Causal models assume directed graphs — A causes B, the arrow is given. Tensor networks describe correlations via undirected graphs — nodes share edges, but no edge points anywhere. The two frameworks describe related phenomena with incompatible assumptions about directionality.
This paper (arXiv:2603.12283) bridges them. The key construction: start with an undirected tensor network (no assumed time direction), then define “signaling” operationally — A signals B if intervening at A changes the distribution at B. Causal order emerges from signaling relations. The direction of time is not an input to the model; it is derived from the correlations the network supports.
The framework permits cyclic and indefinite causal structures. This is where it departs from classical causal inference, which requires directed acyclic graphs. In quantum scenarios, causal order can be indefinite — events lack a determinate “before” and “after” until interaction resolves the ambiguity. The standard requirement for acyclicity is not a law of nature but a constraint of the classical formalism.
The construction of discrete space-time rotations — transformations of causal models that preserve signaling relations — provides a group-theoretic tool for classifying which causal structures are equivalent. Two apparently different causal histories that produce the same signaling structure are physically indistinguishable. This is the Leibnizian argument applied to causal direction: if no measurement distinguishes two orderings, any model that treats them as distinct contains surplus structure.
The application to holographic tensor networks is where the result becomes concrete. In holography, the tensor network IS the spacetime. Causal structure in the bulk emerges from the entanglement structure of the boundary. Graph-separation tools from causal inference now have precise tensor-network translations. The direction of time in the bulk is not fundamental — it is the shadow of correlations on the boundary.
“Emergent causal order and time direction: bridging causal models and tensor networks,” arXiv:2603.12283 (March 2026).