A new look at Bell's inequalities and Nelson's theorem
Version of Record online: 20 MAR 2009
Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 18, Issue 4, pages 231–270, April 2009
How to Cite
Schulz, B. (2009), A new look at Bell's inequalities and Nelson's theorem. Ann. Phys., 18: 231–270. doi: 10.1002/andp.200810345
- Issue online: 15 APR 2009
- Version of Record online: 20 MAR 2009
- Manuscript Accepted: 9 MAR 2009
- Manuscript Revised: 7 MAR 2009
- Manuscript Received: 4 AUG 2008
- stochastic quantum mechanics;
- particle spin.
In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark about 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 the 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 and useful for the formulation of quantum mechanics in curved space-times.