贝尔定理是循环论证
Bell's Theorem Begs the Question
AI总结：
本文指出贝尔定理基于循环推理，其前提暗含要证明的±2界；修正疏漏后贝尔-CHSH界为±2√2，实验排除的是期望值线性可加性而非局域实在论，还指出GHZ变体及冯·诺依曼定理有类似疏漏。
摘要：
我证明贝尔定理基于循环推理，因而是一个根本有缺陷的论证。它无正当理由地假设了贝尔测试实验中涉及的非对易可观测量的语境隐变量理论的无弥散态的期望值可加性，这与假设贝尔-CHSH期望值之和的界为±2是同义反复。因此，其前提以不同形式假设了它要证明的±2界。一旦通过识别导致该问题的障碍来修正贝尔论证中的这一疏漏，并正确实现局域实在论，贝尔-CHSH期望值之和的界将变为±2√2而非±2，从而弱化贝尔定理的结论。因此，任何贝尔测试实验排除的不是局域实在论，而是期望值的线性可加性，而这种可加性从一开始在任何隐变量理论中对非对易可观测量都不成立。我还在贝尔定理的GHZ变体中发现了类似疏漏，这使其关于EPR完备量子力学的论证前提存在不一致的主张无效。从概念上讲，贝尔定理及其GHZ变体中的疏漏可追溯到20世纪30年代Grete Hermann指出的冯·诺依曼反对隐变量理论的定理中的疏漏。
英文摘要：
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of $\pm2$ on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of $\pm2\,$ it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ${\pm2\sqrt{2}}$ instead of ${\pm2}$, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
