以未来为条件：惠勒参与式宇宙的滤过理论形式化
Conditioning on the Future: A Filtration-Theoretic Formalization of Wheeler's Participatory Universe
- Dipartimento di Fisica e Chimica “Emilio Segrè”, Università degli Studi di Palermo（巴勒莫大学埃米利奥·塞格雷物理与化学系）
- DSIMB, Inserm, BIGR U1134, Université Paris Cité & Université de La Réunion（巴黎西岱大学与留尼汪大学）
- Life Actuarial Department, Taiwan Insurance Institute（台湾保险学院精算学部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过滤过理论区分时间对称性与逆向因果，将惠勒的参与式宇宙形式化为选择效应，并构建对应词典，明确其不推导玻恩规则或解决测量问题。
AI中文摘要：
惠勒的延迟选择实验和量子测量的时间对称形式主义长期以来一直引发一场争论，即量子理论中的时间对称性是否意味着逆向因果。我们认为，这场争论混淆了两种不同的结构，而区分它们的框架是经典的 conditioning 理论：在概率方面，包括 Doob h-变换、马尔可夫桥和滤过扩张；在量子方面，包括预选和后选系统的前向态/后向效应（双态矢量）形式主义。我们将惠勒的参与式宇宙、延迟选择和“It from Bit”提炼为三个论题，并构建一个对应词典，将每个论题映射到一种或两种形式主义中的精确陈述。该词典以两个结构同构的结果为锚点：一个操作性命题，即未来的测量选择将过去的系综分类为子系综而不干扰任何早期的边缘分布；以及其经典对应物，即无条件定律分解为未来条件桥——两者都是同一个事实：对最终测量进行边缘化会保持早期边缘分布不变，这在量子方面由 POVM 的完备性连同迹保持保证，在经典方面由条件期望的塔性质保证。条件演算是时间对称的；其因果结构则不然。因此，延迟选择是一种选择效应而非逆向因果，而表面上“来自未来的拉力”是一种桥漂移。我们明确说明该框架不能做什么——它既不推导玻恩规则，也不解决测量问题——并界定量子力学中参与式语言的合法范围。
英文摘要：
Wheeler's delayed-choice experiments and the time-symmetric formalisms of quantum measurement have long fueled a debate over whether time symmetry in quantum theory entails retrocausality. We argue that the debate conflates two distinct structures, and that the framework for separating them is the classical theory of conditioning: Doob $h$-transforms, Markov bridges, and enlargement of filtrations on the probabilistic side, and the forward-state/backward-effect (two-state-vector) formalism of pre- and post-selected systems on the quantum side. We sharpen Wheeler's participatory universe, delayed choice, and ``It from Bit'' into three theses and build a correspondence dictionary that maps each to a precise statement in one or both formalisms. The dictionary is anchored by two structurally isomorphic results: an operational proposition that a future measurement choice sorts the past ensemble into subensembles without disturbing any earlier marginal, and its classical counterpart, the disintegration of an unconditioned law into future-conditioned bridges -- both a single fact: marginalizing over the final measurement leaves earlier marginals fixed, by completeness of the POVM together with trace preservation on the quantum side and by the tower property of conditional expectation on the classical. The conditional calculus is time-symmetric; its causal structure is not. Delayed choice is thereby a selection effect rather than retrocausation, and the apparent ``pull from the future'' is a bridge drift. We state explicitly what the framework does not do -- it neither derives the Born rule nor solves the measurement problem -- and delineate the legitimate scope of participatory language in quantum mechanics.
