Are there limits on very much faster than light propagation at extremely small scales?

Question

Local realist classical models for QM experiments are fairly clearly ruled out by the violation of Bell inequalities, despite various possible saves such as superdeterminism or the memory loophole (PhysRevA 66, 042111(2002), https://arxiv.org/abs/quant-ph/0205016).

If one looks for alternatives, that QFT is a remarkably effective Einstein-local theory is now unquestionable, but in an Einstein-nonlocal classical model set at scales of, say, $10^{-100}$ meters there could perhaps be propagation at, say, $10^{20}$ times faster than light that would wash out in an effective theory as only the correlations we observe at relatively much larger scales. _{$\bigl[10^{-100}$ meters and $10^{20}c$ are just such ridiculously small and fast scales that they're entirely beyond our ability to directly measure them, the particular numbers are not especially a concern. Feel free to substitute $10^{-10000}$ meters and $10^{50}c.\bigr]$} Can \(all\) such FTL Physics be ruled out? The point of Universality in statistical mechanics is that an effective theory wipes out small scale details, but can we prove that any such FTL propagation would not wash out and would be detectable, no matter how small or how fast, and no matter how organized?

At the most extremely ridiculous, one could imagine simplicity comparable to nuclear physics at $10^{-100}$ meter length scales, but with comparable-to-human complexity at $10^{-80}$ meter length scales. With the computing storage this permits and the ability to send messages $10^{20}$ times faster than light, intelligent beings (many, many of them) could deliberately coordinate physics at the 1 meter scale to be as we observe. Not that it's really like this, this is beyond The Matrix stupid, but can we rule out every small and fast model anyone can think of? Can some FTL models be simple enough to be relatively attractive and even, perhaps, useful?

Supposing there is any such theory that reproduced the measurements that make QM so useful, surely there must be an enormous number of such theories, in which case speculation about them would seem to be almost pointless. Actually making such models useful also seems almost hopeless. One also has to keep some perspective: even if such models are possible for any given quantum theoretical model, nonetheless they might eventually all be ruled out by future experiments; the world really might not be classical. Even so, I take this discussion to be slightly helpful in two ways: (1) as a different reason for shut up and calculate (until we actually have evidence that would justify one class of such FTL models over another); (2) as a curb on over-zealous rejection of classical models (unless all such FTL models can be ruled out).

Comments

The question is far too vague. In relativistic QFT, there is no faster than light signalling. But one can speculate about anything at unmeasurablly short durations if one is prepared to leave the standard foundations. 

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The question is far too vague. What kind of limits - theoretical or experimental? We can build any kind of "theory", so what? Experimentally we are in the realm of our relativistic models so far.

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Certainly I can agree that the question is vague. Certainly relativistic QFT, as an effective theory, allows no FTL signalling by construction, and that is supported by experiment as it now exists. But my intended point is that I want to motivate not looking for such models because of the inevitable arbitrariness, while, however, in the absence of explicit no-go theorems, also accepting the possibility of such models as a curb on being over-zealous about the Q(F)T models we find useful at the moment. Are there explicit theorems about the suppression or not of FTL propagation as we consider effective field theories at increasing length scales?

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If you leave the standard foundation there are no theorems at all. Hence nothing to limit speculation.

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FWIW, despite the ridiculous example I had thought of myself as limited to effective field theories, perhaps random or quantum however I am content to restrict to only quantum, but with the one change of introducing much-FTL-Lorentzian propagators at very small scales, resulting, perhaps, in effective Einstein-Lorentzian propagators at scales above perhaps $10^{-20}$ meters. It seems that such a construction would need to be at many orders of magnitude smaller than nuclear scales for the Einstein-Lorentzian propagators to be as accurately effective as they are. This doesn't seem obviously too much of a stretch given that, slightly analogously, for the very special case of Helium in specific conditions, Einstein-Lorentzian propagators at atomic length scales result in effective speed-of-sound Lorentzian propagators, with, say, 8-10 orders of magnitude between length scales.