Probability and Realism in Quantum Mechanics

Claudio Garola, Sandro Sozzo

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.

Stanley Gudder

Claudio Garola, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

Basing on known theoretical results (Bell's theorem, Bell–Kochen–Specker's theorem, etc.) most physicists believe that standard quantum mechanics (SQM) and local realism cannot hold together. Moreover, they also uphold that the experimental tests performed up to now confirm SQM and refute local realism. Some scholars, however, criticize this conclusion, yet maintaining that SQM conflicts with local realism. At variance with both viewpoints, an extended semantic realism (ESR) model has been worked out in Lecce which shows that, if quantum probabilities are interpreted as conditional rather than absolute, a picture of the microworld can be constructed that assumes local realism and embodies the mathematical formalism of SQM. We provide here a new synthetic and improved description of the ESR model, comment on its achievements and limits, and briefly compare it with other approaches.

Bassano Vacchini

Claudio Garola, Sandro Sozzo

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.

Hans Primas