Causality for nonlocal phenomena

Understand

Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime.

• To prepare the ground, we explore the borderland between causality, topology and measure theory.
• We provide various characterisations of the proposed causal relation, which turn out to be equivalent if the underlying spacetime has a sufficiently robust causal structure.
• We also present the notion of the 'Lorentz-Wasserstein distance' and study its basic properties.