On Bell-Type Inequalities in Quantum Logics
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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  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.
KeywordsPhysical System Pure State Classical Mechanic Boolean Algebra Triangle Inequality
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