Seminar

The Hamilton-Jacobi equation for a classical dynamical system naturally leads to a formula for time in terms of the geometry of the configuration space. We illustrate this in particle mechanics on a fixed energy surface, and discuss the generalization to General Relativity where the metric on configuration space -- the de Witt metric -- has indefinite signature. The Thin Sandwich Conjecture (TSC) makes an appearance in the derivation and we recover previous results in the literature on the (lack of) validity of the TSC in general relativity. We illustrate the formula for time in various examples including de Sitter spacetime and asymptotically AdS spacetimes.