Reinterpreting quantum probabilities within a realistic and local framework: the modified BCHSH inequalities

Most physicists uphold that the tests of the Bell–Clauser, Horne, Shimony and Holt (BCHSH) inequalities confirm the predictions of standard quantum mechanics (SQM) and refute local realism. Some scholars, however, criticize this conviction, yet maintaining that SQM conflicts with local realism. Contrasting with both viewpoints, we present here an improved version of the extended semantic realism (ESR) model that has been recently worked out by one of the authors. The ESR model embodies the mathematical formalism of SQM within a more general framework in which local realism is assumed and the probabilities of SQM are reinterpreted as conditional instead of absolute. Hence the ESR model provides predictions that differ from those of SQM whenever absolute probabilities are considered. In particular, we show here that the BCHSH inequalities must be replaced, within the ESR model, by more general inequalities. These depend on parameters (detection probabilities) which may be such that the inequalities are never violated by quantum expectation values. The condition that no violation occurs implies the existence of upper bounds on detection probabilities, which makes the ESR model falsifiable. These results admit an intuitive explanation in terms of unfair sampling but basically differ from the seemingly similar results obtained by other approaches in which the efficiency problem is discussed in order to vindicate some kind of local realism.