The shape dynamics formulation of gravity possesses a physical Hamiltonian that generates evolution of spatial conformal geometry. This disentangles the problem of time in quantum gravity: The gauge problem (the choice of foliation in the spacetime description) is replaced by the problem of finding spatial conformal geometries, leaving an evolution that is comparable to a system with time dependent Hamiltonian. The problem of time is suggested to be completely solved by restricting oneself to "objective observables," which are those observables that do not depend on any external clock or rod.