Quantum clocks, gravitational time dilation, and quantum interference

A proper time observable for a quantum clock is introduced and it found that the read by one conditioned on another reading different obeys classical dilation in accordance with special relativistic kinematical dilation. Here, we extend this proposal to weak gravitational field order investigate whether equivalence principle holds matter. We find general states similar relativity. However, unlike case, involves external (a background coordinate at observer Earth) as well times of two clocks. also effect induced superposition wave packets localized momentum space or position propose setup observe interference