A new look at Bell's inequalities and Nelson's theorem

TL;DR

This paper revisits Nelson's stochastic mechanics approach to Bell's inequalities, demonstrating that local hidden-variable models can violate Bell's inequality without instantaneous communication, and extends this to quantum formalism and potential relativistic theories.

Contribution

It extends Nelson's stochastic mechanics to a modified version that reproduces quantum formalism and challenges Bell's theorem's implications for locality.

Findings

Bell's inequality can be violated without instantaneous communication.

Quantum formalism for spinning particles derived from stochastic mechanics.

Potential for relativistic extension of the local hidden-variable model.

Abstract

In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark on Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on Bell's theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended.