The role of time in relational quantum theories

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the classical dynamics of the full system. We propose a new strategy for consistently quantizing systems with a relational notion of time that captures the full classical dynamics of the system and allows for evolution parametrized by an equitable internal clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics, an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time, our proposal constitutes a natural methodology for describing dynamical evolution in quantum gravity.