The Problem of Time in Canonical Quantum Gravity: A Model Study

The incorporation of quantum mechanics with general relativity has remained one of the greatest challenges in theoretical physics, fundamentally manifest in the problem of time. This problem appears primarily in the canonical quantization of general relativity. For example, in Wheeler-DeWitt equation the resulting dynamics are invariant under time reparameterizations which leads to a static, time-independent description of the universe. In this paper we briefly outline the origin of the problem of time and then discuss the deparametrization scheme for a system whose motion is non-linear and coupled between two variables.