Quantum interferometric visibility as a witness of general relativistic proper time

Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matterĝ€" wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonovĝ€"Bohm effect, where a particle in a flat spaceĝ€"time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'ĝ€"a particle with evolving internal degrees of freedomĝ€"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 spaceĝ€"time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics.