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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.

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