We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional spacetime structure as would be provided by a (possibly dynamical) foliation of spacetime. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time.