arXiv 2512.005752025-12quant-phphysics.hist-phphysics.pop-ph

Everett诠释中的物理概率与贝尔不等式

Physical Probability in the Everett Interpretation and Bell Inequalities

Merton College, University of Oxford（牛津大学默顿学院）

Simon Saunders

备注：: To appear in Alyssa Ney (ed), Everett and Nonlocality, Oxford University Press, 2026

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AI总结：

本文提出一种适用于 Everett 诠释的物理概率理论，该理论与 Born 规则一致，违反贝尔不等式，并展示了其与局部因果性原理的一致性。

摘要：

我定义了一个局部因果性LOC的概念，其 closely 模仿贝尔原理，被构造成一个条件：单个案例概率不能被空间状分离上的动作所修改。新的原则，如同贝尔原则一样，迫使贝尔不等式成立，但有两个漏洞：一个是回溯因果，已知贝尔所知，但另一个是非唯一性远程结果，仅对LOC有效，而非贝尔原则。我还提出了适用于 Everett诠释的物理概率理论，与Born规则一致，因此违反贝尔不等式。我展示了它与LOC一致。令人惊讶的是，两个漏洞都被利用。我得出结论，不仅 Everett诠释中的概率不涉及超距作用，而且观察到的贝尔不等式违反是多重世界理论的有力证据。

英文摘要：

I define a notion of local causality LOC closely modelled on the Bell principle, construed as the condition that single case probabilities cannot be modified by actions at spacelike separation. The new principle, like that of Bell, forces Bell inequalities, but with two loopholes: one is retrocausation, known to Bell, but the other is nonuniqueness of remote outcomes, a loophole only for LOC, not for the Bell principle. I also set out a theory of physical probability, applicable to the Everett interpretation, in agreement with the Born rule, and therefore violating Bell inequalities. I show it is consistent with LOC. Surprisingly, both loopholes are exploited. I conclude not only that probability in the Everett interpretation involves no action at a distance, but that the observed violations of Bell inequalities is powerful evidence for many worlds.

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