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Bell's theorem rests on two main assumptions: locality and independence. Locality has its basis in relativity and it seem to be a property of all known physical theories accepted today (General relativity and the quantum field theory).

The independence assumption (also known as "freedom", "free-will", "no-conspiracy") implies that the hidden variables and the measurement settings are independent variables. This seems intuitively appealing, but is there any reason to accept this assumption?

The modern theories I mentioned above are field theories. In such theories the state of a subsystem is not independent of the state of the entire system. Stars in a galaxy do not move independently of other stars, charged particles do not move independently of other charges even if the distance separating them is large. But the source of the entangled particles and the detectors are nothing but such subsystems of the whole experimental setup. They are nothing more than large groups of charged particles (electrons and nuclei/quarks). So, it seems to me, that the independence assumption is in fact contradicted, not supported by the mainstream physical theories.

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Experimental science is based on the idea that what you measure is independent from your measuring device. Or at the very least that it is not a part of the measuring device.

What can you make of any experimental result if each experiment is taken to be a specific expression of the whole (aka the universe), without any sensible division between an observed system and a measuring system?

Without that independence assumption, there is no science. And since researchers over the ages actually did find more or less valid laws of physics, through uncountable experiments, such independence somehow holds. Rejecting it would immediately raise the question of why do experiments actually yield results from which one can infer generic laws and principle governing the behavior of (sub)systems?

It is for good reasons that explaining away the violation of Bell's inequalities by giving up this principle is seen as a "conspiracy theory": it would mean that while the universe appears to follow specific patterns implying the separation of systems, everything is actually connected together in the background so tightly that all that happens is strictly predetermined (one then talks of superdeterminism).

Now perhaps the true nature of things is beyond these distinctions, as in this zen quote:

The blue mountain is the father of the white cloud. The white cloud is the son of the blue mountain. All day long they depend on each other, without becoming dependent on each other. The white cloud is always the white cloud. The blue mountain is always the blue mountain.

But is this what physics is about?

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  • $\begingroup$ I think that the property of physical systems you are referring to is not the Bell independence assumption but Einstein's separability criterion. Separability maintains that "any two spatially separated systems possess their own separate real states" (Don Howard, Einstein on locality and separability). This is what enables one to do science, perform measurements, etc. Separability is a consequence of locality which in turn is a consequence of classical field theories, like general relativity or electromagnetism. - to cont. $\endgroup$ – Andrei Jul 23 at 4:11
  • $\begingroup$ cont: A planetary system can be described on its own if the relevant parameters (positions, velocities of the objects and the gravitational field at all locations) are known. You can do that for our Solar system and, say, for Alpha-Centauri system. The two systems are separable in Einstein's sense, but not independent in Bell's sense because the gravitational field at the two locations are related (pointing more or less towards the galactic center). Oddly enough no one seems to complain that general relativity implies conspiracies. $\endgroup$ – Andrei Jul 23 at 4:17
  • $\begingroup$ The problem with things like this is that I tend to feel they are effectively demanding that reality be shoehorned in such a way that our concept of "science" works out, instead of letting reality "choose" for us. It doesn't work that way. Reality is under no obligations to us, at all, and to treat it as such is not valid reasoning, imo. $\endgroup$ – The_Sympathizer Jul 26 at 3:16
  • $\begingroup$ The thing you have to do is ask, "is it logically possible you could have a world with such deep, holistic ties between observers and that which they observe and yet not have it inevitably provide nothing but a completely incoherent, unpredictable mess to either?" If the answer is "yes", then we could be living in just such a world and thus it has to be on the table. $\endgroup$ – The_Sympathizer Jul 26 at 3:17

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