Quantum Corrections to Classical Time Dilation

At the intersection of quantum mechanics and relativity lies the possibility for a clock to move along a superposition of two distinct classical trajectories — perhaps these trajectories correspond to different speeds or locations in a gravitational field of the clock. It is then natural to ask: what time dilation would such a quantum clock observe? Using covariant time observables, I will introduce a formulation of relational quantum dynamics that allows for a probabilistic formulation of relativistic time dilation. This framework will then be used to describe quantum time dilation effects that occur when a clock moves in a superposition of different relativistic momenta and is at rest in a spatial superposition of an external gravitational field. I will argue that these time dilation effects may be observable with present-day technology and offer a new test of fundamental physics in the regime where quantum coherence and relativistic effects play an important role.