Bell型不等式问题、量子非定域性的起源和纠缠的满/空波模型
A problem with Bell-type Inequalities, the origin of the quantum non-locality, and a full/empty waves model for entanglements
摘要：
量子力学是否具有非定域性是一个长期存在争议的问题。Bell型不等式的违反被认为是证明这种非局部性。然而，这些不等式构造在一类局部隐变量上，它们服从正概率微积分。这样的演算是相当适合台球，而QM处理波包的复振幅。毫无疑问，正数的微积分与复数的微积分不匹配。本文描述了一种不同的纠缠隐变量模型，该模型在不同的实验中再现了量子预言，并解释了为什么QM是非局域的。该模型处理波浪，其中一些是满的，另一些是空的，隐变量标记哪些波浪是满的。模型运作的基本物理概念是概率的联合振幅，而不是概率。后者是次要概念，结果组合的概率等于所有贡献联合振幅之和的绝对平方。因此，非局部性出现：a）联合振幅忽略了距离，它处理远处的粒子，就好像它们是在一个单一地方的一个单一粒子一样，b）联合振幅是复数，几个贡献的总和可能为零，阻止了波包的相应组合，从而阻止了结果的组合。虽然展示了模型的成功，但本文并不提倡满/空波。它表明，这个假设的作品，只要一个不考虑移动的观察者，并没有比较他们的结论。这里的真正目的是指出一个严重的僵局：假设存在一个优选的框架与相对论相矛盾，而反驳满/空波的想法则会遇到其他无法克服的困难。
英文摘要：
Whether the quantum mechanics (QM) is non-local is an issue disputed for a long time. The violation of the Bell-type inequalities was considered as proving this non-locality. However, these inequalities are constructed on a class of local hidden variables, which obey the calculus with positive probabilities. Such a calculus is rather suitable for billiard balls while the QM deals with wave-packets of complex amplitudes. There is no wonder that a calculus with positive numbers does not match a calculus with complex numbers. The present text describes a different model of hidden variables for entanglements, model that reproduces the quantum predictions in different experiments, and also explains why the QM is nonlocal. The model deals with waves, some of them full and the others empty, and the hidden variables mark which waves are full. The basic physical concept with which the model operates is joint amplitudes of probability, and not probabilities. The latter are a secondary concept, the probability of a combination of results being equal to the absolute square of sum of all the contributing joint amplitudes. Thus the non-locality appears: a) a joint amplitude ignores distance, it handles distant particles as if they were one single particle at one single place, b) joint amplitudes are complex numbers and the sum of several contributions may vanish, blocking the respective combination of wave-packets and therefore of results. Although showing the success of the model, this text does not advocate for full/empty waves. It is shown that this hypothesis works only as long as one does not consider moving observers, and does not compare their conclusions. The real purpose here is to point to a severe impasse: assuming the existence of a preferred frame contradicts the theory of relativity, while refuting the full/empty waves idea one runs into other insurmountable difficulties.
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