Tolga T said:
As for Bell's assumptions, my primary concern is localism, not realism.
Just as a comment here. The two are connected in some sense. The principal condition used to derive Bell inequalities is a condition called Bell locality, or factorisability. It is, roughly, the condition that any correlations between distant events be explicable in local terms.
Factorisability is the better term, but they are often used interchangeably. Even recognised experts like Tim Mauldin, because he fundamentally believes in realism (as I do, actually), get confused and say things that are not strictly true. Bell Locality is NOT the same as locality as it is usually used in physics, ie an object is influenced directly only by its immediate surroundings.
Suppose two particles are entangled. If they were factorisable, then we could consider them as still being particles A and B. However, when entangled, you cannot tell the state of either particle - they are no longer two distinct particles, but a single quantum state; the idea becomes meaningless, at least superficially. What Bell proved is that you can't do that (i.e., consider they are still particles A and B) and have locality. But as I said, basic QM suggests something funny is going on anyway (it is tied up with the principle of superposition). Bell proved it was not locally factorisable, which is the humour of Feynman's famous remark:
If you believe in 'naive' reality, you think it is still two particles when entangled. Some get confused, but the thing Bell showed is QM is not Bell local.
So in QM, what is real? QM is merely an approximation to a more comprehensive theory, Quantum Field Theory (QFT). Most physicists believe the Quantum Field is real - it possesses energy, among other properties- and, as a result of E=MC^2, mass is considered a form of energy. According to the criteria of Victor Stenger (an interesting individual; look him up), reality is what "kicks back." Mass is undoubtedly thought of as real (it certainly kicks back), so Quantum Fields are considered real. Particles are sort of like 'knots' in the Quantum Field. Hence, they are real. But separate? When two particles are entangled, they can be thought of as a sort of single double-knot; each particle has lost its individuality. The 'double knot' is real, but each particle is not. It's possible to have an observation (an interaction) that turns the double knot back into two single knots. The entanglement is broken. An analogy would be a single string that was cut into two strings. Nothing non-local weird in that analogy. Indeed, QFT combines Special Relativity and QM, so it must be local in the ordinary sense.
Thanks
Bill