Abstract

Based on the new general framework for the probabilistic description of experiments, introduced in [E.R. Loubenets, Research Report No 8, MaPhySto, University of Aarhus, Denmark (2003); Proceedings Conference “Quantum Theory, Reconsideration of Foundations”, Ser. Math. Modeling, Vol. 10 (University Press, Vaxjo, 2004), pp. 365–385], we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint experiments upon a system of any type and the physical concept of “local realism”. We prove that the violation of Bell-type inequalities in the quantum case has no connection with the violation of “local realism”. In a general setting, we formulate in mathematical terms the condition on “local realism” under a joint experiment and consider examples of quantum “locally realistic” joint experiments. We, in particular, show that quantum joint experiments of the Alice/Bob type are “locally realistic”. For an arbitrary bipartite quantum state, we derive quantum analogs of the original Bell inequality. In view of our results, we argue that the violation of Bell-type inequalities in the quantum case cannot be a valid argument in the discussion on locality or non-locality of quantum interactions