Time evolution of Hamiltonian constraint system: an idea applicable to quantum gravity

TL;DR

This paper explores the concept of reference observables as a potential notion of time in Hamiltonian constrained systems, with applications to particles and general relativity.

Contribution

It introduces the idea of reference observables for understanding time evolution in Hamiltonian constraint systems, applicable to quantum gravity.

Findings

Reference observables can serve as a notion of time in constrained systems

Application to non-relativistic and relativistic particles demonstrates the concept

Outline of potential application to general relativity

Abstract

The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other observables evolve. We study if it plays the role of time. As simple examples, we study the theories of non-relativistic and relativistic particles. We outline an application of the idea to general relativity.