On the tests of quantum theory: How many different theoretical frameworks?

Abstract

Beyond Bell 's inequality. The growth of the interest in the foundations of quantum mechanics (QM), start ing from the contributions of Bell around the half of the sixties, has clarified the feasability of experimental tests, at least for dieotomic observables. Bell 's inequali ty (~) was the tool for such investigations: this inequali ty was in fact violated by QM, but satisfied by all the local hidden variable (1.h.v.) models and the so-called first-kind states, or proper mixtures (p.m.) (~-). Only during the last year i~ was understood (s) the existence of more than two experimental ly distinguishable theoretical models for the description of the physical situat ion corresponding to the singlet state of QM: it was shown that a particular (the most natural) l.h.v, model, a conveniently symmetrized p.m. (4) and QM are all observably frameworks. I t was shown also that certain nonlocal models give also further different descriptions (~). I t must be stressed tha t in these recent papers use was made of both Bell 's inequali ty and the so-called ~,sensitive observables ,> introduced by the Bali group (s). A further investigation has convinced us of a couple of points that could put an end to the main physical aspects of the problem. First of all we show that, at the present stage of understanding, the use of Bell 's inequali ty has become misleading from