Seminarium Teorii Względności i Grawitacji

The problem of time is a notorious conundrum arising in generally covariantquantum theories. In this talk, I will describe progress on several aspects of the problemof time discussed by Isham and Kuchar in their classic reviews 30 years ago. This will include(i) establishing the equivalence of three approaches to relational dynamics (relational observables,Page-Wootters formalism and deparametrizations), (ii) addressing the multiple-choice problem(non-uniqueness of the clock choice), (iii) addressing the global problem (absence of monotonicclocks), (iv) elucidating how to sidestep Unruh's and Wald's claim that realistic quantum clockshave non-vanishing probability to run backwards, and (v) resolving Kuchar's three criticismsagainst the Page-Wootters formalism. Time permitting, I will also summarize how one cangeneralize these insights to quantum reference frames for general symmetry groups (i.e. notonly temporal reference frames).