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Fredrik said:A "classical" theory is a theory that only makes predictions that can be tested without significantly disturbing the system. So maybe we shouldn't be asking why QM is so weird, but instead be asking why there are classical theories that are actually pretty good.
I think that the distinction you are making is important, but I don't see how it is the full story. It's completely understandable that if you try to measure the position of an electron using light, then you end up disturbing it and making the momentum uncertain. However, why should measuring the spin of one particle of an EPR pair disturb the spin of the other particle? As I said, it's not the fuzziness or uncertainty or nondeterminism of quantum mechanics that makes it so mysterious--it's the combination of uncertainty with very strong nonlocal correlations that makes it mysterious.
We can understand the uncertainty and nondeterminism in terms of the observer disturbing the system by his measurements. But then why would such measurements show such strong correlations, in the case of entangled particles?