Vacuum Dependent Bell Local Hidden Variable Models and Generalized C.H.S.H. Inequalities

Gianpaolo Bei

doi:10.4236/jamp.2022.101002

Abstract

We extend a previous model of the author which generalizes Bell local hidden variable models to the case of entangled photon pairs assuming that the standard Bell correlation functions depend on a hidden vacuum index. We deduce a generalization of Bell theorem assuming that classical observables are not dichotomic and that photon pair emission and detection is not a stationary stochastic process. We derive a photon imperfect polarization correlation functions due to rotational invariance breaking induced by hidden vacuum spin currents. We implement formally this approach deducing a generalization of C.H.S.H. inequalities which asymptotically converges to the standard one and which might be competitive with standard quantum mechanics predictions. We suggest to test this inequalities conceiving new E.P.R.-Bell like tests with time dependent detector efficiency and photon flux. Finally, we suggest to apply these generalized inequalities to the correlation functions of entangled classical spinning waves realized recently with metamaterials.

Highlights

A consistent group of researchers questioned the non contextual description of photon polarization used for deducing Bell theorem, arguing that Bell tests cannot be used to demonstrate intrinsic non local property of quantum states [1]-[6]
We extend a previous model of the author which generalizes Bell local hidden variable models to the case of entangled photon pairs assuming that the standard Bell correlation functions depend on a hidden vacuum index
Our generalized inequalities gives an alternative way to bypass Bell theorem, different from the followers of the contextual reformulation of quantum measurement and hidden variable models [2] [3], even if we agree with them that is unrealistic the Bell assumption of one singular probability distribution independent from the detectors settings. We hope that this new model may stimulate new search of time dependent hidden variable models for realistic approach to unstable process of entangled pairs of decaying nuclear particles, excited atoms or ions; we suggest that this non stationary stochastic processes, might be described by path dependent hidden variable models similar to our tentative one, and could be tested by modulating the detector efficiency with the laser induced temperature waves recently investigated T ( x,t,ω )

Summary

Introduction

A consistent group of researchers questioned the non contextual description of photon polarization used for deducing Bell theorem, arguing that Bell tests cannot be used to demonstrate intrinsic non local property of quantum states [1]-[6]. This new contextual classical reformulation of hidden variable theories gave strong support to the old research program of Einstein to build a deterministic theory which completes Quantum Mechanics.

Bei DOI

Conclusions