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Bell's argument makes very weak assumptions about the behavior of the two particles (which is why it's interesting). In effect, the particles are black boxes that take an angle as input and produce a spin direction as output. There is no restriction on how they choose the spin direction; there could be a source of true randomness in there, or a human being ...

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I think you misunderstood the significance of could for a classical theory. The text below the picture you took from Wikipedia says: "Many other possibilities exist for the classical correlation subject to these side conditions", so classicality does not imply linearity. It does, however, rule out the cosine, by the following (slightly heuristic) argument: ...

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My understanding is that the measurement at 45° matches the measurements at 0° and 90° more than it should (assuming local hidden variables) given how often 0° and 90° match. Think of two detectors that move between 0°, 45°, and 90°, so that you get the 90° measurement when one is at 0° and the other at 90° and the 45° measurement when one is at 45° and the ...

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