Emergent causal order and time direction: bridging causal models and tensor networks

TL;DR

This paper bridges causal models and tensor networks, revealing how causal structures and time directionality can be inferred and mapped between these frameworks, with applications to holographic tensor networks and emergent causality.

Contribution

It introduces two-way mappings between causal models and tensor networks, linking correlation functions and signalling, and explores emergent causal structures including cyclic and indefinite causality.

Findings

Established mappings between causal models and tensor networks.

Analyzed emergent causal structures using graph-separation techniques.

Enabled transfer of causality analysis methods across frameworks.

Abstract

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs, with intrinsic ordering; the latter describes multipartite systems on undirected graphs, without presupposing directionality. We construct two-way mappings between these two frameworks, linking direction agnostic correlation functions and operational notions of signalling. This clarifies the operational meaning of causal influence in tensor networks and introduces discrete "space-time rotations'' of causal models which preserve signalling relations. Applying our framework to holographic tensor networks, we use tools from causal inference, like graph-separation, to analyse emergent causal structures. By permitting cyclic and indefinite causal structures, our results enable transfer of techniques across tensor networks and a range of causality frameworks.