No‑superluminal‑signalling forbids testable causal loops in higher‑dimensional “conical” spacetimes
This paper shows that the rule “no superluminal signalling” (NSS) prevents any operationally detectable time‑loop behaviour in a broad class of spacetimes that the authors call conical. In plain terms: if you demand that no information can be sent faster than light, then in these spacetimes you cannot build a detectable causal loop—an arrangement of signals that would let events influence their own past. This contrasts with an earlier theoretical example that found detectable loops were possible in a one‑dimensional space plus time (1+1) setting.
To reach this conclusion the authors work from an information‑theoretic description of causal structure called the affects framework. In that framework one models observed variables and the signalling relations between them. Those signalling relations are then placed, or “embedded,” into a model of spacetime that records which events can lie in the light cone of which others. Compatibility with NSS is imposed as a simple requirement: whenever the signalling pattern says one set of observed variables can influence another, their putative spacetime locations must be able to send light‑cone signals in the required directions.
A key geometric input is the property the authors call conicality. Roughly, conicality says that the joint future region of a finite set of spacetime points determines uniquely which of those points actually contribute to that joint future. Minkowski spacetime with more than one spatial dimension satisfies this property, while the 1+1 case does not. Using this property the authors perform a two‑step proof. First they show that complicated, higher‑order signalling patterns can be reduced to simpler, ordinary signalling relations without changing the conclusions that matter for NSS in conical spacetimes. Second they prove that no non‑degenerate embedding of those simple signalling loops is compatible with NSS in a conical spacetime. Put together, these steps imply their main theorem: NSS rules out all operationally verifiable causal loops in conical spacetimes.