Reconciling local realism with quantum mechanics: the generalized BCHSH inequalities

Most physicists uphold that the tests of the Bell–Clauser, Horne, Shimony and Holt (BCHSH) inequalities confirm quantum mechanics (QM) and refute local realism. Some scholars, however, criticize this conviction, yet maintaining that QM conflicts with local realism. At variance with both viewpoints one of the authors has recently worked out an extended semantic realism (ESR) model which shows that, if quantum probabilities are interpreted as conditional rather than absolute probabilities, a picture of the microworld can be constructed that is simultaneously consistent with local realism and QM. 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.