Ehtibar N. Dzhafarov, Janne V. Kujala
Since Bell's celebrated work, we know that correlations of spins measured along various directions in a system of entangled particles cannot be explained within the framework of classical probability theory, provided all spins are modeled as random variables defined on a single probability space, with the identity of each spin determined only by the choice of its direction, irrespective of measurements on other particles. Here we show the same failure for classical probability models of a more general kind, in which different combinations of measurement directions across all particles correspond to different probability spaces. We found that any such model necessarily mismatches quantum mechanics (QM): if it allows for all QM-compliant correlations, then it also allows for some correlations forbidden by QM; if it forbids all QM-forbidden correlations, then it only allows for correlations satisfying Bell-type inequalities (i.e., those within the scope of classical mechanics).
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http://arxiv.org/abs/1305.3649
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