Seminar "Temporal Insights from the End of Space" by Justin C. Feng

In this talk, I present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum General Relativity by way of boundary (Weiss) variations. One feature of this approach is that it does not require an explicit 3+1 splitting of spacetime in the bulk. For spacetimes with spatial (timelike) boundary, I show that the dependence of the transition amplitudes on spatial boundary conditions is determined by a Wheeler-DeWitt equation for the spatial boundary surface. I also show that variations in the induced metric at the spatial boundary can be used to describe time evolution--time evolution in quantum General Relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary.