论柯尔莫哥洛夫概率论在描述量子现象中的适用性。第二部分：贝尔不等式
On the applicability of Kolmogorov's theory of probability to the description of quantum phenomena. Part II: Bell inequalities
AI总结：
本文从柯尔莫哥洛夫概率论视角分析贝尔不等式，提出并研究贝尔实验中的语境性概念，证明一类情境模型满足BCHSH不等式，但强局域性下仍可违反，揭示常见物理结论的概念误解。
AI中文摘要：
在量子力学基础的各种“不可行定理”中，贝尔不等式是少数不隐含依赖量子力学数学结构的定理之一。相反，贝尔不等式通常被认为建立在柯尔莫哥洛夫概率论和“局域性”假设之上。因此，支持其违反的实验证据被视为反对这两个假设中至少一个的证据。本工作从柯尔莫哥洛夫概率论的角度，对贝尔不等式的物理争论进行了全面分析，重点关注贝尔-克劳泽-霍恩-希蒙尼-霍尔特不等式（BCHSH不等式）。核心贡献是对贝尔实验中语境性概念的动机和数学研究：在所谓的情境贝尔模型中，探测器本身随机行为，且随机探测器参数的分布依赖于所选择的探测器设置。我们展示了即使是“经典”贝尔实验也能激发这样的描述。考虑语境性的必要性此前已被德·拉·佩尼亚、塞托、布罗迪、洛查克、博姆、希利等人指出。我们证明了一大类情境模型满足BCHSH不等式，从而推广了吉尔和兰巴雷之前的结果。然而，即使在强局域性要求下，情境贝尔模型也可能违反BCHSH不等式：基于波佩斯库和罗利奇的工作，我们考虑了一个展示最大可能违反的“概念验证”例子。与贝尔不等式经验检验中备受争议的“漏洞”相反，语境性揭示了通常从贝尔不等式违反中得出的物理结论中的概念性误解。
英文摘要：
Among the various "no-go theorems" in the foundations of quantum mechanics, Bell inequalities are among the few, which do not implicitly rely on the mathematical structure of quantum mechanics. Instead, Bell inequalities are commonly understood to rest on Kolmogorov's theory of probability and a "locality" assumption. Physical evidence supporting their violation is hence taken as evidence against at least one of these two assumptions. This work provides a comprehensive analysis of the physical debate on Bell inequalities from the point of view of Kolmogorov's theory of probability, focusing on the Bell-Clauser-Horn-Shimony-Holt inequality (BCHSH inequality). The central contribution is the motivation and mathematical study of the notion of contextuality in Bell experiments: in so-called contextual Bell models the detectors themselves behave randomly and the distribution of the random detector parameters depends on the chosen detector settings. It is shown how even "classical" Bell experiments motivate such a description. The need to account for contextuality was pointed out before by de la Peña, Cetto, Brody, Lochak, Bohm, Hiley and others. A broad class of contextual models is proven to satisfy the BCHSH inequality, thereby generalizing a previous result by Gill and Lambare. Nonetheless, even under strong locality requirements, contextual Bell models may violate the BCHSH inequality: based on work by Popescu and Rohrlich, we consider a "proof of concept" example exhibiting the maximum possible violation. Contrary to the much debated "loopholes" in empirical tests of Bell inequalities, contextuality thus reveals a conceptual misunderstanding in the physical conclusions commonly drawn from Bell inequality violations.
