arXiv 0807.33692008-07quant-ph

Bell不等式和Nelson定理的新认识

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

Benjamin Schulz

备注：: The stochastic model presented in this article was defect. The parts of this work that are correct are now in a separate article on arxiv.org
发表信息：: Annalen der Physik (Berlin) 18, No. 4, 231 (2009)
DOI：: 10.1002/andp.200810345

摘要：

在1985年，爱德华·纳尔逊，谁制定了随机力学理论，提出了一个有趣的评论贝尔定理。纳尔逊根据随机行为的经典场分析了后者。他发现，如果一个随机隐变量理论满足一定的条件，贝尔不等式可以违反。此外，Nelson能够证明这可能在两个空间分离的测量站之间没有任何即时通信的情况下发生。由于纳尔逊的文章几乎被物理学家忽视，我们试图回顾他对贝尔定理的评论。我们认为，修改随机力学最近发表的Fritsche和Haugk可以扩展到一个理论，满足纳尔逊的分析要求。文章接着推导出自旋粒子的量子力学形式和泡利方程从这个版本的随机力学。然后，我们调查玻姆的版本的EPR实验。此外，其他的设置，如纠缠交换或时间和位置的相关性，从我们的本地隐变量模型的观点解释。最后，我们提到这个理论也许可以相对论地扩展。

英文摘要：

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.

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