Abstract
Bell-type inequalities are studied within the framework of quantum logic approach. It is shown that violation of Bell’s inequalities indicates that pure states are not dispersion-free, whenever they are Jauch-Piron states which is true both in classical and in quantum mechanics. This result completes the results obtained by Santos [4] who has shown that violation of Bell’s inequalities implies that a lattice of propositions for a physical system is not distributive. Connections between Jauch-Piron properties of states, non-dispersive character of pure states and distributivity of a logic are studied and it is shown that if a logic is finite the former two properties imply the latter.
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© 1989 Kluwer Academic Publishers
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Pykacz, J. (1989). On Bell-Type Inequalities in Quantum Logics. In: Bitsakis, E.I., Nicolaides, C.A. (eds) The Concept of Probability. Fundamental Theories of Physics, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1175-8_12
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DOI: https://doi.org/10.1007/978-94-009-1175-8_12
Publisher Name: Springer, Dordrecht
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