The Solution to the Problem of Time in Shape Dynamics

TL;DR

This paper presents a complete solution to the classical problem of time in gravity by using Shape Dynamics, an alternative formulation that trades spacetime refoliation invariance for conformal invariance, potentially aiding quantum gravity development.

Contribution

It offers a logical completion of Shape Dynamics, providing a dimensionless, classical solution to the problem of time in gravity, distinct from traditional spacetime approaches.

Findings

Classical problem of time is fully resolved in Shape Dynamics.

Shape Dynamics offers a dimensionless, conformally invariant description of gravity.

This approach may be crucial for developing quantum gravity theories.

Abstract

The absence of unique time evolution in Einstein's 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 Shape Dynamics provides a key ingredient for the creation of quantum gravity.