论文标题
循环因果结构与一般理论中的时空结构的兼容性
Compatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions
论文作者
论文摘要
通过关联和订购事件，因果关系构成了我们世界的关键特征。一方面，根据代理的信息处理能力和另一方面，有因果关系的信息理论概念，另一方面，存在与时空相关的因果关系的概念。 In this thesis, we improve upon a framework introduced by V. Vilasini and R. Colbeck in PRA, 106, 032204 (2022) and PRL, 129, 110401 (2022) for connecting these notions, where the possibility of operationally detectable causal loops embedded in (1+1)-Minkowski spacetime without superluminal signalling was demonstrated.在第一部分中，我们采用信息理论的角度，其中提出了高阶（HO）影响关系的概念，以在存在环状，微调和非经典因果影响的情况下进行一般建模信号传导。我们建立HO的新特性会影响关系，并将其应用于推断因果结构。然后，我们展示了一种完整而建设性的方法来检测一组HO影响关系的因果循环。在第二部分中，我们研究了信息理论因果结构的嵌入到部分有序的空间中。我们提出了时空嵌入的稳定条件，以排除一类可检测到的循环，这些循环不能仅由无信号的原则（在相对论的未来之外）排除。然后，我们提出了新的订单理论属性，我们猜测在Minkowski时空中拥有$ d \ geq 2 $空间维度。这意味着与（1+1）-minkowski时空相比，在较高的维度上，无信号原理确实足以排除这类循环。最后，我们介绍了一种关系，该关系可以通过有关缺乏信号关系的知识来进行因果推论，并将其与时空的新秩序理论特征相关联。
By relating and ordering events, causality constitutes a pivotal feature of our world. On the one hand, there are information-theoretic notions of causality defined in terms of the information processing ability of agents and on the other hand, there are relativistic notions of causality tied to a spacetime. In this thesis, we improve upon a framework introduced by V. Vilasini and R. Colbeck in PRA, 106, 032204 (2022) and PRL, 129, 110401 (2022) for connecting these notions, where the possibility of operationally detectable causal loops embedded in (1+1)-Minkowski spacetime without superluminal signalling was demonstrated. In the first part, we take the information-theoretic point of view, where the concept of higher-order (HO) affects relations was proposed to generically model signalling in the presence of cyclic, fine-tuned and non-classical causal influences. We establish new properties of HO affects relations and apply them to infer causal structures. We then demonstrate a complete and constructive way to detect causal loops from a set of HO affects relations. In the second part, we study the embedding of information-theoretic causal structures into partially ordered spacetimes. We propose stability conditions on the spacetime embedding to rule out a class of operationally detectable loops that cannot be ruled out by the principle of no-signalling (outside the relativistic future) alone. We then propose novel order-theoretic properties that we conjecture to hold in Minkowski spacetime with $d \geq 2$ spatial dimensions. This would imply that in contrast to (1+1)-Minkowski spacetime, in higher dimensions, the no-signalling principle is indeed sufficient for ruling out this class of loops. Finally, we introduce a relation which allows for causal inference through knowledge about the absence of signalling relations and we relate it to novel order-theoretic features of spacetime.
