Is it possible that QM is just GR?

Question

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?

EDIT:

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.

Answer 1

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.

Answer 2

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.

Answer 3

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".

Answer 4

The situation addressed by the question may be called the Einstein's Revenge Scenario - that of emulating the weird properties of Quantum Theory entirely from weird properties found in solutions or models that may be devised in General Relativity, particularly if they involve things (such as the inherent non-determinism of naked singularities or closed time-like curves) that there are no clearly-established methods currently in place to handle.

I won't answer the question directly, but will provide a short list of references that seem to be heading in that direction and which provide pieces in a puzzle that may actually fit together.

First, there's Hadley's thesis, which I've been aware of for quite a while...

QM from GR
https://drmarkhadley.com/quantum/quantum2/

He apparently wants geoids that are acausal in their close proximity as a way to synthesize or emulate the von Neumann logic structure associated with quantum physics, starting from a purely classical grounding.

Dirac - Kerr-Newman Electron
https://arxiv.org/abs/hep-th/0507109

which is Burinskii's baby, but descends from Israel (1970) and Lopez (1984). There is a deep correspondence between the Dirac equation and its solutions with the Kerr-Newman solution that goes beyond the semi-classical level of first quantization and includes some of the features found at the level of second quantization.

It bears pointing out that a solution to Einstein's equations that has the same charge, angular momentum (as spin) and mass as any of the fundamental fermions - possibly except the right-handed neutrinos and left-handed anti-neutrinos, if they exist - is not just a Kerr-Newman solution, but a naked Kerr-Newman ring singularity. The neighborhood of such a solution has the kind of acausality that Hadley seems to be looking for.

It's like a mini-stargate.

Kerr-Newman Metric (Wikipedia)
https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric

also makes passing reference to the modelling of fermions by Kerr-Newman solutions. It notes that Burinskii's version generalizes Israel and Lopez's version, because they cut off the back side of the singularity, if I understand that right. (It's called the "negative sheet" in the article.)

To really make this correspondence work for all the fundamental fermions, you should be considering not just electrical charge, but also the gauge charges. That means, it's not sufficient to just look at the Kerr-Newman solution, which solves the coupled Einstein-Maxwell equations, but what the analogue of it is for the coupled Einstein-Yang-Mills-Higgs (EYMH) equations. I don't know enough about those to say anything more. I don't even what they're called, or if there even is any kind of well-known established EYMH analogue of the Kerr-Newman solution.

ER=EPR, Entanglement Topology and Tensor Networks
https://arxiv.org/abs/2203.09797

This is actually Susskind's and Maldacena's baby; but this reference is something more recent from Kauffman, the knot-theory guru over in Chicago. That's a surprise. I didn't even know he was still active; and this is an unexpected direction for him.

This is the premier reference from Susskind and Maldacena on ER = EPR:

Cool horizons for entangled black holes
https://arxiv.org/abs/1306.0533

Section 3 is ER = EPR.

This is later reference by Susskind, trying to tie it together with the duality between Everett and Copenhagen

Copenhagen vs Everett, Teleportation, and ER=EPR
https://arxiv.org/abs/1604.02589

So ... how do these pieces in the puzzle fit in with the others? If the fermions-as-Kerr-Newman solutions are wormhole mouths perhaps with "pair production" itself arising by the production of the opposite ends of wormholes (and note that Hadley wanted such pairs in his model, the last time I reviewed his work) then that may be one way to implement the ER of ER=EPR.

Susskind's vantage point, it is worth pointing out, is firmly couched in quantum theory and even string theory. So, notwithstanding his hypothesis, I don't think he's outright advocating for any kind of Einstein's Revenge Scenario.

However... in more recent times, Susskind has raised the ante a bit with

Dear Qubitzers, GR=QM
https://arxiv.org/abs/1708.03040

You can almost hear Lubos-fits coming out of this one. I'll just put up the opening paragraph:

"Dear Qubitzers, GR=QM? Well why not? Some of us already accept ER=EPR [1 = Cool Horizons reference above], so why not follow it to its logical conclusion? It is said that general relativity and quantum mechanics are separate subjects that don’t fit together comfortably. There is a tension, even a contradiction between them—or so one often hears. I take exception to this view. I think that exactly the opposite is true. It may be too strong to say that gravity and quantum mechanics are exactly the same thing, but those of us who are paying attention, may already sense that the two are inseparable, and that neither makes sense without the other."

So, maybe he is starting to head in the Einstein's Revenge Scenario direction, after all.

In fact, that's what attracted my attention to this thread. I thought you were all talking about Susskind's recent promotion of ER = EPR to QM = GR; but as I look at the date, I see that this actually precedes these later developments. Only Hadley and Burinskii were out, when this question first arose. Susskind and Maldacena were still on the horizon.

So, can anyone fit the pieces to the puzzle, that I laid out here, together? If I can find some spare time, I might more closely examine the references, and other related references, and give it a try to see if they can be synthesized into some kind of coherent big picture for a bona fide Einstein's Revenge Scenario.

If you're really adventurous, feed all of this to AI and see what it can synthesize, under guidance.