Exact Results in Quantum Theory

Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising from the Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Additionally, all current experiments with matter-waves probe only the Newtonian limit of gravity. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a clock - a particle with evolving internal degrees of freedom - that will not only display a phase shift but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space-time. In quantum mechanics, there is a tradeoff between the visibility of interference pattern obtained with a single particle in a superposition and the amount of the information about the path taken by the particle. Such a tradeoff is an example of the quantum complementarity principle, first proposed by Niels Bohr. Therefore, the visibility of interference pattern will drop to the extent to which the path information becomes available in the clock. Experimental verification of this gravitationally induced decoherence would thus provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.