Simple demonstrations of Bell inequalities

Bell’s inequality exposed one of the most fundamental aspects of quantum mechanics: the theory is incompatible with the usual way of interpreting basic concepts such as reality and locality. Although Bell’s original argument is not difficult to follow, there are more accessible ways to demonstrate similar inequalities. In this article we present two of these proofs, proposed by Nick Herbert and Asher Peres, both very simple and, it seems, relatively little known despite their pedagogical interest. We also discuss how locality and elements of reality described by hidden variables are introduced in these proofs.

Keywords:
Bell’s inequality; Bell’s theorem; realism; locality