Even if a nonlocal statistical theory

You are already misinterpreting what I am saying. I am saying quantum mechanics is a non-local statistical theory. I am not advocating some alternative theory to replace quantum mechanics. To my knowledge, this viewpoint was first put forward by Dmitry Blokhintsev in the early 1950s. Einstein defended both locality and the idea that quantum mechanics should be interpreted as a statistical theory. Blokhintsev strongly agreed that it should be interpreted as a statistical theory, but disagreed that it should be taken to be a local theory. This was long before Bell’s theorem was ever published, which people treat as proof Einstein was wrong and therefore quantum mechanics cannot be interpreted as a statistical theory. But Bell’s theorem is not in conflict with Blokhintsev’s views. Blokhintsev was also critical of Einstein’s commitment to determinism, advocating that nature should be understood to be fundamentally unpredictable.

that would still remain at the level of describing outcomes, wouldn’t it?

No, because a statistical theory admits that the system has a definite configuration at all times, it just evolves randomly so that you cannot track its definite values. We can imagine a perfectly classical universe where the laws of physics are still fundamentally random, but in a classical sense that cannot violate Bell inequalities, and this would prevent you from being able to track the definite states of particles at all times. But it does not then logically follow that the particles do not possess definite states at all times. The denial of this fact is where all the exotic views of quantum mechanics stem from, all the “quantum weirdness” and claims it is somehow in conflict with realism or requires a multiverse, or something absurd like that.

“The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. In that case the whole “egg-walking” performed in order to avoid the ‘physically real’ becomes superfluous.” — Albert Einstein, “Albert Einstein: Philosopher-Scientist”

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In reality, the unification of quantum mechanics and relativity has remained unresolved for over 150 years, and the deeper issue is that the framework itself does not define the structure of observation.

No, the issue between unifying GR and QM comes from renormalizability, although it is really only an “issue” at high energies. The reality is not that GR and QM are incompatible, but that we just don’t know what happens at high energies because we’ve never built anything that can probe there. I’d recommend you look up John Donoghue’s discussion on this topic; you can combine GR and QM just fine if you stick to the energy regimes we can actually probe. You can also combine GR and QFT just fine under an semi-classical gravity, which is correct for all fields we can meaningfully probe.

The issue is less that we cannot unify the two theories, but we cannot unify them under regimes we have not even probed yet, and any attempt to unify them will be speculative anyways since they would only have implications for things we cannot currently measure. The dire need to build a “theory of everything” at the moment is just overblown. It makes no sense to build a “theory of everything” unless you can probe everything, otherwise it will inherently be overly speculative.

If you think this speculation somehow solves the problem at high energies, then take it further and actually build a model of GR and QM that does not break down at high energies. Otherwise, I don’t see this as particularly relevant, but it is trying to resolve pseudoproblems, like the measurement problem, which are self-imposed problems.

This theory, on the other hand, addresses that very point by defining the conditions under which outcomes are realized— that is, the structure of observation itself— and treats quantum mechanics and relativity as aspects of a single generative process.

If supposedly this fixes the renormallization issue then actually fix it. Construct a theory of quantum gravity. You won’t be able to because this isn’t going to help you out. It’s “solving” a different “problem,” and that is a pseudoproblem.