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\(p\)-adic probability interpretation of Bell’s inequality. (English) Zbl 0910.60001
Summary: We study the violation of Bell’s inequality using a \(p\)-adic generalization of the theory of probability. \(p\)-adic probability is introduced as a limit of relative frequencies but this limit exists with respect to a \(p\)-adic metric. In particular, negative probability distributions are well defined on the basis of the frequency definition. This new type of stochastics can be used to describe hidden-variables distributions of some quantum models. If the hidden variables have a \(p\)-adic probability distribution, Bell’s inequality is not valid and it is not necessary to discuss the experimental violations of this inequality.

60A99 Foundations of probability theory
81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
Full Text: DOI
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