Jonathan Oppenheim, "A postquantum theory of classical gravity?"

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Jonathan Oppenheim, "A postquantum theory of classical gravity?",

Jonathan Oppenheim et al, "Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity", Nature Communications (2023). DOI: 10.1038/s41467-023-43348-2

thoughts on A postquantum theory of classical gravity

The hypothesis is a little arbitrary. Every other field we know about is quantized.

For me, the larger issue which this borders on, is the question of which possible properties become actual.

In quantum mechanics, you can't have definite values for all observables at once - this goes back to the uncertainty principle, and the tradeoff between precision in position and precision in momentum. Which properties do become actual, is one of those basic questions, that is answered differently in different "interpretations".

One of the interesting proposals is associated with the "decoherent histories" or "consistent histories" program of Omnes, Gell-Mann, and Hartle. You have a wavefunction of the universe, and a set of possible histories, each of which is defined by a particular choice of observables and values for the observables; and you can assign an apriori probability to each history.

Consistent histories gives you a quantum formalism in which you don't need to talk about an external observer - which is good for cosmology - but it still doesn't tell you which observables become actual. So Gell-Mann and Hartle proposed that maybe our universe belongs to a set of consistent histories that is maximally fine-grained in some sense. That is, although not all possible properties can be definite at the same time, thanks to the uncertainty principle, you can suppose that you squeeze in as many definite properties as quantumly possible. This was called a principle of "maximality".

In Oppenheim's combination of classical gravity and quantum fields, the gravitational field will have "more" or "a greater density of" definite properties, than is possible in a theory with quantized gravity. I could find this aspect of what Oppenheim is doing, conceptually interesting - it's probing the consequences of going beyond the quantum maximum of fine-graining the gravitational field.

mitchell porter said:

The hypothesis is a little arbitrary. Every other field we know about is quantized.

For me, the larger issue which this borders on, is the question of which possible properties become actual.

In quantum mechanics, you can't have definite values for all observables at once - this goes back to the uncertainty principle, and the tradeoff between precision in position and precision in momentum. Which properties do become actual, is one of those basic questions, that is answered differently in different "interpretations".

One of the interesting proposals is associated with the "decoherent histories" or "consistent histories" program of Omnes, Gell-Mann, and Hartle. You have a wavefunction of the universe, and a set of possible histories, each of which is defined by a particular choice of observables and values for the observables; and you can assign an apriori probability to each history.

Consistent histories gives you a quantum formalism in which you don't need to talk about an external observer - which is good for cosmology - but it still doesn't tell you which observables become actual. So Gell-Mann and Hartle proposed that maybe our universe belongs to a set of consistent histories that is maximally fine-grained in some sense. That is, although not all possible properties can be definite at the same time, thanks to the uncertainty principle, you can suppose that you squeeze in as many definite properties as quantumly possible. This was called a principle of "maximality".

In Oppenheim's combination of classical gravity and quantum fields, the gravitational field will have "more" or "a greater density of" definite properties, than is possible in a theory with quantized gravity. I could find this aspect of what Oppenheim is doing, conceptually interesting - it's probing the consequences of going beyond the quantum maximum of fine-graining the gravitational field.

But gravity is different as in GR it is the result of spacetime geometry.

if Jonathan Oppenheim theory is correct, does it falsify string theory, loop quantum gravity, supergravity, or even entropic gravity, or could it be combined with the other approaches?

Jonathan Oppenheim theory of gravity + QFT and standard model + any dark matter or MOND = TOE?

kodama said:

if Jonathan Oppenheim theory is correct, does it falsify string theory, loop quantum gravity, supergravity, or even entropic gravity, or could it be combined with the other approaches?

In my world, a theory is falsified by experiment, unless you can show contradictions within the theory itself. However if a theory that solves the same set of problems can be formulated in a simpler framework, I would consider today's theories redundant.

Kontilera said:

In my world, a theory is falsified by experiment, unless you can show contradictions within the theory itself. However if a theory that solves the same set of problems can be formulated in a simpler framework, I would consider today's theories redundant.

is Jonathan Oppenheim theory a simpler framework?

kodama said:

if Jonathan Oppenheim theory is correct, does it falsify string theory, loop quantum gravity, supergravity, or even entropic gravity, or could it be combined with the other approaches?

The prototype for what Oppenheim is doing, is the general idea of something classical (with all properties always definite) interacting with something quantum (that is described by something out of the quantum formalism). There are general formalisms, that Oppenheim calls CQ (classical-quantum), for this kind of interaction. Oppenheim's approach to gravity, is to have a CQ formalism in which the classical variables are those that describe space-time (such as the metric), and everything else is quantum. The prevailing attitude has been that this is simply inconsistent, but in papers like the one above, he and his coauthors single out conditions under which such an interaction is well-defined.

To construct a CQ theory of gravity from an existing theory of quantum gravity, you have to single out the variables in the theory that are gravitational, and make them classical while keeping everything else quantum. Possibly you could do this with supergravity or loop quantum gravity, since the gravitational variables are distinct. Entropic gravity could be a problem because gravity is supposed to be emergent - there aren't fundamental variables that are specifically gravitational. As for string theory, again it seems difficult because the gravitational modes of the string are so intimately related to all the other modes. It would almost be easiest to do this, not for space-time gravity, but for the topological "gravity" on the worldsheet.

When it comes to coupling classical gravity to quantum fields, like those in the standard model, I'm not sure that Oppenheim's procedure for constructing a CQ gravity theory is well-defined. He supposes that there is a Hilbert space for the quantum part of the theory, and then at each point of classical space-time, a certain kind of operator from that space is attached. My issue is the role that renormalization plays in defining quantum field theories, it's an extra complication that may not fit his framework. The other issue for the standard model is UV-completeness. Even if we suppose that a CQ gravity theory could be constructed if the quantum variables were a UV-complete field theory like pure QCD, the actual standard model also contains a U(1) hypercharge gauge field, and U(1) quantum fields aren't UV-complete because of the "Landau pole".

Also, on the gravity side, I wonder how generally applicable the CQ framework is. In general relativity, a classical space-time geometry is deterministic only if it is "globally hyperbolic". Any deviation from this might also cause problems for a CQ theory.

arXiv:2401.05514 (gr-qc)
[Submitted on 10 Jan 2024]
Diffeomorphism invariant classical-quantum path integrals for Nordstrom gravity
Jonathan Oppenheim, Andrea Russo, Zachary Weller-Davies

The excellent paper "Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity" of Oppenheim, J., Sparaciari, C., Šoda, B. et al. (Nat Commun 14, 7910 (2023). https://doi.org/10.1038/s41467-023-43348-2)
could perhaps be more accessible to the lesser gods (like me in the first place) if some remarks could be taken into account: Matters Arising: On Testing the Quantum Nature of gravity: manuscript and support material

The (as far as I can tell) original Oppenheim paper on this type of model is here:

https://arxiv.org/abs/1811.03116

mitchell porter said:

To construct a CQ theory of gravity from an existing theory of quantum gravity, you have to single out the variables in the theory that are gravitational, and make them classical while keeping everything else quantum. Possibly you could do this with supergravity or loop quantum gravity, since the gravitational variables are distinct.

what would be the reason to To construct a CQ theory of gravity from an existing theory of quantum gravity? CQ theory of gravity is to do away with quantum gravity

doesn't string theory posit smooth space like GR?