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.

@article{Belinskii:1997,
	author = {A. V. Belinskii},
	title = {Bell's theorem for trichotomic observables},
	publisher = {Physics-Uspekhi},
	year = {1997},
	journal = {Phys. Usp.},
	volume = {40},
	number = {3},
	pages = {305-316},
	url = {https://ufn.ru/en/articles/1997/3/f/},
	doi = {10.1070/PU1997v040n03ABEH000225}
}