian to be time dependent, and study the unitary evolution with respect to any such choice. And that same freedom appears on the bulk side as a choice of boundary conditions.

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  152. bhg,

    I am not objecting, I simply don't understand what you mean. Let me get this straight there. You say you put an initial condition on the slice t_0, that also gives you an initial condition for the boundary CFT at t_0. Since AdS is not globally hyperbolic, this doesn't entirely fix the time-evolution for the gravity-theory in the bulk, you also need some boundary values at all times. This is compatible with the CFT because you use a time-dependent Hamiltonian for the CFT (that basically couples in sources) to match that.

    Now, I can see that that would be unitary by construction, but it's in a rather trivial sense not even deterministic, is that what you're saying? Like, you know what's happening in the CFT if I give you the Hamiltonian for all times, but if I give you the initial state you can't tell? If that was so, then in what sense do you even solve the BH information loss problem - you couldn't even evolve the theory forward. Sorry, I don't get this matched up in my head, clearly I'm missing something here.

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  153. Paul Hayes,

    I can't understand what you are claiming here. How am I refusing Landsman anything? He can model the state of the source however he likes on his computers. He can use complex numbers or quaternion or octonians for all I care. You want to "generalize" probability, whatever that means? Be my guest: surely you have a clear mathematical model of how to do that, which you can use to your heart's content.What I won't let you do is take information about what choice of measurement was chosen in one room and convey it to another room.nBut if the physics is local, in any decent sense of local, then the information about what choice was made in one room just will not be available in any other room. And without it you are screwed no matter what "probability" you decide to use. If you mean that I will not let Landsman use an entangled quantum system, then you are right! that would beg every question.

    As for PBR, it proves what it proves: namely every psi-epistemic approach is dead. Period.

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  154. Paul Hayes,

    There's a reason that Tim and many others call Bell nonlocality simply 'nonlocality', and that is because it is more than sufficient for having, in some sense, "spooky action at a distance" of the kind that Einstein was unprepared to accept, and which classical thinking had mostly ruled out (setting aside Newtonian gravity!) for centuries. If the results of my experiments over here on Earth can be shown to depend on either the measurement setting chosen (simultaneously in my frame) on the Moon, or on the outcome of the measurement on the Moon (which I take to be an indeterministic event, if I reject hidden variables), that's bloody nonlocality! It doesn't matter that I can't use it to send a message or to teleport mass-energy faster than the speed of light. It's a goddamn connection between spacelike separated events.

    Now, you are free to define locality/nonlocality in some more stringent sense if you like, and then declare that QM is local. But if it makes you feel comfortable, feel like there's nothing puzzling going on in EPR or GHZ experiments, then I'm afraid you really don't understand those phenomena - or you have lulled yourself into thinking you there's nothing puzzling here after all because you can represent it with a fancy nonstandard probability apparatus.

    Your explanation of why Landsman would refuse Tim's wager is telling: Sets of physical systems not appropriately described by probability theory as entangled can't be made, not even by clever programming, to behave as though they were.
    'Entangled' is, indeed, what they are; what happens here on Earth depends on what happens on the moon at the same time. That's what I (and anyone ought to) call nonlocal influence. Building that influence into your probability representation doesn't make it any less a genuine physical phenomenon.

    But I am also puzzled about why you think that in QM there is no violation of Einstein locality (defined as faster-than-light transfer of energy/momentum). Suppose I send electrons, one at a time, through some appropriate beam-splitter that directs them to opposite ends of my lab where I have detector screens in place. The QM story is that the electron is not fully on one side or the other until detected. So if we ask "where was the mass/energy of the electron prior to detection?, the honest answer would have to be: on both sides of the lab, equally, in the instants just prior to detection. (The mass/energy expectation, you might prefer to say, is equal on both sides of the lab just before impact. Massage the language however you like.) But once the detection happens, instantaneously we must say that all of the mass/energy is on one side. That sounds an awful lot like an instantaneous transfer of mass/energy from one side of the lab to the other, if you ask me.

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  155. Bee,

    Consider a forced harmonic oscillator. This is clearly a deterministic system, but to determine the evolution to some final time it's not enough to know initial conditions, I also need to know the force function F(t) for all times between now and the final time. The situation in the CFT is the same: I choose the "forcing function" and then I can evolve forward in time given some initial conditions. This is still totally unitary, deterministic etc. More generally, you need to know the dynamical equations for all relevant times as well as the boundary conditions, and AdS/CFT conforms to these standard rules.

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  156. travis,

    No, I don't agree with that. Bell's theorem doesn't show it and proper definitions of locality can't be disregarded.

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  157. Paul,

    That paper says nothing about whether the wave function collapses. It also doesn't mention any hidden variables. So the only interpretation they can be working in is the Everett interpretation, and indeed it is still unknown whether the Everett interpretation is local or not, which is why we have to be careful to preface the results of Bell's theorem by specifying that it only deals with single-world theories.

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  158. Tim,

    I'm claiming that the impossiblity to program computers to 'know' things they can't 'know' in this GHZ game case dosn't imply the ontic nonlocality which you take it to imply. Quantum "nonlocal" correlations can be "spookier" than classical "nonlocal" correlations, but they're still just correlations. All this stuff is very old and I don't understand why you don't understand it. The generalised probability framework in which such phenomena are most clearly understood not to imply such 'spookiness' is also very old, yet say you don't know what I mean by that either. You've spent half your career studying these things, and I've referred you to Summers and Redei's paper and Tao's article and other resources before, but you still don't know what I mean by it?!

    Likewise, I've tried to explain to you why PBR clearly doesn't prove that "every psi-epistemic approach is dead" (a fact pointed out in the paper itself) and referred you to the much better explanations by Yemima Ben-Menahem and Matt Leifer. Yet you just dismiss all this and reassert your false claim.

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  159. All single-world theories must convey information faster than the speed of light, so by both definitions of local, QM is nonlocal.

    I think non-relativistic QM is actually non-local, not because of quantum entanglement, but because it is, well, non-relativistic (and hence wrong), having no finite upper bound on the propagation speed of energy, etc. For relativistic quantum mechanics, I don’t think any energy or action propagates faster than light (outside uncertainty), and I don’t think localized information can be propagated without energy.

    This doesn't mean that *we* can convey information faster than light, but it means that information of some kind must go faster than light in order to account for the outcomes of Aspect/GHZ-type experiment.

    When you say “information of some kind”, are you talking about hidden variables? Because if not, then there is no hidden information. The choices of measurements and results at each end of the EPR experiment are available to us, and they don’t provide any information from the other side of the experiment.

    I don’t think the existence of spacelike-separated quantum correlations implies that information propagated directly across the spacelike interval. After all, for two spacelike separated events (such as people making measurements at opposite ends of an EPR experiment), each of them precedes the other in some inertial coordinate system, so in which direction would the information propagate? The situation is symmetrical. And it wouldn’t just be “faster than light”, it would be backward in time (in some frames). You might say information “propagates in both directions” along the spacelike interval between A and B, but that’s saying the results at A are conditioned on the results at B, which are conditioned on the results at A. It’s a chicken and egg explanation unless we simply admit that the results are not separable, and not try to claim information is flowing asymmetrically from A to B (or from B to A).

    Moreover, the correlations don’t logically require any superluminal flows of information. Even from the standpoint of classical causality, every pair of spacelike separated events in Minkowski spacetime shares some common causal past, so as Bell himself said there is always the “super” deterministic option, and there are others as well. This is not to say that any one or the other of these options is correct, but merely that the existence of quantum correlations doesn’t logically imply superluminal propagation of information.

    I don’t think the subject of “information” and how it moves from place to place is completely settled. Correlations between separate events might be regarded as “non-local information”, but even that is questionable. To give a stark example, suppose you believe in free will, and suppose that, of your own free will, you think up a string (s1) of binary bits in one location A, and some stranger thinks up a string of bits (s2) in a different location B, spacelike-separated from you. By the stipulated free will, these strings are “new information” at the respective locations (not implicit in antecedent conditions). Someone in the future light cone of A can see s1, and someone in the future light cone of B can see s2, but what about the correlation between those strings? No one has access to the string s1 XOR s2 until the future light cones of A and B intersect. For any event outside the intersection of those future light cones, at least one of the string selections is not yet in the causal past, so can we say the correlation even exists? What is the actual flow of information? It would be nice to have something like a Poynting vector giving the "information flux" at any point as the cross product of… something. But that assumes information is localizable.

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  160. Carl3,

    I'm afraid it's your understanding that's deficient: there is no spooky nonlocality in quantum correlations and good explanations abound (e.g. here).

    The idea that there is ontic superposition (facilitating FTL energy transfer) - and that that really is the QM story - is even worse. The honest/sane answer to the question "where is/was the [mass/energy of the] electron before detection" is the same in quantum probability as it is in classical probability: "we don't know".

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  161. Paul Hayes,
    the article you link defines Einstein locality as follows: the observables in spacelike separated regions commute. If you think this is the only "proper" definition of locality, you're welcome to your opinion. But there are other notions of locality/nonlocality, and other people have the right to consider them important as well.

    Einstein locality as defined above is one way to capture the idea that measurements in one region cannot reveal what's going on in the spacelike separated region, and hence, there is no FTL communication possible between the regions. This does not mean that there is no "transfer of information" between the two regions in a distinct sense, one not linkable to communication. This other sense is what Travis is talking about. Now, if you want to deny that there is any such transfer of information in this weaker sense, then you should be happy to assert that the results of experiments in one of the regions do not depend in any sense on what goes on in a spacelike separated region. And then you should be willing to take Tim's wager. Because you are endorsing the claim that whatever happens in one of the regions is entirely independent of what happens in the spacelike separated region; that other region might just as well not exist, for all we care when modelling or describing what happens in our region.

    But we both know that this is wrong, and you won't take the wager. The results in one region do depend on what happens in the other region -- just not in a way that lets us talk to each other FTL.

    Again, if you want to say "that's not nonlocality in a sense I care about", fine. But others - both philosophers and physicists - do care about it and think it is important and interesting.

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  162. Regarding Bell and locality, it is strange there is so much dust thrown about this. Simple, precise, correct definition of local is that operators commute outside lightcone. They do commute.

    As yourself this. Do you agree correlations over distance in classical physics do not indicate that classical physics is non-local? If you do not agree, you have a strange definition. If you agree, you can create EPR situation just by replacing real probabilities by complex amplitudes (plus Born rule for measurements) and considering correlated (entangled) system over distance. Correlation is created by past event just like in classical physics. Is replacing real probabilities with complex amplitudes non-local? No. Is Born rule non-local? No. So, why do you say QM is non-local? Correlations over distance are there also classically.

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  163. Bee,

    regarding metrics that are exactly AdS outside, you wrote

    "I don't know about string theory but about Einstein's equations I don't see what would prohibit it. (See Tim's earlier remarks about gluing etc.) Depends of course what you allow as sources. "

    Yes, it depends on allowed sources. If exactly AdS outside it means ADM mass is zero. That means some negative energy must balance positive energy in change in metric/fields. Some kinds of negative energy might be OK, but some are certainly not consistent with AdS/CFT. For example, (large) violations of null energy condition.

    Anyway, even if it is allowed, it is not invisible to CFT. Some operators in CFT are not local, like Wilson loops. I think those probe interior, not just boundary values.

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  164. bhg,

    Thanks for your patience. After some head-scratching I think what you say actually agrees with my previous understanding, just that it wasn't really clear to me you want (need?) to change the Hamiltonian. I was thinking you put an initial condition on a bulk slice, which gives you an initial condition for the CFT and the Hamiltonian evolution from the CFT gives you the missing boundary condition for the bulk theory. You seem to be saying now (please correct me if wrong) that this is only one specific case and that you can instead change the Hamiltonian by custom-designing source-terms, which generates a variety of boundary conditions.

    Regarding determinism, I think we're using the term in different ways. I'd say if you can't predict the state of a system at t>t_0 from the initial condition at t_0, then it's not deterministic. In any case though, let me just ask the following question: If I give you a CFT state at a time t_f, can you calculate what was the state at t_0<t_f. The answer, for all I can tell from your above explanation, is "no" because I'd also have to tell you the time-dependence of the Hamiltonian. If that is so, then in what sense does AdS/CFT solve the black hole information loss at all? I don't get it. Best,

    B.

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  165. Physphill,

    Commutation at spacelike separation means nothing for locality so long as we interpret the wavefunction as being ontologically real, as PBR forces us to. What happens when you observe one of the observables that commutes at spacelike separation? The wavefunction collapses everywhere, if you're using a collapse picture. That's massively nonlocal. If you're not using a collapse picture, then you have to use hidden variables, and then Bell's theorem kicks in.

    Of course classical correlations exist, and they are not mysterious. The whole point of Bell's analysis was to explore whether the correlations in quantum mechanics can be of that non-mysterious type, i.e., things interact and are correlated when they separate. It turns out that this is impossible: there is no way to produce the observed correlations by having the systems interact in their past light cone and then separate. Try Tim's experiment: program three computers however you want so that, after they separate, three different users choose an input and the outputs must be obey the rules of GHZ. You provably can't do it, even though you can easily create any type of classical correlation that you like.

    Amos,

    Bell's result does not depend on any particular formulation of QM, relativistic or otherwise. It depends only on the actual observed outcomes of Aspect-type experiments. He assumes only that the polarizer directions are uncorrelated (they can be "freely" chosen), and shows that there's no way for the observed correlations to happen without communication between the two sides of the experiment.

    The "information of some kind" basically must be hidden variables. If it's not hidden variables, then there is just collapse of the wavefunction, and collapse is very nonlocal as I mentioned above. If there is neither hidden variables nor collapse, then you have Everett, and Bell's theorem doesn't apply to Everett.

    As for superdeterminism: anything at all can be explained by superdeterminism, so it is not scientific. Tim, Travis Norsen, Hans Westman, and I spent a good part of two months arguing with 't Hooft about the implications of Bell's theorem, and this got brought up a lot: https://www.facebook.com/tim.maudlin/posts/10155641145263398?pnref=story

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  166. travis,

    "That paper says nothing about whether the wave function collapses. It also doesn't mention any hidden variables. So the only interpretation they can be working in is the Everett interpretation"

    Not true. Like Tim, you seem to believe that single-world, "radical psi-epistemic" [aka "neo-Copenhagen"] interpretations have been ruled out. They haven't.


    Carl3,

    Considering other notions of locality - and even calling them by that name - is fine so long as a) they're properly defined and they're not conflated with other notions of locality and b) false conclusions aren't drawn from them - perhaps because of a failure of a).

    And I'm certainly not going to disagree with your last remark: I've been drawing on the work of philosophers and physicists who I believe really do care about the different senses of locality.

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  167. Bee,

    There is one particular choice which preserves the conformal symmetry, namely don't add any source terms to the CFT Hamiltonian and in the bulk demand normalizable falloff for all fields. So if you like, you can just focus on this case, which is picked out by symmetry and satisfies all your desired conditions.

    For any deterministic system, to evolve in time I need to know both initial conditions and the equations of motion. In any QFT I always have the freedom to add time dependent sources, but I wouldn't say that means that QFT is not deterministic. In our world we observe translation invariance of the laws of physics, which means that there are no spacetime dependent source terms; but this is of course really an assumption, since how do I know such a source terms won't turn on the day after tomorrow?

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  168. Physphill,

    They wouldn't actually be able to create entangled states but it's a good point. Max Born once said,

    It is misleading to compare quantum mechanics with the deterministically formulated classical mechanics; instead, one should first reformulate the classical theory, even for a single particle, in an indeterministic, statistical manner. After that some of the distinctions between the two theories disappear, others emerge with greater clarity.

    And of course CM has been reformulated in the general probability framework and compared with QM.

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  169. Since Physphill has already agreed with me I am emboldened to describe the thought experiment which occurred to me on this issue (which I previously suggested in a different thread at this site, in passing).

    Joe is getting rid of his marble collection and has two left, one red and one blue. He asks his friends Bob and Alice if they would like one, and if so, which color they would prefer. Both ask for red, so he tells them, "I will flip a perfect coin to decide who gets the red, then mail both marbles and when you open the boxes you will know who got red and who got blue."

    Bob gets his box and opens it to find he has a blue marble. Instantaneously he knows that Alice has or will get the red marble, although she is far away. Spooky information at a distance? No, in my thinking it is a deduction based on previous information (the above scenario) and local information (the blue marble); and it could be wrong. The other marble might have been lost in the mail, or maybe Joe is color-blind and thought he had a red marble but actually had two blue marbles. To be certain, Bob should visit Alice and observe her marble.

    I am willing to extend this to the QM case in which the marbles are replaced by two particles with complementary but as-yet unobserved properties. Physicist Bob measures the property of his particle and instantaneously deduces, based on his knowledge of QM, that Alice's particle has the complementary property. Again, he could be wrong - maybe the experiment was screwed up, or something happened to the particles during transportation. To be sure he should go and measure the other particle.

    That is not Bell's experiment, which is more complicated and adds the mathematical properties of QM, but again the certainty of the outcomes is assumed by deduction in advance of observational proof. Deduction is the spooky action, it seems to me.

    What if there are no observers and/or no deductions? Is there Platonic information which gets transferred? Philosophy may be interested in that question, but I don't know how science can answer it. It may be a matter of personal taste.

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  170. Paul Hayes,

    All this stuff is very old and I don't understand why you don't understand it. back atcha, mate.

    The combination of Bell's theorem plus experimental verification of violations of his inequality with spacelike separated measurements demonstrates that nature is nonlocal. Period. Bell understood this, as have thousands of physicists since 1964. If my understanding is deficient, so is that of thousands of your colleagues.

    Caveats: Yes, I know there is still the superdeterminism loophole - but to reach for that is literally insane, to leave behind science altogether. There are also ways to in a sense restore locality by having information propagate backwards in time. No such proposal has ever made much sense. Nor have you endorsed any of these ideas, so let's set them aside.

    You link to an article by Rovelli that claims that his "relational" interpretation of QM makes the nonlocality go away. Now, I don't think anyone has ever fully understood the relational interpretation, because it is ambiguous and (probably) incoherent. But one thing that happens at times when you press on the view is that it starts to sound like Everett expressed in different language. In so far as it is like Everett, then it's not a single-world interpretation of QM, and my (and Travis') claims about nonlocality being demonstrated do assume that we're working in a single-world viewpoint. But I don't have time to read Rovelli's paper to try to figure out what's going on. The interpretation given there, even if it is coherent, is certainly very nonstandard (and not widely discussed, much less accepted). So let's set that aside too.

    I am willing to admit that it's not very perspicuous to talk about information going from one region to another, for reasons Amos expressed nicely. Nonetheless, as Bell made crystal clear, the measurement outcomes in one region depend on what happens at spacelike separation, in some sense or other that is very puzzling indeed. Because if there was no such dependence, Bell's inequalities could not be violated. I know that Redei has been trying to sell various tricky common-cause explanations for EPR correlations for decades, and it sounds like you have found a nonstandard probability framework that lets you think that you get rid of the nonlocality. In my opinion, it's all smoke and mirrors.

    The honest/sane answer to the question "where is/was the [mass/energy of the] electron before detection" is the same in quantum probability as it is in classical probability: "we don't know".

    Actually, I agree with you here. And "we don't know" is also the answer to the question of how to understand EPR nonlocality. But if we pretend that it doesn't exist, then we definitely can't make any progress. Calling the EPR pairs "nonseparable" or "entangled" doesn't make their nonlocal correlations any less in need of explanation.

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  171. I'm afraid I am also going to express a thought on the computer simulation of a quantum experiment. It does not seem feasible to me because, while a computer can simulate a simple situation from our universe, three different computers with the same program that don't share information will simulate three different universes--assuming they have a good random-number algorithm, which they should have to model the scenario, and could have (it was done on Apple II microcomputers in the 1980's). That is a single probabilistic event in one universe will have one random outcome, but could have three different outcomes in three different copies of that universe, and there will be no correlation among the outcomes. (They could be forced to have the same outcome, but this would require connections among them.) It would be like running parts of the experiment in different universes (without transferring anything from one universe to the others).

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  172. Amos,

    I realized I didn't answer your question about which direction the information propagates. That's a tricky question that Tim goes into in some detail in his book. The short answer is it depends on what interpretation you're using.

    In any deterministic hidden variable theory conceived of so far, Lorentz invariance no longer holds. There is a preferred reference frame, so the question of which measurement occurred first has a perfectly clear answer. It's almost certain that all deterministic hidden variable theories have a preferred frame, although it hasn't been proven (note also that there are hidden variable theories that perfectly reproduce QFT, given some regularization. They also use a preferred frame, but just like with the nonrelativistic versions, there's no way for us to discover what the preferred frame is).

    In Flash GRW, a collapse theory, a flash occurs when a particle collapses, and subsequently causes the entire wave function to collapse. The macroscopic objects we observe are then composed of millions of these flashes in every small amount of time. It's possible to maintain Lorentz invariance by having the time between collapses be (stochastically) determined on hyperboloids in spacetime that are a fixed proper distance from the previous flash. This is clearly nonlocal, since the collapse occurs across all space at the same time (where "same time" is defined by the hyperboloid centered on the flash), but different observers will disagree about when the collapse occurs at each point in space. Here, there's not really a good answer to which direction the information propagates. It's weird. There's no way to describe what happens without appealing to a collapse that happens across all space at the same time (and thus information travels faster than light because a flash in one location causes the wave function to collapse everywhere), and yet different observers disagree about when that collapse occurred.

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  173. JimV,

    In the computer experiment, you're allowed to connect the computers at the beginning, so you can make them as correlated as you like (so you can in fact choose to have all three computers give the same output, for instance, or any more complicated scheme you want). Then you take them to three different rooms, and at this point they have to be disconnected. Then a person in each room chooses to enter either a 1 or a 0 into the computer, and the outputs of the three computers must be correlated according to GHZ. It is impossible to achieve this.

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  174. bhg,

    That the laws of nature don't suddenly change tomorrow is one of the fundamental assumptions of science per se. Of course you can't prove it, but if you want to throw it out, you can't do science to begin with.

    Having said that, you do not of course have the freedom to add sources to any QFT just so. If you have the full QFT that supposedly describes all the matter in your space-time there won't be no additional sources popping up. If I give you the Hamiltonian and the initial conditions, that's all you need.

    I see that we don't seem to agree on what 'deterministic' means, but I don't see the point of arguing about words either, so let me just phrase the question without that. If I give you the CFT state at some late time (say, after the black hole has evaporated), can you tell me the initial state? The answer seems to be "no." Is that correct?

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  175. Bee,

    For someone who claims to reject arguments based on beauty, it seems to me that you are now doing precisely that (I hope you can take this in the good natured spirit in which it is intended). No, "science" does not require that the law of physics are time translation invariant. Suppose someone came up with a theory theory in which the top quark Yukawa coupling varied linearly in time and it happened to fit the data better than the alternatives. Would that mean the end of science? I don't think so.

    Spacetime translation invariance of the laws of physics buys you more symmetry and hence more beauty, and since it seems to fit the data we are happy and don't ask too many questions. But in fact we would be just as happy if the assumption failed, as long as we could understand the failure in some controlled way.

    As to your question: yes I can retrodict the initial state provided you tell me that the CFT Hamiltonian preserves translation invariance. Since you regard translation invariance as one the fundamental tenets of science, this should be satisfactory. My point is just that assuming translation invariance for all times is mathematically equivalent to assuming a property of the Hamiltonian for all times, so you are kidding yourself if you think that you can really predict the future based on just knowing the state and the Hamiltonian now, without making any further assumptions.

    In any case, any critique you have of AdS/CFT based on the freedom to modify the Hamiltonian/boundary conditions in some time dependent way can, I claim, be leveled with equal force against any system of equations in physics.

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  176. Carl3,

    Deficient understanding, even among the highly intelligent and educated and even of classical probability, is indeed common. Paul Erdős famously refused to accept the correct solution to the Monty Hall problem until given an empirical demonstration. People still struggle with Sleeping Beauty, Two Envelopes, Bertrand, etc. Clearly the situation in general probability is even worse. If Bell and thousands of other physicists had drawn the conclusion from Spekkens toy model that "nature is nonlocal" I wouldn't have been surprised.

    Your understanding of RQM is also deficient but the same thing - no ontic nonlocality - is true of 'the' CI (and certainly not just Landsman's take on it) and QBism and more generally of any interpretation in the "radical psi-epistemic" / "neo-Copenhagen" camp.

    There's nothing nonstandard about the long-established probability framework which "I've found". It's an empirically established fact that Planck's constant is nonzero. It's an inescapable consequence of that that a probabilistic description of mechanics needs to be applicable to noncommuting observables. From those two facts and the appropriate probability theory follow a number of consequences, including the existence of entangled states and their associated "super-Bell" correlations. None of them justify ontic assertions of nonlocality or multiple worlds or whatever.

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  177. bhg,

    You've totally lost me there. Of course you can postulate a time-dependent law, eg that linear time-dependence in the Yukawa coupling you mention. But that's still a deterministic law, where by deterministic I mean you can evolve it forwards and backwards from any given initial state. What I say doesn't make any sense is to state that since you cannot know that a law doesn't change tomorrow you have no law. That's essentially what you seem to be saying by pulling sources for the CFT out of the hat as you wish.

    I merely pointed out that if you make such a claim you are throwing out science in its entirety. Indeed, we can't prove the sun will rise tomorrow. So why bother making any predictions if the world may end any moment?

    What you think this has to do with translation invariance I don't know. Whatever law you have may or may not be invariant under this or that symmetry. Point is that you can't just go and change a law as you please as time evolves because that's not a law.

    In any case, that seems to be a rather philosophical discussion and I'm not sure it's of much use. Regarding the black hole evaporation. Fine, then let's take the case you suggest, where you've fixed the CFT. It seems to me then that by making this assumption you dictate the gravitational theory to only work in a very specific subsector, that is all those bulk states which comply with this condition. As I've said a few times before, this is probably self-consistent, but why would you think this has anything to do with reality? Best,

    B.

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  178. Paul Hayes,

    None of them [consequences of your generalized prob. theory, such as entanglement and super-Bell correlations] justify ontic assertions of nonlocality or multiple worlds or whatever.

    The issue is not one of ontic vs epistemic interpretations of QM; think of the quantum state however you like. The violation of Bell's inequalities can be understood just at the level of purely observable phenomena in labs (apparatus settings and lights flashing, which we record in notebooks). That's the only sense in which I am claiming that the nonlocality is "ontic". When you understand the premises that go into deriving the inequalities, you see that if they are violated there is some sort of strange dependence between events in one place and those in another. Real, observable, macroscopic events - hence, I hope, "ontic" in everyone's view.

    You know all this, you just don't want to acknowledge that it is a serious form of nonlocality. OK, that's your choice.

    best,
    C

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  179. Aside from PBR, any Bayesian theory of reality can't get off the ground without leeching on some other theory of reality, for the simple reason that there is no such thing as a pure observation. It is impossible to describe an observation without some background theory. What does it mean to "observe" that the energy/momentum/position of a particle is E/p/x? These are not quantities that are just handed to us by nature. We don't look out into the world and see a bunch of variables with assigned values, so that our job is merely to find the correlations between them. We understand what the variables mean and assign them values using some theory. In practice, in QM they are assigned by assuming that the rest of the world other than the quantum system under consideration obeys some standard classical theory. In other words, we describe the observations using the classical theory as our background theory. When we measure that a particle has energy E, we mean that its surroundings are behaving in a manner that they would if they absorbed something with energy E in the classical theory. And then in Bayesianism we're supposed to count that as just a bare observation that a particle has energy E, and plug that into a generalized rule for updating probabilities about other observations. It's ironic then that many Copenhagenists/QBists have claimed that other interpretations of quantum mechanics are just classical theories in disguise.

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  180. Bee,

    You were bothered by the freedom to add sources to the CFT, viewing it as some sort of breakdown of determinism. My point was just that this freedom arises in every QFT, including the Standard Model. So whatever your complaint is here, it is not specific to AdS/CFT.

    But let's leave this issue, and just take H=H_CFT with no added sources (as is preferred by symmetry). Then we consider all states of the CFT, and in the bulk we allow all configurations with normalizable falloff at spatial infinity. I don't understand your complaints about this. It's exactly the same as what we would do for a QFT in Minkowski space, namely there we typically demand that fields have normalizable falloff at spatial infinity. E.g. massless fields should falloff like 1/r as r->\infty. Again, whatever your complaint is here, it is apparently not specific to AdS.

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  181. bhg,

    If you add sources to the SM it's because you are using some effective limit. But fundamentally there aren't any other sources, so I don't know why you think the situation is comparable.

    You seem to be claiming now that actually Minkowski-space isn't globally hyperbolic.

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  182. Travis,

    you wrote "Commutation at spacelike separation means nothing for locality so long as we interpret the wavefunction as being ontologically real, as PBR forces us to. What happens when you observe one of the observables that commutes at spacelike separation? The wavefunction collapses everywhere, if you're using a collapse picture. That's massively nonlocal. If you're not using a collapse picture, then you have to use hidden variables, and then Bell's theorem kicks in."

    PBR does not prove anything of interest. PBR assume that if QM state is "state of knowledge" it corresponds to distribution over hidden variables. We already know hidden variables are not compatible with QM. QM state can be a state of knowledge and not correspond to any distribution over any hidden variables. Then, its collapse is not indication of non-locality.

    Real problem is that no one agrees what "non-local' means in QM world. Until we agree, debate over whether QM is local is pointless.

    Even so, I ask again. Which part is non-local in

    * replacing real probabilities with complex numbers
    * imposing Born rule to get real probabilities for results of (local) measurements
    * local interactions (that create entanglement over distance after some time, just as local interactions create correlations with real probabilities over distance after some time)

    ?

    If none of the above is non-local, QM is local, because the above is QM. PRB says nothing because it makes assumption incompatible with the first two.

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  183. Well, Carl and Travis have things well in hand, so I will just make a couple of comments about non-locality.

    1) The spooky action-at-a-distance that worried Einstein about the Copenhagen Interpretation was obviously not a matter of being able to send superluminal signals. If Einstein had thought that quantum theory allows for such a thing he would have advocated testing the prediction. In particular, it was obvious to Einstein that the EPR correlations could be explained perfectly locally. What he could not understand is why Bohr would paint himself into a corner on a straightforward case like that, which did not require any non-locality.

    2) All the talk about probability and extensions of probability are pointless. The relevant predictions for GHZ are all probability one.

    3) The claim that there is some additional assumption of "realism" that Bell and PBR use has never been backed up by any account of where such a contentful assumption appears in either derivation. The truth is that it doesn't because no contentful assumption is made.

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  184. I just read Tim’s "What Bell Did" and he righteously points out that EPR is primarily about non-locality. EPR shows that QM “must be non-local if it is indeterministic” - and it is.
    Sure, Alice and Bob cannot use this non-locality for superluminal signaling, because of QM randomness, but nevertheless there is this distant spacelike correlation.
    And it must be like this, since QM uses a state (wavefunction) that connects spacelike separated events and determines (unitarily) the probabilities that are realized in the measurement.
    QM and SR are the perfect marriage, working like a charm in QFT including this non-locality.
    The eq. of motion e.g. Klein-Gordon (d^2+m^2) \psi = 0 projects out states that are not on mass shell, but the propagator D, (d^2+m^2)D=1 need not be on mass shell, it just has a pole there. Remember to get the electrostatic 1/r the exchanged virtual particle has no energy only momentum, thus way off mass shell, violating Einstein’s E^2-p^2=m^2 (m=0 photon).
    Further in different frames of reference particles can be particle or antiparticle (e.g. in Compton scattering the electron hit by the photon “propagates spacelike a while” as particle or antiparticle before it emits the photon again), i.e. “crossing”, thus QM and SR belong together and demand antimatter.
    You get the spin-statistic theorem because spacelike observables commute, again QM and SR work together.

    I think there are two reasons why many theorists, not especially dealing with EPR think there is no non-locality, besides all the non-locality under the hood:
    1.) The density matrix, sometimes also called state is regarded as better description of a QM system, since it elegantly combines classical and QM probabilities. The reduced density matrix (tracing out Bob) that Alice uses to measure her spin is the perfect tool if one wants to focus only on the local aspect and ignores the “distant correlation” caused by the state (vector).
    2.) Since the Lagrangian has Lorentz symmetry all seems to be ok. But this Lagrangian is put in the path integral and here we go.
    Symmetries like Lorentz and local gauge symmetries were the breakthrough but now we must go further.
    They must work together with the symmetries of GR, i.e. diffeomorphism and local Lorentz symmetry.
    And maybe there we need to integrate the measurement in the process. Remember all the gauging is allowed because of the Ward(-Takahashi) identity, that depends on putting external electrons on mass-shell.
    SR told us once that physics should be formulated observer independent. Maybe we need an observer independent triggered measurement, beyond a certain threshold of entangled mass/energy Рa natural cutoff Рno huge Schr̦dinger cats anymore Рexactly what we observe.

    CONT

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  185. And maybe this is the “new” physics of an effective field theory – just integrate the measurement beyond a threshold and thus solving the measurement problem.
    Embracing the measurement as a part of the process makes QM not exclusively unitary, but only unitary between measurements.
    A not exclusively unitary evolution immediately solves the BH information loss paradox – information is lost all the time and the evolution is not reversible – the arrow of time.
    I very much advocate Penrose’s OR, but not in the form of his Schrödinger-Newton eq., that messes with unitarity. Maybe the trick is just not to quantize gravity and let the tension between massive particles in superposition and a not quantized spacetime, not being able to be in superposition trigger the measurements.
    If we clearly separate between unitary evolution (U) and the measurement (R) then there is no problem anymore with non-locality in U – well, this is what the QM state does for a living. And one better does not try to imagine a particle “travelling”, only after the measurement particles are back on mass shell, back in our reality or better generates our reality.
    Tim also mentions in "What Bell Did" the Elitzur‐Vaidman bomb problem. It is not a problem at all, if we accept that in U just the probability (amplitude) is calculated and in R the real outcome is generated with QM randomness. If on the contrary we imagine a real particle hitting the bomb trigger or not hitting it, you get into mental dissonance. Let U and R be just part of a process that generates our reality.

    When I read Tim’s "What Bell Did" I remembered Einstein’s “At the heart of the problem is not so much the question of causality but the question of realism.” (Letter from Einstein to Jerome Rothstein, 22 May 1950). Maybe Tim can explain what Einstein meant with “realism”. My guess is: realism is the independence of an observer (“the moon is there even if nobody is watching”). Or is it the belief in determinism (hidden variables…)?

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  186. Bee,

    Sources are just coupling constants that are allowed to be spacetime dependent. I disagree with you that there is a "fundamental" reason why there can't be such terms in the Standard Model Lagrangian. Instead it's purely pragmatic: physics seems to respect translation invariance and so there is no reason to add such terms. I have no idea where your "fundamental" requirement is coming from.

    The difference between AdS and Minkowski (tied the (non) global hyperbolicity), as I have said, is that in AdS you need to choose boundary conditions for all times, but I don't understand why you find this problematic. It's just saying that AdS is like a box, and you have to say what happens at the boundary of the box. Surely you don't have any problems in studying the Standard Model in a box with some boundary conditions, do you? This is called doing physics in a lab. Also, our observable universe is much more similar to the box case than the idealized Minkowski case, since we have a finite cosmological horizon and so new information is continuously being transferred in and out of this "boundary".

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  187. Travis, thanks for the reply and explanation. It implies that computer C's output to its input should depend upon computer A's and B's output to their input, and since it doesn't know what computer A's and B's input were, it can't fulfill that dependence. That makes sense (of course). The computers are simulating different universes, but in an even worse way than I thought.

    Suppose I did a three-marble (red, blue, green) experiment with two computers, showing each program a different one of the three and asking it to guess the unshown color, without knowing what color the other program was shown. They would also fail, half of the time (assuming randomness). (No reply is necessary, you must have more important things to do, I am just trying to think of what such experiments do and do not prove, and whether one result should be more surprising than the other.)

    I am also failing to see what BHG and Dr. Hossenfelder's disagreement over initial conditions is. BHG seemed to be making the point, that, no, initial conditions are not always enough to predict future behavior of an isolated system, you also need to know if any forcing function, or external influences are going to occur. Practical cases tend to be isolated, so that is a thought that would occur to someone who works on such problems.

    Dr. SH seems to be saying that if you know all the physical laws and are modeling an entire universe, there are no external influences and initial conditions are all you need. Both statements seem to be true, to me (at least classically), but are referring to different sorts of problems (isolated vs. universal).

    (That is just a side-issue, not the main issue, though.)

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  188. Physphill,

    You didn't describe all of QM with your list. What happens after the measurement is performed? Does the wave function collapse?

    Also, there's a sense in which the part where you use the Born rule to get probabilities is non-local. Knowing the local probability doesn't tell you everything (i.e., the marginal distributions of two random variables does not tell you their joint distribution). You also need to know how the probabilities are correlated. You will never get correlations of that kind in a classical theory. It's important to note why: it's because the probabilities are not just probabilities for certain events to occur (in which case you can get any kind of correlation in a classical system). They are probabilities for certain events to occur *given that a particular unknown-in-advance action is performed on the system*. The photons don't know what the polarizer is going to be in advance. If they did, they could easily correlate themselves to give any probability distribution. But without that knowledge, they have to communicate somehow after discovering what the polarizer is in order to display the right correlation. There is no equivalent of this in classical physics.

    (Also, what do you mean by we know that QM is not compatible with hidden variables? There are explicit hidden variable theories that reproduce all of the empirical observations of QM, and do so in a much clearer way than CI because they actually explain what happens when a measurement is performed rather than postulating measurements as fundamental features of the universe. Do you disagree that these theories do so?)

    As Carl pointed out, you don't even need to look at the specifics of QM. Just have rooms where a light flashes green or red after the user inputs a 1 or 0. There's no way for the correlations of the flashes in the three rooms to match the GHZ outcomes without communication between the rooms. Do we agree on this?

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  189. Bell's result does not depend on any particular formulation of QM, relativistic or otherwise.

    Sure, but the question was whether “Bell’s result” (non-classical correlations due to quantum entanglement) signifies that QM is not “local”, which obviously depends on the definition of ‘local’, a word that unfortunately has different connotations in different contexts. My point about non-relativistic QM is just that, being non-relativistic, it has no finite upper bound on the propagation speed of energy, and hence is inherently non-local in the strong sense that it permits superluminal signaling, etc., so it’s a strange context within which to discuss whether physics is “local”.

    In a relativistic context we have strict “locality” in the sense that there is no superluminal signaling, no superluminal propagation of any energy or action, spacelike separated observables commute, etc. This is sometimes called “Einstein causality”, which is ironic considering that Einstein famously said we can never decide if the world is causal or not. It’s also ironic that we so often see articles declaring that Einstein’s disbelief in “spooky action at a distance” has been proven wrong by yet another demonstration of quantum entanglement, when in fact there really is no action at a distance in these experiments, in the literal sense of “action”, meaning there is no violation of “Einstein causality”, which some people call locality – and some people don’t.

    The "information of some kind" basically must be hidden variables.

    So you’re saying that some hidden variables are conveyed (or propagate) superluminally over the spacelike interval from A to B during an EPR experiment… or is it from B to A? Isn’t the situation directionally symmetrical? Do these hidden variables carry any energy or momentum, or perform any action? I’m uneasy about “explaining” things by postulating (non)actions in indefinite directions of unobservable entities with no palpable physical qualities. I’d rather just say the wave functions are not separable, but they still satisfy locality in the “Einstein causality” sense of the word. It’s okay to say they are “non-local” in the sense of being not separable, but the fact that so many people jump from this to thinking that some action or information propagates across a spacelike interval (albeit in some indeterminate direction) shows the risk of using a term with two meanings.

    As for superdeterminism: anything at all can be explained by superdeterminism, so it is not scientific.

    It’s good to be careful about slippery-slope arguments. For example, Einstein argued that if wave functions are not separable, then science itself is impossible, because science relies on being able to talk about separate things. If the result of an experiment here on Earth may depend on something happening in the Andromeda galaxy, which we can’t know, then science itself is completely impossible. Ergo the claim that wave functions may not be separable is unscientific! Well… not so fast. The only lack of separability needed to account for the effects of quantum entanglement is just the amount necessary to account for the effects of quantum entanglement. We needn’t extrapolate from this to complete lack of separability and the collapse of science. Likewise for superdeterminism we only need the common causal past of two measurement events to impose on them the observed correlations, and nothing more. We may not have a clear idea of how this happens in detail, but at least it acts across timelike or lightlike intervals, and is no less clear than hidden variables doing who-knows-what across spacelike intervals, and it need not result in the collapse of science. Similarly for so-called backward causation, etc.

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  190. Carl3,

    It is about ontic vs epistemic interpretations of QM. The understanding you appeal to (purely observable phenomena level) is the trivial hidden variables 'interpretation' (p 5). The only thing I'm refusing to acknowledge is that these strange dependencies can't be understood in essentially the same way as classical "nonlocal" correlations are understood. Making a clear separation between the physical and probabilistic / informational content of QM and avoiding spurious ontology inflation.

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  191. Help! I'm arguing with a string theorist who believes all coupling constants in the standard model have an undetermined time-dependence!

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  192. bhg,

    Consider the following. You make an AdS black hole from some initial condition at time t_0, say, collapsing dust or what have you, CFT on the boundary. Stuff collapses, forms a horizon, evaporates. At a much later time t_1 I ask you if you can tell me what formed the black hole. You nod triumphantly and produce the CFT state you forward-evolved from t_0. Great.

    Now consider the same scenario, but now at a time t* between t_0 and t_1 I throw in a book from the boundary. At t_1 I ask you if you can tell me what was in the book. You seem to say for that you need to know what I did there at the boundary. Hence, your answer is basically you can tell me what was in the book if I tell you what was in the book. I'm not impressed.

    Having said that, I am still missing something about the boundary-condition I think. You spoke above about how to encode the bulk state in the boundary operator. Can you point me to a reference that says how to do that, say, for a delta-function? Best,

    B.

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  193. Sabine:

    You have my sympathy. Maybe the wisdom of having people reveal who they are is becoming more manifest. For example, if people knew who was actually posting it, would "physphil" ever dare to post this:

    "PBR does not prove anything of interest. PBR assume that if QM state is "state of knowledge" it corresponds to distribution over hidden variables. We already know hidden variables are not compatible with QM."

    The sheer ignorance and incompetence of this statement is impossible to overstate. Do we know that "hidden variables are not compatible with quantum mechanics"? No: we know that von Neumann announced such a theorem and Grete Hermann (philosopher!) diagnosed the flaw in von Neumann's argument (and was ignored), that Einstein diagnosed the flaw in von Neumann's argument, that Bell, once he could read the English translation, saw the flaw (which he later called "foolish") and, most critically and decisively, that since at least 1952 (if not 1927) there has existed a concrete explicit counterexample to this claim, namely the pilot wave theory. But the anonymous posters just blather on with all the self-confidence in the world. I have not been following your exchange with BHG in microscopic detail, but as far as i can tell you are putting your finger right on the fatal flaws in his argument every time.

    Maybe it bears repeating: the only evolution that has a chance to conserve information is the evolution of the universal physical state, and there can, in principle, be no "outside interventions" in that state to have to account for. If BHG thinks that the universal Hamiltonian can unpredictably vary, then the whole idea of information conservation is hopeless from the get go. And in a non-globally-hyperbolic space-time like AdS the only chance for information conservation requires that there be some strict universal boundary conditions for the timelike boundary. Anything less and it is all over before it has even begun.

    Cheers,

    Tim

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  194. > “Help! I'm arguing with a string theorist who believes all coupling constants in the standard model have an undetermined time-dependence!”
    I am not at all sure, but isn´t this what they call “landscape”.
    Don´t worry as long as the “landscape” is beautiful (and supersymmetric ;-)

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  195. travis,

    "You didn't describe all of QM with your list. What happens after the measurement is performed? Does the wave function collapse?"

    I am agnostic. Collapse or "many worlds", either is OK for my point here.

    "Also, there's a sense in which the part where you use the Born rule to get probabilities is non-local. Knowing the local probability doesn't tell you everything (i.e., the marginal distributions of two random variables does not tell you their joint distribution). You also need to know how the probabilities are correlated. You will never get correlations of that kind in a classical theory."

    First step is to replace real probabilities with complex amplitudes. It is not classical theory.

    "But without that knowledge, they have to communicate somehow after discovering what the polarizer is in order to display the right correlation."

    False. Easiest to see in MW. All interactions between photons and polarizers are local but all sets of results are consistent with QM.

    "Also, what do you mean by we know that QM is not compatible with hidden variables?"

    Local hidden variables.

    "As Carl pointed out, you don't even need to look at the specifics of QM. Just have rooms where a light flashes green or red after the user inputs a 1 or 0. There's no way for the correlations of the flashes in the three rooms to match the GHZ outcomes without communication between the rooms. Do we agree on this?"

    No. You are assuming world is classical. Again, it is false in MW.

    Your mistake, also Tim's and everyone who thinks PBR is important, you all assume world is classical underneath. Then you are amazed when some QM experiment is not consistent with that. Then you think some crazy thing must be true, like QM is non-local classical physics. QM is not classical. Probabilities are complex and depend on what you are measuring. That is all, but it is a lot.

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  196. Amos,

    The hidden variables themselves don't propagate across spacelike distances, at least not in Bohmian mechanics. It's just that the particles in one location influence the particles everywhere, so there is a superluminal influence. Again, the situation isn't directionally symmetrical because in Bohmian mechanics (and probably in all deterministic hidden variable theories) there is a preferred frame, even in "relativistic" versions of Bohmian mechanics. But we could never discover what that frame is, and hence we would never know which direction the influence went in, even though there would be a fact of the matter about it.

    It's just not true that we can claim that in a relativistic context we have no superluminal signaling, if by relativistic context you mean QFT. Bell's theorem shows that superluminal signaling of some kind is going on, at least if we assume a single world. In QFT as it's usually formulated, there is explicit action at a distance: measurement in one location collapses the wave function everywhere, which then affects the results of subsequent measurements everywhere. That's where the superluminal signaling comes in, even though we ourselves can't take advantage of it to communicate superluminally. If you don't have collapse, then you have to have hidden variables or Everett.

    I agree Einstein was wrong about separability. But superdeterminism really is unscientific as an explanation. It is *certainly* less clear than hidden variables. With hidden variables, we have specific laws that the particles obey at all time, just like any other deterministic physics. It's completely non-mysterious. With superdeterminism, you can't just postulate laws; you also have to postulate hyperfine tuning to make the initial conditions just right so that the observed outcomes happen. And there's no way to know what those initial conditions are without first simulating the entire universe to see which initial conditions give you the outcomes that you want.

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  197. Bee,

    "Help! I'm arguing with a string theorist who believes all coupling constants in the standard model have an undetermined time-dependence!"

    I think the problem here is that you are loathe to admit that you are making an argument based on beauty. I ask: what reason do have to prefer the usual SM Lagrangian from one in which the top Yukawa coupling constant varies in time at a rate of 1 part in 10^(-1000)? Is it because of some "fundamental" requirement? If so, please spell that out. The correct answer is that the theory with constant Yukawa coupling has more symmetry, and it seems to be a good rule of thumb that nature chooses the more symmetrical equations when possible. I.e. Nature prefers symmetry (beauty). Without such a symmetry/beauty rule of thumb to follow, you would have to assign equal "probability" to both theories, since they fit the data equally well. It's just a question of identifying your assumptions.

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  198. Tim,

    I omitted the word "local" in "local hidden variables" in what I wrote before. That was a small mistake, yes. I made that mistake because idea of non-local hidden variable theories is nonsense of no interest and I forgot that others need to be reminded of that.

    You write "since at least 1952 (if not 1927) there has existed a concrete explicit counterexample to this claim, namely the pilot wave theory."

    That is not counterexample. It works only in non-relativistic QM where there is no issue with causality. It does not work and never will work in relativistic QFT, that is the QM that describes the real world. So, actually there are no counterexamples.

    Why cannot you just accept that QM is QM? Why you must insist the world is classical? Beauty of physics is that it teaches new unexpected things.

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  199. Bee,

    "Now consider the same scenario, but now at a time t* between t_0 and t_1 I throw in a book from the boundary. At t_1 I ask you if you can tell me what was in the book. You seem to say for that you need to know what I did there at the boundary. Hence, your answer is basically you can tell me what was in the book if I tell you what was in the book. I'm not impressed. "


    All of your discomfort will disappear once you think of AdS as quantum gravity in a box. The CFT tells us about the evolution inside the box, but we retain the freedom to inject energy/information into the box, let it evolve, and then examine what comes out. This is exactly what we want since it is how physics is always done, and is also how we would actually in principle go about verifying the purity of Hawking radiation. Just think about an experimentalist with a box inside of which is some quantum system of interest. We *want* the freedom to be able to inject stuff into the box, we don't want there to be some "law" that restricts this in some artificial way. The freedom of the experimentalist to probe the system in this way is represented mathematically by the freedom to add sources at the boundary of the box. This is a feature not a bug.


    Also, note that Tim apparently agrees with your comment, which you should of course take as a bad sign given his track record.


    You can look in Harlow's recent TASI lectures (and references therein) for how to represent a delta function in the CFT. It is quite straightforward.

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  200. bhg,

    I am happy to be accused of making an argument from beauty, but I don't make any such argument. I am saying firstly that I don't think you are using a common definition for standard model. In fact I have never heard anyone say that the constants in the standard model have an unknown time-dependence. But leaving aside the nomenclature, maybe more importantly if the constants had an undetermined time-dependence the model would be useless. That's not an argument from beauty, it's an argument from what-science-is-all-about.

    Your example once again seems to indicate that you have a function whose time-dependence you actually know. Presumably you know that time-dependence from some meta-law? Where does that law come from, etc etc. This issue has been discussed by philosophers forwards and backwards. Not that it matters because you don't know the time-dependence.

    "we retain the freedom to inject energy/information into the box, let it evolve, and then examine what comes out. This is exactly what we want since it is how physics is always done, and is also how we would actually in principle go about verifying the purity of Hawking radiation."

    There are a lot of pure states. Solving the information loss problem doesn't merely entail showing that the final state is pure if the initial state was, but that you can reconstruct the initial state from the final state. Now, roughly speaking what you seem to be doing is to move part of the initial state onto the boundary and then simply add this information to the final state. It looks like cheating to me.

    Having said this, you keep speaking about my supposed objections and discomfort, but really I am just trying to make sense of what you say and don't really manage to. Quite possibly that's my fault.

    Not sure what your comment about Tim is supposed to mean. Is this something like an argument from non-authority? It might not have come across all that well in my blogpost but I largely agree with him.

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