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First, I’d like to apologize for yet another question about crazy ideas on how quantum mechanics might actually work. I have no background in quantum mechanics. Recently, though, I started to study quantum computing, which turned my attention to Bell’s inequality and its experimental violations.

Latest of those experiments claim to be loophole-free. As I understand it, they place the measurement devices such far away from each other, that no speed-of-light communication is possible before the measurements took place.

But one thing bothers me: we can’t be sure what exactly happened at those remote devices unless classical information travels back to us from there. So it seems like a possibility that there is some kind of action, propagating as fast as light, that causes any measurements of the entangled pairs to be observed as correlated. (I imagine it as some kind of bit-flipping in cellular automata.)

Apparantly, either nobody had such ideas, or everyone regards them as obviously ridiculous. So my question is: what exactly does this idea contradict? Why do actual experimenters never care about it?

UPD

Below is the process that I picture in my mind. Please note that I'm showing it purely to clarify what I mean by post-measurement conspiracy. My question is not why this particular scheme is not going to work, but rather why any such post-measurement magic can't work, in the spirit of how far-away separation kills any possible communication channel between measurement devices.

  1. Entangled pair of particles is created. Label "A" means that they both belong to the same pair. These labels travel along each of the particle. Two entangled particles marked with "A" moving apart.

  2. The particles are measured in some bases denoted by B and C. Left particle is measured in B. Right one is measured in C.

  3. Measurement devices send back classical information about the outcomes. But here goes the magic: B(A) and C(A) tags get attached to it. If information gets copied at some point, so do the tags. Classical information about the measurement moves back, carrying tags B(A) and C(A).

  4. When the tags (with the same "A" label in parentheses) spatially collide, they rewrite each other by adding remark in superscript meaning "relative to". In this way they "agree" with each other. And there is enough things to magically rewrite the outcome (classical information) to reproduce required correlations. Upon collision, tags get rewritten to their relative counterparts: B^C(A) and C^B(A)

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  • $\begingroup$ A local "bit flipping" counts as a hidden variable. This is precisely what Bell's inequality violation rules out. $\endgroup$ – Stéphane Rollandin Feb 7 '18 at 22:24
  • $\begingroup$ @StéphaneRollandin, even when it happens after the measurements? $\endgroup$ – Dmitri Urbanowicz Feb 7 '18 at 22:41
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    $\begingroup$ I don't see how you can have anything happen after the measurements that makes them "look correlated". $\endgroup$ – Stéphane Rollandin Feb 7 '18 at 22:48
  • $\begingroup$ @StéphaneRollandin, updated the question to clarify what I mean. $\endgroup$ – Dmitri Urbanowicz Feb 8 '18 at 13:52
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I don't think you can rule out conspiracy, in the same way you can't rule out superdeterminism (which perhaps is one class of conspiracy). But I don't think either notion makes any prediction which is testable, even in principle (certainly superdeterminism does not). As such ideas like this lie outside the realm of physics, which deals in experimentally testable theories.

This is not to say such ideas aren't interesting: they may be, they're just part of philosophy rather than science.

Of course, if you can come up with a test for your 'conspiracy theory' (not in the normal derogatory sense of that term), then I'm wrong and it is part of science, but I suspect you can't.

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