This course will provide an introduction to current research on the problem of time in quantum gravity and cosmology. This is one of the key problems that any successful quantum theory of gravity must solve. Different approaches to quantum gravity assume different answers to fundamental questions such as whether time is emergent or not, whether causality is emergent or not, and what is an observable in a theory of gravity. These problems have aspects which are technical as well as conceptual and philosophical aspects and we will discuss them all as well as their inter-relations.
The course will begin with an introduction to the canonical formulation of general relativity and related dynamical systems. We will then study the standard material on the Hamiltonian quantization of general relativity and related time reparametrization invariant systems. This gives us the technical setting in which the problem of time is usually encountered in the contemporary literature on quantum gravity and quantum cosmology.
Following this physical introduction we will read the key texts from the history of physics and philosophy concerning the meaning of time, such as Newton, Leibniz, Mach, Einstein etc.
This will be followed by readings of papers and books from contemporary sources on this issue by physicists and philosophers. We will focus on two opposite views, the idea that time is emergent in quantum cosmology and the opposing idea that time is fundamental and is perhaps the only aspect of our macroscopic reality that is not emergent.