Mathematical and physical meaning of the Bell inequalities

Emilio Santos

Universidad de Cantabria

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 is defined as a mapping between a set of quantum projectors 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).