THE BREAKDOWN OF QUANTUM-MECHANICS IN THE PRESENCE OF TIME MACHINES

General Relativity allows for the existence of closed timelike curves. Various attempts have been made to exploit this possibility and build a ''time machine,'' that is a spacetime that has closed timelike lines inside some compact domain. We examine a simple model of a time machine, and construct the quantum-mechanical propagator for free particles in the vicinity of the causality violating domain. We discover that it is impossible for such propagators to be consistent with the law of conservation of probability. We speculate on the possible deeper consequences of our calculations.