Thanks Ron, I find this answer much less condescending and more helpful than Lubos' answer. What I still don't understand is that you say this is a local hidden variables theory ruled out by Bell, and yet both from my linked papers and your own comments about the test particle and extremal black hole, it sounds like GR is not necessarily globally causal (only locally, away from too extreme metric curvature). Wouldn't this acausality imply that it is a non-local theory, and therefore not constrained by Bell?

@user1247: Lubos's answer, condescending or not, is correct. The thing I was talking about is not an acausal thing with closed timelike loops, but a case where the closed timelike loops only superficially appear, in reality, they are only time-like close in a skin too close to the horizon to be physical--- within a tiny part of a Planck length of the horizon itself. In quantum gravity (string theory) you get rid of this region as unphysical, and this is why you need quantum mechanics to make full sense of this behavior. It is not acausal at all.

But aren't CTCs not obviously ruled out in GR? I mean, Godel's solution is contrived, but at least it shows CTCs are not fundamentally inconsistent with GR... is it really so trivially obvious that such funny business isn't possible when extremal black holes eat each other (I'm asking seriously, not rhetorically)?

I think this question about CTCs really gets to the heart of the question I am asking, so perhaps if you have an answer I or you could add it to your answer so I can give you a gold star.

@user1247: What's a "gold star"? Classically, you get a closed timelike curve whenever you exit the same black hole you enter any time later, because the geodesics which cross the horizon going in get frozen forever in t, while geodesics going out also get frozen in t, so they meet somewhere impossibly close to the horizon. This is a well-known artifact, discovered by 't Hooft, of horizon descriptions, it is also the reason black hole entropy is naively infinite, and the resolution is to say that you exclude a brick wall. There are no CTC's in classical GR, so people assumed BH's don't emit.

But quantum gravity, with the holographic skin, allows (and requires) near extremal black holes to emit classical stuff. It's not complicated, and it doesn't change much of what is known. CTC's of the usual sort are still not allowed.

By "gold star" I was being silly, meaning to accept your answer. Discovered by 't Hooft? I'm reading Wikipedia now about the Kerr metric slightly before 't Hooft chronologically (it says "all rotating black holes will eventually approach a Kerr metric"). It seems to state fairly clearly that there are CTCs and "it is possible for observers in this region to return to their past". Are you and wikipedia in disagreement, or is wikipedia simply dramatizing the "artifact" you describe?

@user1247: The CTC's in Kerr metric are near the "ring singularity", and are in a region where you can't trust the classical theory completely. I am talking about exterior observers which never get close to the singularity. These, if they go in and out, as I believe they do, in a technical sense return to their "past" (not really, this is not their past, except in an unwarranted and known-to-be-false near-horizon extrapolation). This is supportable by classical calculations and precise quantum models. What happens near the Kerr singularity, I can't say for sure. I don't know.

What do you mean "where you can't trust the classical theory completely"? Are you referring to quantum effects, because here I am working under the hypothetical that quantum effects ARE just GR. Or do you mean that the classical solutions are ill-understood? Finally, if you don't know what happens near the singularity, how can you be sure that nothing crazy happens? I'm curious because this seems like just a naively compelling idea to me that it would be surprising if these questions had not been nailed down completely.

@user1247: Your hypothesis as explained already, is ridiculous--- quantum effects have nothing to do with GR. I am not quite talking about quantum effects, only sort of. If the singularity has closed timelike loops, they have to be noncontractible and you then have to unwrap it to a simply connected causal thing, and I don't know how to do that. There are no CTC's in the exterior, nor are there actual CTC's in exterior plus interior in-out traversal, although there are phony CTC's. The CTC's don't give quantum mechanics, they can't do anything like reproduce Bell's inequality violations.

Dear @Ron, as a high school teenager, I was thrilled by that sentence by Einstein about explaining quantum phenomena as something... that I would interpret as solitons. I think we were affected by the same sentence here. ;-) I found some "new solution" - a new type of solitons - as a result. What he wanted to solve was just the quantization of photons' energy and the electric charge. That's of course much more modest than what an actual competitor of quantum mechanics, as developed in the 1920s, would have to do. The character of the "main goal" changed as people understood QM more properly...

@Ron, maybe you are using "exterior" differently, but the Wikipedia article says there are CTCs in the "exterior" in the Kerr vacuum, and also your own first line of your answer linked to in my OP is "The reason is that the classical solution allows matter to escape." I don't know how to reconcile these different kinds of statements.

@Ron, if you add to the end of your answer something like "The CTC's cannot reproduce Bell's inequality violations," then I will accept it, and also open a new question trying to better understand why.

@user1247: If Wikipedia says there are CTC's on the exterior, they are totally completely and unequivocally wrong. There are no CTC's except inside the horizon, the exterior is always causal. Why can't CTC's reproduce Bell's inequality violations? Because the CTC's are always inside one black hole, and don't link two distant points. To get Bell's violation, you need to go back in time a long ways and fiddle with the hidden variables in the far past.

@Ron, then what did you mean in that other answer that "The reason is that the classical solution allows matter to escape."? In any case, I urge you to put what you just wrote into your answer, and I'll accept it. Thanks.

@LubošMotl: Yes, I know. I was also intrigued by Einstein's program, but perhaps more skeptical, as I never seriously believed it would work to reproduce QM. I also halfheartedly looked for solitons early on, but never found anything, then I read Skyrme and Coleman, and gave up. What was your soliton? Was it GR? I think Einstein had a trick for getting Bohr Sommerfeld quantization from an action condition in GR (it is reproduced in a GR book without attribution, but I suspect it's Einstein's claw). Your biography can be turned into mine, if you substitute East for West and stop in 1995.

@user1247: I meant the classical solution has geodsics that go in and out in r, going in and out of identical black holes. In classical physics, these entry and exit events are disconnected, but they are linked quantum mechanically, so that the coming out is only a finite time later than the coming in. In strict classical mechanics, the coming in is not linked to going out.

@Ron, I thought that was what we were discussing, the classical GR solution. It is unfair to invoke QM when the hypothetical was that all there are are classical GR solutions...

@user1247: Ok, then, the pure classical GR solution doesn't allow things to enter and leave in this universe, it requires the black hole to link to another universe. This picture doesn't make sense at all, and you get endless paradoxes, like "what happens if I throw positive charge into a neutral black hole to make it near extremal, fly in, come out, then throw negative charge behind me to neutralize the hole again?" These questions only become clear if the classical in-out is an actual in-out in one universe, not in the classical way, between separate universes.

@Ron, I didn't understand your example of a paradox. You are saying that the classical GR solution doesn't allow things to enter and leave in the same universe, so how is there any paradox? But even if they could enter and leave in the same universe, your specific example would not be a paradox. But there is surely room for many paradoxes, but that's where all of the fun comes in, requiring that CTC's be consistent. This is the "game" of CTC's, no? You go back, kill your mother, then discover that you slept with some woman who turns out to actually be your mother, etc...

Ron, something interesting is that CTC are computationally NP-complete, so they can compute QM and then some

@lurscher: The point is there are no CTC's in GR outside of some ridiculous black hole interiors, so this is a game of make-believe. There are no actual CTC's even in the case I gave, where you come out of a black hole in this universe, since the only closure happens in un unphysical trans-Planckian skin around the horizon. The OP was asking about CTC's, and there aren't any.

OK, Ron, thanks a lot, I accepted your answer. It seems to me you are basically saying that all this hype from people like Michio Kaku about wormholes are lies... this I will have to simply accept, but it is a bit surprising.

@user1247: I didn't say anything about wormholes.

@Ron Maimon, aren't black holes allowing CTCs the same thing as wormholes?

@user1247: The "CTC"'s in traversable black holes (going in and out) are completely unphysical (this is the only reason one should take this picture seriously)--- it's just a mathematical CTC in a tiny unphysical skin near the horizon. It's not a real CTC, it's something that's washed out by the proper quantum definition of horizon.

@Ron, then what is a wormhole (you didn't answer my question)? Also, again, it's not fair to talk about the "proper quantum definition" in this context, since the hypothetical is that QM is emergent from a classical picture + CTCs.

@user1247: You are repeating the same annoying points--- a wormhole is when you go in one black hole and out another disconnected one. This is much less plausible than going in one black hole and coming out the same black hole later. QM just doesn't emerge from GR or any other classical field thery, it is a different kind of theory, it has amplitudes for superpositions of different GR fields, it has a global notion of wavefunction that has no relation to classical fields. I don't know why you think that GR has to explain QM, other than that Einstein hoped this was so. It doesn't work.

@user1247: My skepticism is based on the fact that the linear superposition aspects of QM are not reproduced from any classical theory so far, even when I say "go make one up, no constraints, do whatever!" This makes it doubly implausible when someone comes up and says "maybe it's classical fields". There are no CTC's produced exterior to black holes in classical GR, and the interior and exterior of black holes are causally disconnected in classical GR. But even if you make up laws that say they are produced, you still can't reproduce QM from this, because it's a tall order to reproduce QM.

@Ron, fair enough. But this is why I'm trying to understand what is and what is not understood about CTCs in GR: having absolutely no constraints can make a problem more difficult, so knowing what is constrained within GR can at least help me to think about this problem for myself, and (hopefully) come to the same conclusion that such classical models are impossible. As I described in my response to you in Lubos' answer's comments, off the top of my head I can think of some ways in which CTCs could reproduce QM-like behavior... I'll think some more and get back to you...

@Ron, I should add that, just to be clear, I completely agree that without CTCs it is ridiculous to try to get QM from GR. It's just that with CTCs things are so complicated that unless I am missing something, I don't see how the idea is obviously wrong (for example, you cannot make the computational argument you tried at the beginning to rule it out).

@user1247: The problem is that CTC theory the way you envision it is not a real deterministic theory, there are constraints on the data which require self-consistency. It is a little silly, for example, if you take a thermodynamic system around a CTC, there must be a maximum entropy point, and entropy goes down on both sides of this. It's really not the way physics works, and it would be worse than QM philosophically, it would require constrained computations to determine the future, and it would have miraculous entropy reducing moments along CTC's. It would be magic.

Ron's problem with the infinite dimensionality of QM is solved in a classical 4D theory like GR by simply using different frequencies for each 'k' in his '3k' dimensionality. An analogy would be that we can run many different radio controlled cars by using different communication channels, all using the same EM fields. Any model of 1000 radio controlled cars would naturally use 4000 dimensions if the model were built by someone ignorant of the underlying real physics. The thought that QM is anything more than a toy is kind of funny. Infinite dimensions and infinite computing power?