  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.
