Two hidden hypothesis in the Bell inequalities

ALEJANDRO HNILO.

La Plata

Jornada; Sextas Jornadas de Fundamentación Cuántica; 2016

CONICET

Recently, the famous original paper by J.S.Bell?s reached the 50 anniversary of its publication. In that paper, the contradiction of the predictions of Quantum Mechanics (QM) with the intuitive ideas of Locality and Realism (LR) was demonstrated, for the correlation between the measurements performed on a pair of remote entangled particles. The experiments performed until now show that that correlation is higher than allowed by LR. However, there are two non-evident hypotheses, additional to LR, in the derivation of the Bell?s inequalities: the first one is that ?proper? integrals (in the Riemann?s or Lebesgue?s sense) in the space of the hidden variables exist; the second one is similar to the ergodic hypothesis. Both hypotheses are not valid in some complex systems. Therefore, the experimental results can be interpreted as a refutation of the validity of LR in the Nature or, else, as the evidence of the existence of an underlying dynamics, which would be chaotic and non-ergodic. In this contribution, the origin and meaning of the additional hypotheses is discussed.