BELL THEOREM FOR TRICHOTOMIC OBSERVABLES

Bell's paradoxes, due to the fundamental properties of light and the n ature of the photon, are discussed within a single framework with a vi ew to checking the hypothesis that a stationary, nonnegative, joint pr obability distribution function exists. This hypothesis, related to th e local theory of hidden parameters as a possible interpretation of qu antum theory, enables experimentally verifiable Bell's inequalities to be formulated. The dependence of these inequalities on the number of observers Vis considered. Quantum theory predicts Bell's inequalities to break down in optical experiments. It is shown that as V increases, requirements on the quantum effectiveness of tbe detector, eta, are r educed from eta > 2/3 at V = 2 to eta > 1/2 for V --> infinity. Exampl es of joint probability distribution functions are given for illustrat ive purposes, and a way to resolve the Greenberg-Horne-Zeilinger (GHZ) paradox is suggested.