Bell’s theorem for trichotomic observables
Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
Bell’s paradoxes, due to the fundamental properties of light and the nature of the photon, are discussed within a single framework with a view to checking the hypothesis that a stationary, non-negative, joint probability distribution function exists. This hypothesis, related to the local theory of hidden parameters as a possible interpretation of quantum theory, enables experimentally verifiable Bell’s inequalities to be formulated. The dependence of these inequalities on the number of observers V is considered. Quantum theory predicts the breakdown of Bell’s inequalities in optical experiments. It is shown that as V increases, the requirements on the quantum effectiveness of the detector, η, are reduced from η>2/3 at V=2 to η>1/2 for V \rightarrow \infty . Examples of joint probability distribution functions are given for illustrative purposes, and a way to resolve the Greenberg-Horne-Zeilinger (GHZ) paradox is suggested.