The more I learn about General Relativity, the more it seems like it isn't fully understood. It seems that before it's full consequences were exhaustively understood, not 10 years after its discovery, QM came on the scene and stole the limelight. Now it seems like a "boring" field without much funding, even though all but the most trivial and artificial types of solutions to the field equations are known. Here, for example, @Ron Maimon describes how classically a type of black hole allows solutions in which a particle can cross the event horizon, and then exit the event horizon at an earlier time, seemingly leading to causal paradoxes. It sounds like this is an issue that was never fully resolved. It seems the sort of very messy thing that, once properly understood, could lead to some very odd physical behavior.

Is it possible that all particles are just extremal black holes, and that Quantum Mechanics is just an emergent property of the solution to Einstein's field equations for the interactions between extremal black holes going backwards and forwards and time? Does something like Bell's inequality rule out this sort of idea?


There are some papers purporting to do this. Mitchel Porter pointed out these: McCorkle, Hadley

I also found: McCorkle

And then there is Mendel Sachs who has written a number of books purporting to derive QM from GR.

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    $\begingroup$ Mark Hadley wants to get QM from CTCs in GR, e.g. arxiv.org/abs/gr-qc/0703150. And R.A. McCorkle tried to get the whole standard model from vacuum GR, adsabs.harvard.edu/abs/1989PhyS...40..721M arxiv.org/abs/hep-th/9612045. You might find those interesting to puzzle over; try to figure out why they don't work. $\endgroup$ – Mitchell Porter Sep 4 '12 at 11:54
  • $\begingroup$ @Mitchell Porter, I'm afraid I may need more of hint as to why these don't work. If you took Lubos' answer to heart you would think such people were complete imbeciles. I'm curious whether what they did was stupid, or didn't work for some other technical reason. It would seem incredibly surprising to me that such an idea would almost work, and yet not be true, or not have a larger group of suitors. $\endgroup$ – user1247 Sep 4 '12 at 13:50
  • $\begingroup$ I'd like to point out en.wikipedia.org/wiki/Penrose_interpretation here too. Since it links space-time curvature to wave function collapse. $\endgroup$ – pepper_chico Sep 4 '12 at 21:31
  • $\begingroup$ @Chico, Penrose's interpretation doesn't purport to derive QM as a consequence of GR. All it does is attempt to motivate the collapse of the wave function. $\endgroup$ – user1247 Sep 4 '12 at 21:46
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    $\begingroup$ @Larry Harson, I certainly keep it in mind, but it's pretty depressing if this is the strongest argument regarding the content of the papers that physicists here can come up with. $\endgroup$ – user1247 Sep 6 '12 at 17:25

I would like to add a little to Lubos's answer:

First a historical note: this is what Einstein proposed as a way of understanding quantum mechanics in 1919 or thereabouts, in the paper "do gravitational fields play a role in the composition of the elementary particles?" Einstein was of the opinion that a complicated enough classical theory, like general relativity, would lead continuous waves to collapse into standard-size soliton-like particles and these particles he felt might then bang around along the wave in such a way to reproduce quantum mechanics.

This idea reappears several times in the literature, but it demonstrably doesn't work. A field theory, like GR, is a classical theory, and it therefore is local hidden variables (the variables aren't even hidden in this case). This is ruled out by Bell's theorem--- the correlations in quantum mechanics don't allow local fields to carry the data that determines the experimental outcome, not without conspiracy (superdeterminism) or nonlocal equations (faster than light changes in the variables). Neither works in a straightforward field theory like GR.

Secondly, GR is not as badly understood as all that, although it is not as well understood as one would like, mostly because numerical methods are in their infancy, and one's intuition must come laboriously from analyzing exact solutions when these are available. The example I gave of particles oscillating into and out of an extremal black hole is not really new (don't give me too much credit), the new thing there is the holographic interpretation, namely that the coming-out is an ordinary coming out event in this universe. The oscillations of particles into and out of a near-extremal black hole were appreciated in the 1960s, but each oscillation takes you to a disconnected branch classically, because crossing a horizon takes an infinite amount of t-time. This is not possible quantum mechanically, since this disconnected maximally extended thing is not compatible with unitarity.

The nice thing about the in-out solution for geodesics in the extremal Reissner Nordstrom is that if you replace the test particle with a little charged black hole, you can make nonrelativistic oscillations if both black holes are near extremal. The external field of the two black holes does not have a full merger, the little black hole, now not considered as a test particle, but as a solution to GR proper, just smears out on the horizon, then bounces back. I didn't calculate this in detail yet, but it can be solved completely with an analysis along the lines of Atiyah and Hitchin in their famous paper on slow soliton scattering (the Atiyah Hitchin space), except here, unlike the other case, I am not optimistic there will be a simple geometrical solution, rather one has to bite the bullet and trace the bouncing behavior in the solution either by numerical integration or solving for the near-static phase-space geometry of the two extremal black holes.

Causalities and CTC's

The basic idea you are giving is that perhaps hidden variables plus closed time-like curves can reproduce Bell inequality violations. I will give some sentences about why this is extremely unlikely.

Quantum mechanics has entangled wavefunctions. What this means is that the wavefunction for k particles is in 3k dimensional space, not in 3 dimensional space. The growth in dimensions means that quantum mechanics packs a stronger computational punch than classical mechanics, and you can't simulate quantum mechanics of k-particles with less than exponentially much classical information. This is why quantum computation works in pure quantum mechanics.

So the structure of quantum mechanics is exponentially big and has the entanglements that violate Bell's inequality. If you wish to reproduce this from something like GR, you need gross nonlocality and some way of reproducing nonlocality.

So if you have a pair of electrons that bind to an atom (so that their spins anti-align), and then you knock out the nucleus, and do Bell measurements on the two outgoing electrons, you need to reproduce the nonlocal correlations from CTC's in GR. This means that the electron needs to have CTC's "inside" which go back in time and magically alter the attributes of the other electron. This only became required once you put them together in an atom, and let the photons radiate, and during this process the two point electrons didn't necessarily come close to each other (assuming they are classical and described in space). How do CTC's help correlate them?

To make this work, you would have to go all the way back in time to where the two electrons were created from the inflaton field, and correlate them back then. This type of back-and-forth in time description is utterly conspiratorial, and very unconvincing. There is also no shred of a hint that this will reproduce anything like QM, it's just not ruled out, because you are postulating little tiny internal back-in-time paths on all electrons, something we have no evidence for.

There are no real CTC's in physical exterior solutions of GR. The CTC's in the intepretation I gave of oscillations into and out of extremal black holes are unphysical--- they are only closed in time because of the wrongness of the classical picture of the horizon.

The CTC's in the interior of a Kerr solution can only occur when you wind around the ring singularity, and then it should be possible to unwrap the interior so that it has a pure-causal description, simply by including the winding number of your path around the ring. I don't know the interior Kerr well enough to see how to do this, and this must work in any number of dimensions, not just 4, so I hesitate to say it is what happens, but there must be a reconciliation of causality and Kerr interior, because you can set up fields at the horizon of Kerr, and let them traverse the interior, and the evolution equation shouldn't have additional constraints, as come from CTCs.

All in all, the form of the two theories, GR and QM, is completely different, the descriptions are of a different computational complexity, and the causality notion is totally different in the two schemes, so it is implausible in the highest degree that GR can explain QM.

What's more, today we have a good quantum version of GR, string theory, which subsumes and extends the classical theory, so that it is a mistake to pretend that this progress does not exist, and to work as if we were living in 1926. Within string theory, you give a full accounting of all GR effects on flat and AdS backgrounds in principle, from an ordinary unitary quantum theory. This quantum GR means that we know how GR and QM are reconciled (in perturbations to flat and AdS backgrounds), and the classical limit where GR is reproduced is just not quantum, it's an ordinary classical field theory.

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Apr 7 '17 at 23:55

No, it is not possible. It is impossible in the same sense in which it is impossible that a truck is just a carrot. Those are completely different theories addressing totally different issues about Nature. Quantum mechanics is a framework, addressing in a new way how observables are represented, how we describe the set of possible states in which a physical system may find itself, and how predictions about the future measurements of the observables may be extracted from the mathematical formalism.

Quantum mechanics doesn't say anything specific about the actual Hamiltonian – number of degrees of freedom and the law by which they evolve.

General relativity is something completely different. It doesn't say anything about the logical framework of physics – most typically, we mean the classical (=non-quantum) general theory of relativity by the term "general relativity" – but it does say what is needed about the actual laws describing the evolution of time, the equivalent of a Hamiltonian.

A classical theory can't be quantum because it violates the postulates of quantum mechanics. Or, if one needs more experimentally rooted contradictions, a classical theory implies that Bell's inequalities and similar laws always hold while quantum mechanics routinely violates them.

Quantum mechanics "can be" general relativity if it is combined with the principles of general relativity. However, it must be done in a non-obvious way and string/M-theory is the only known mathematical consistent way how to merge the principles of quantum mechanics with those of general relativity. But once again, even in string/M-theory, the postulates of QM are completely different insights from the insights of GR.

  • $\begingroup$ This is a boilerplate answer that seems to miss the point. Bell's inequality may rule it out, but I'd like to hear some other points of view on that, given that I've seen none other than 't Hooft on this board advocating something that would violate the inequalities (there being loopholes). $\endgroup$ – user1247 Sep 4 '12 at 13:46
  • $\begingroup$ To expand on why your answer is so terrible Lubos, consider the papers linked to by Mitchel Porter. In one of the abstracts, there is: "It is shown how the logical structure of propositions and the probabilities of quantum theory arise from such acausal space times." Of course I understand that, as you say, "General relativity is something completely different", but it is not so clear to me that QM, though having completely different postulates, cannot arise emergently from a careful consideration of "such acausal space times". $\endgroup$ – user1247 Sep 4 '12 at 13:54
  • $\begingroup$ "...but I'd like to hear some other points of view on that" - Apologies, I always submit answers or "points of view" that I consider correct rather than "other points of view" - and I think that correct answers is exactly what the authors of questions are supposed to expect. Concerning your second comment, it's again the case that "causality of spacetimes" has nothing whatsoever to do with "quantum mechanics". These refer to different portions and features of Nature. Your suggestion is similar to the suggestion that a Swedish truck on ice stadium could become a carrot. $\endgroup$ – Luboš Motl Sep 5 '12 at 16:10
  • $\begingroup$ It is not that you are wrong (I am not sure whether you are right or wrong) it is that your "answer" is a non sequitur in that it does not attempt to address the content of my question beyond perhaps a cursory reading of its title; it is patronizing (I am a physics grad student who is well aware of the postulates of QM and GR), and as a result almost completely vacuous and unhelpful to me. And please don't act so obtuse; of course superficially acausality does not equal QM, but it is surely not so obvious what the consequences are, and Bell's constraint is bypassed. $\endgroup$ – user1247 Sep 5 '12 at 16:34
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    $\begingroup$ Also, Lubos, you say you read my EDIT with links to papers claiming to do exactly what I'm asking about, but you did not mention them or give any hint to where they are going wrong. Doing so would be very helpful. $\endgroup$ – user1247 Sep 6 '12 at 8:43

Some observations on the taxonomy and history of such claims.

"QM is just GR" is a subset of "QM is just a classical theory".

Attempts to derive QM from GR can be divided into those which think they have a loophole in Bell's theorem, and those which don't even notice the issue.

Einstein is the original physicist who wanted to get QM from GR. He wanted to get quantization of allowed values for observables through special boundary conditions. This was before Bell's theorem and it's the grandfather of all the QM-from-GR ideas which don't address Bell's theorem. Sachs and McCorkle fall into this category.

Then we have the people who acknowledge the existence of Bell's theorem but look for a loophole. Gerard 't Hooft's latest work, recently discussed on PSE, falls into this category.

I won't attempt a proper taxonomy of loopholes. But for this discussion, the unifying idea has to be that QM will be derived from classical probability distributions over states and/or histories in an underlying "classical" (realist, objective) theory. This is what Bell's theorem says is impossible, at least if the underlying theory is local, and there are other theorems which pose further problems for realism.

For this discussion, I would then make the further taxonomic distinction between seeking a loophole from the existence of CTCs in the underlying theory, and seeking a loophole in some other way. For example, 't Hooft doesn't talk about CTCs as part of his theory, he talks about cosmic initial conditions.

This is the "superdeterminism" loophole and it shouldn't work in the following sense: It may be possible to create probability distributions over histories in the underlying theory, such that the expected outcomes of EPR-type experiments match QM; but only by cheating - by finetuning the choice of histories and the choice of distributions in order to match the QM predictions, in a completely artificial way.

To my knowledge, the "CTC loophole" or "time-loop loophole" has never been coherently discussed, nor has it been coherently advocated in the terms I just described - i.e. that QM is to be obtained from probability distributions over space-times with CTCs in them. Mark Hadley has written several papers about getting QM from CTCs in GR, but he comes at it via "quantum logic". That is, he tries to show that propositions about counterfactuals in a CTC space-time would have a "complementary" or "nondistributive" property.

So the issue of whether classical probability distributions over space-times with CTCs, would have to be finetuned as in the "superdeterminist" case, to produce QM, has never been examined. I would add that this issue is also relevant to any attempt to get QM from an underlying retrocausal theory, e.g. an amended version of Wheeler-Feynman theory. Such theories may not have CTCs in the sense of GR, but they will contain causal loops (possibly locally stochastic rather than locally deterministic) resulting from the combination of causal and retrocausal chains of influence.

The closest thing to such a study is found in a very recent paper by Wood and Spekkens, which employs simple methods of causal inference to show the need for finetuning in various models of QM. They consider superdeterminism, and they also consider retrocausality, and show that one form of retrocausality also requires finetuning; but they only consider retrocausality without time loops. So someone needs to start looking at classical probability distributions over families of causal graphs that contain cycles, in order to address the general "CTC loophole".


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