PUG Seminar

In this seminar, we will explore the interplay between quantum mechanics and general relativity by examining the behavior of a quantum clock in curved spacetime. Unlike a classical point mass, a quantum clock with nonzero position fluctuations cannot travel along a single geodesic. Instead, it behaves as an extended object influenced by tidal forces and a superposition of time dilations at different altitudes. Using a geometrical formulation of quantum mechanics, we will show that quantum correlations between spatial directions introduce a non-Riemannian structure to the spacetime experienced by the clock. A specific version of Finsler geometry provides a new setting for a combination of quantum and gravitational effects. The Finsler structure is parameterized by entropy and purity of the state, and uncertainty relations prevent it from being Riemannian. By unifying quantum and gravitational effects in a geometric framework, this approach offers new avenues for advancements in our understanding of quantum reference frames and their applications in semi-classical gravity.