Reference Fluids as Standards of Space and Time

TL;DR

This paper explores the use of reference fluids, modeled as incoherent dust, to define a physical notion of time in general relativity, leading to a Schrödinger-like equation and simplifying the constraints in quantum gravity.

Contribution

It introduces a phenomenological approach using reference fluids to address the problem of time in quantum gravity, resulting in a simplified Hamiltonian and explicit solutions to constraints.

Findings

Reference fluids lead to a conserved inner product.

The true Hamiltonian depends only on gravitational variables.

Space can be endowed with privileged coordinates from the dust.

Abstract

The idea that spacetime points are to be identified by a fleet of clock--carrying particles can be traced to the earliest days of general relativity. Such a fleet of clocks can be described phenomenologically as a reference fluid. One approach to the problem of time consists in coupling the metric to a reference fluid and solving the super--Hamiltonian constraint for the momentum conjugate to the clock time variable. The resolved constraint leads to a functional Schr\"{o}dinger equation and formally to a conserved inner product. The reference fluid that is described phenomenologically as incoherent dust has the extraordinary property that the true Hamiltonian density for the coupled system depends only on the gravitational variables. The dust particles also endow space with a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. (Contribution to the Proceedings of the Lanczos Centenary Conference.)