The solution to the problem of time in shape dynamics

The absence of unique time evolution in Einsteinʼs spacetime description of gravity leads to the hitherto unresolved 'problem of time' in quantum gravity. Shape dynamics is an objectively equivalent representation of gravity that trades spacetime refoliation invariance for three-dimensional conformal invariance. Its logical completion presented here gives a dimensionless description of gravitational dynamics. We show that in this framework the classical problem of time is completely solved. Since a comparable definitive solution is impossible within the spacetime description, we believe that shape dynamics provides a key ingredient for the creation of quantum gravity.