  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 full classical
dynamics of the system and must therefore be deemed inappropriate. We propose a
new strategy for consistently quantizing systems with a relational notion of
time that does capture 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 can be shown to constitute
a natural methodology for describing dynamical evolution in quantum gravity and
to lead to a quantum theory analogous to the Dirac quantization of unimodular
gravity.
