Causal paradoxes: a conflict between relativity and the arrow of time

Abstract

It is often argued that superluminal velocities and nontrivial spacetime topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA) that points from the past to the future, the apparent paradoxes appear to be an artefact of the wrong tacit assumption that the relativistic coordinate TA coincides with the physical TA. The latter should be identified with the thermodynamic TA, which, by being absolute and irrotational, does not lead to paradoxes.