发表机构
University of California, Irvine; Halıcıoğlu Data Science Institute and Department of Philosophy, University of California, San Diego; Department of Logic and Philosophy of Science, University of California, Irvine（加州大学尔湾分校; 加州大学圣地亚哥分校哈奇奥卢数据科学研究所与哲学系; 加州大学尔湾分校逻辑与科学哲学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用算法随机性理论（马丁-洛夫随机性）为物理典型性提供精确刻画，并以玻姆力学中的分布公设为例，通过玩具模型证明该约束保证标准玻恩统计，从而为统计定律赋予严格内容。
AI 中文摘要
在物理学中，诉诸典型性的论证很常见，但通常不清楚相对于某个概率测度，物理状态是典型的意味着什么，相应地，诉诸典型性的定律所断言的内容也不清楚。在此，我们考虑如何利用算法随机性理论中的思想来刻画物理典型性。作为一个具体例子，我们展示了当物理状态相对于可计算测度是马丁-洛夫随机时，将其视为典型的，如何使得玻姆力学中的分布公设能够被表述为该理论的一条统计约束定律。通过一个玩具模型，我们展示了这一约束如何保证可计算实验协议的标准玻恩统计。算法玻姆力学（aBM）因此说明了算法随机性如何被用来为统计定律提供精确的内容。
英文摘要
Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.
CommentsAccepted version, forthcoming in The Proceedings of The 2026 Meeting of the Philosophy of Science Association
