Reinterpreting Quantum Probabilities in a Realistic and Local Framework: The Modified BCHSH Inequalities

Most physicists uphold that the tests of the Bell inequalities (BI) performed up to now confirm the predictions of standard quantum mechanics (SQM) and refute local realism. But some scholars criticize this conviction, defending local realism in various ways. We present here a new viewpoint based on 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 into a more general framework in which not only local realism but also objectivity of physical properties holds, and the probabilities of SQM are reinterpreted as conditional instead of absolute. Hence the ESR model provides some predictions that are formally identical to those of SQM but have a different physical interpretation, and further predictions that differ also formally from those of SQM. In particular, we show here that the BI introduced by Clauser, Horne, Shimony and Holt (BCHSH inequalities) must be replaced by modified BCHSH inequalities. These depend on detection probabilities which may be such that the new inequalities are never violated by the conditional expectation values predicted by the model. 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. C. Garola Dipartimento di Fisica dell’Università del Salento and INFN, Sezione di Lecce Via Arnesano, 73100, Lecce, Italy Tel.: +39-0832-297438 E-mail: [email protected] S. Sozzo Dipartimento di Fisica dell’Università del Salento and INFN, Sezione di Lecce Via Arnesano, 73100, Lecce, Italy Tel. +39-0832-297441 E-mail: [email protected]