Relational dynamics and quantum time dilation

The lesson of general relativity is background independence, which results in a Hamiltonian constraint. This presents a challenge for quantum gravity because the quantization of this constraint demands that physical states of geometry and matter are frozen, leading to the problem of time. We must then explain how the conventional notion of time evolution emerges, which motivates the need for relational quantum dynamics. Using covariant time observables, I will demonstrate the equivalence of two previously thought to be distinct approaches to relational quantum dynamics: the evolving constants of motion program and the Page-Wootters formalism. Using this framework I will then describe a novel quantum time dilation effect that occurs between two clocks when one moves in a superposition of different relativistic momenta. I will argue that this time dilation effect may be observable with present-day technology and offers a new test of relativistic quantum mechanics.