Compatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions

Abstract

By relating and ordering events, causality constitutes a pivotal feature of our world. However, different notions of causality exist, whose relation is not completely understood so far. In particular, we may consider both information-theoretic causality, covering the operational idea of information processing, and relativistic causality, linked to a light cone structure limiting signalling to the future. In this work, we improve on various results on the connection between both notions, as studied by V. Vilasini and R. Colbeck in [1][2], in particular for questions of cyclicity. In the first part, we take an information-theoretic point of view, reviewing general, potentially cyclic or fine-tuned causal models. Here, the most general way of signalling is given by a concept of generalized affects relations, which use interventions on the model to uncover relations between nodes in these graphs. Building from their results, we study the properties of these affects relations and establish new ways to use them to characterize causal structures. focusing on higher-order (HO) affects relations in particular, we can use knowledge of the absence of affects relations for causal inference. Further, we demonstrate a complete and constructive way to detect causal loops from a set of affects relations. In the second part, we embed these causal structures into a generic spacetime whose causal structure forms a partial order. Here, it was shown in [2] that limiting signalling to the relativistic future does not suffice to generally rule out operationally detectable causal loops. In light of this, we propose additional stability conditions on the spacetime embedding and find that this can 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 a number of order-theoretic properties that we conjecture to hold in Minkowski spacetime with d ≥ 2 spatial dimensions. This would imply that in contrast to our result for generic spacetimes, in that Minkowski case, the no-signalling principle is indeed sufficient for ruling out this class of loops. Finally, we deduce novel restrictions for compatibility for certain HO affects relations. Her excitement and commitment to the project have always encouraged me to dive further into its various facets, ever increasing my enthusiasm over its framework. Even in the final weeks and days of this project, she has provided me invaluable feedback an uncountable number of times and was always available for last-minute questions and discussions. Beyond that, I thoroughly enjoyed discussing a variety of fascinating foundational questions not directly related to this thesis in our meetings.Furthermore, I am grateful to Prof. Renato Renner and the Quantum Information Theory Group as a whole, allowing me to learn about the foundations of this world, culminating (for now) in this thesis, in such a stellar environment with lectures, seminars, and of course the Discussion Group on the Foundations and P...