Mathematical and physical meaning of the Bell inequalities

Emilio Santos

Published 2014-10-18Version 1

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values {0,1} . A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, a possibility showing a conflict between quantum mechanics and local realism (Bell's theorem).