arXiv quant-ph/04100152004-10-01quant-ph

贝尔定理：对有不等式和无不等式证明的批判

Bell's theorem: Critique of proofs with and without inequalities

Karl Hess, Walter Philipp

备注：: 13 pages
DOI：: 10.1063/1.1874568

摘要：

贝尔定理的大多数标准证明都是基于概率论的柯尔莫哥洛夫公理。我们发现，这些证明包含的数学步骤，不能调和与Kolmogorov公理。具体来说，我们证明，这些证明忽略了结论的定理伏罗勃'ev的一致性的联合分布。因此，贝尔定理在其完全普遍性方面仍然没有得到证明，特别是对于仍然是客观局部的扩展参数空间并且包括与时间和仪器设置相关的仪器参数。虽然贝尔定理正确地排除了某些小类的隐变量，但对于这些扩展的参数空间，标准的证明就停止了。Greenberger-Horne-Zeilinger（GHZ）方法基于类似的谬误论点。对于这种情况下，我们能够提出一个客观的本地计算机实验，模拟实验测试的GHZ潘，Bouwmeester，丹尼尔，Weinfurter和Zeilinger进行，并直接矛盾，他们声称，爱因斯坦局域元素的现实既不能解释量子力学理论的结果，也不能解释他们的实验结果。

英文摘要：

Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate that these proofs ignore the conclusion of a theorem of Vorob'ev on the consistency of joint distributions. As a consequence Bell's theorem stated in its full generality remains unproven, in particular, for extended parameter spaces that are still objective local and that include instrument parameters that are correlated by both time and instrument settings. Although the Bell theorem correctly rules out certain small classes of hidden variables, for these extended parameter spaces the standard proofs come to a halt. The Greenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious arguments. For this case we are able to present an objective local computer experiment that simulates the experimental test of GHZ performed by Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts their claim that Einstein-local elements of reality can neither explain the results of quantum mechanical theory nor their experimental results.

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