We construct the propagator of a non-relativistic non-interacting particle in a flat spacetime in which two regions have been identified. This corresponds to the simplest "time machine". We show that while completeness is lost in the vicinity of the time machine it holds before the time machine appears and it is recovered afterwards. Unitarity, however, is not satisfied anywhere. We discuss the implications of these results and their relationship to the loss of unitarity in black hole evaporation.

翻译：我们在一个平坦的时空里建造一个非相对性、非相互作用的粒子的传播器,在平坦的时空里已经确定了两个区域。这相当于最简单的“时间机器 ” 。 我们表明,虽然在时间机器出现之前它所持有的时间机器附近就失去了完整性,而在时间机器出现之后又恢复了它。 但是,在任何地方都无法满足统一性。 我们讨论了这些结果的影响及其与黑洞蒸发中统一性丧失的关系。