概率与贝尔定理

Probabilities and Spin Correlation

本文证明:贝尔不等式可以追溯到一个显然不成立的经典概率论的公式,而量子力学的自旋相关公式则可以追溯到一个已经被实验证实的量子力学公式。贝尔对贝尔定理有两点误解:第一,他把自己所用的特殊的隐变量理论当作一般的隐变量理论;第二,这个隐变量理论可以导出两个结论,其中的一个与量子力学相容,而另一个则导致贝尔不等式。而贝尔把前一个理解为贝尔不等式的前提,却把后一个结论看作不言而喻的。G·洛查克揭示了贝尔的第一个误解,但没有揭示其第二个。因此,他正确地指出贝尔不等式与定域性原理无关,却没有发现贝尔不等式其实也与隐变量理论无关。

Bell’s inequality can be traced back to a classical probabilistic formula that is invalid clearly, while spin correlation formula in quantum mechanics to a formula that has confirmed both by facts and quantum mechanics. Bell’s two misunderstandings about Bell’s theorem are pointed out: Firstly, the hidden variable theory Bell’s used, which is a special form of such theories, is regarded as a general one. Secondly, there are two theses obtainable from Bell’s hypotheses; one is compatible with quantum mechanics, the other leads to Bell's inequality. Unfortunately, the former is regarded as a property of local hidden variable theory, while the latter as self-evident. G.Lochak has revealed the first thesis, and thereby he pointed out that Bell’s inequality has nothing to do with locality, but he did not find the second one, so that he still analyzed this problem starting from hidden variable theory, which is actually without regard to Bell’s inequality.