论文标题
关于在贝尔-Chsh不平等中使用客观概率的评论
Remarks on the use of objective probabilities in Bell-CHSH inequalities
论文作者
论文摘要
违反贝尔不平等的行为通常被解释为表明，如果存在隐藏的变量，则必须是上下文和非局部。但是，也可以解释它们质疑所采用的概率空间或Kolmogorov公理的有效性。在本文中，我们探讨了可以从两种广泛使用的虚拟概率理论中推论的其他约束：频繁主义和倾向。 扣除一个版本的贝尔不等式中最强烈的反对意见之一是概率空间，该空间假设每个运行中实验的输出值的值都存在，而每次可以测量四个值中的两个值，从而使它们相反。结果表明，频繁主义拒绝使用反事实情况的可能性，而长期倾向则可以使用它们。在这种情况下，引入局部性和上下文无助于解释违规行为，另一种解释可能表明概率失败。 单个病例倾向的设计是将概率与单个事件相关联，但是它们需要以整个宇宙为条件，并且与观察到的相对频率没有明确的联系。它严重限制了他们的使用。
The violation of Bell inequalities is often interpreted as showing that, if hidden variables exist, they must be contextual and non local. But they can also be explained questioning the probability space employed, or the validity of the Kolmogorov axioms. In this article we explore the additional constrains which can be deduced from two widely used objetive probability theories: frequentism and propensities. One of the strongest objections in the deduction of one version of Bell inequalities goes about the probability space, which assumes the existence of values for the output of the experiment in each run, while only two of the four values can be measured each time, making them counterfactual. It is shown that frequentism rejects the possibility of using counterfactual situations, while long-run propensities allow their use. In this case the introduction of locality and contextuality does not help to explain the violation, and an alternative explanation could point to a failure of the probability. Single case propensities were designed to associate probabilities to single events, but they need to be conditional to the whole universe, and do not have a clear link with the observed relative frequencies. It heavily limits their use.
