Characterizing Signalling: Connections between Causal Inference and Space-time Geometry
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刻画信号传递：因果推断与时空几何的联系
- 研究问题
- 信息论意义的因果关系与相对论时空中的因果约束如何联系？在不忠实因果模型中，缺乏信号传递能否仍为因果推断提供信息？
- 方法与思路
- 作者分析 affects 关系中的冗余，提出序理论的锥性性质，并研究信息论因果模型嵌入时空时与无超光速信号原则的相容性。
- 材料陈述的贡献
- 摘要称改进了信号传递的刻画，给出不忠实模型中的推断技术，并建立锥性时空与忠实因果模型在两类约束关系上的对应。
- 阅读关注点
- 应核对 affects、忠实性和锥性的形式定义、空间维数结论的条件，以及所证明的对应究竟涉及哪些约束和模型范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未给出完整证明与模型条件，其物理因果概念不能直接套用为经济处理效应识别。
原文摘要
Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories, we study their interplay. Here, information-theoretic causality is defined through a causal modelling approach. First, we improve the characterization of information-theoretic signalling as defined through so-called affects relations. Specifically, we provide conditions for identifying redundancies in different parts of such a relation, introducing techniques for causal inference in unfaithful causal models (where the observable data does not "faithfully" reflect the causal dependences). In particular, this demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, showing that it is satisfied for light cones in Minkowski space-times with $d>1$ spatial dimensions but violated for $d=1$. Finally, we study the embedding of information-theoretic causal models in space-time without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a space-time and those imposed by purely information-theoretic causal inference behave differently. We then prove a correspondence between conical space-times and faithful causal models: in both cases, there emerges a parallel between these two types of constraints. This indicates a connection between informational and geometric notions of causality, and offers new insights for studying the relations between the principles of NSS and no causal loops in different space-time geometries and theories of information processing.