Khrennikov, A. \(p\)-adic probability interpretation of Bell’s inequality. (English) Zbl 0910.60001 Phys. Lett., A 200, No. 3-4, 219-223 (1995). 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. Cited in 4 Documents MSC: 60A99 Foundations of probability theory 81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy Keywords:\(p\)-adic probability interpretation; Bell inequality violation; relative frequency limit; \(p\)-adic metric; negative probability distributions; frequency definition; hidden variables distribution; quantum models PDF BibTeX XML Cite \textit{A. Khrennikov}, Phys. Lett., A 200, No. 3--4, 219--223 (1995; Zbl 0910.60001) Full Text: DOI References: [1] Einstein, A.; Podolsky, B.; Rosen, N.: Phys. rev.. 47, 777 (1935) [2] De Broglie, L.: La physique quantique: restera-t-elle indeterministe. (1953) · Zbl 0053.32402 [3] Bohm, D.; Vigier, J. P.: Phys. rev.. 96, 208 (1954) [4] Freistadt, H.: Nuovo cimento. No. Suppl. 5, 1 (1957) [5] Silva, J. L. Andrade E.; Lochak, G.: Quanta. (1969) [6] Bell, J. S.: Physics. 1, 195 (1965) [7] Home, D.; Selleri, F.: Nuovo cimento riv.. 14 (1991) [8] Vladimirov, V. S.; Volovich, I. V.; Zelenov, E. I.: P-adic numbers in mathematical physics. (1993) · Zbl 0812.46076 [9] Khrennikov, A. Yu.: P-adic valued distributions in mathematical physics. (1994) · Zbl 0833.46061 [10] Frampton, P. H.; Okada, Y.: Phys. rev. Lett.. 60, 484 (1988) [11] Borevich, Z. I.; Schafarevich, I. R.: Number theory. (1966) [12] Khrennikov, A. Yu.: Sov. phys. Dokl.. 35, 867 (1990) [13] Cianci, R.; Khrennikov, A. Yu.: Phys. lett. B. 328, 109 (1994) [14] Kolmogoroff, A. N.: Grundbegriffe der wahrscheinlichkeitsrechnung. (1933) · Zbl 0007.21601 [15] Von Mises, R.: The mathematical theory of probability and statistics. (1964) · Zbl 0132.12303 [16] Dirac, P. A. M.: Proc. R. Soc. A. 180, 1 (1942) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.