Current Research Programme
The central issues guiding my research are:
- What is general relativity? Is it irreducibly a theory of curved four-dimensional spacetime or is it a dynamical theory of the evolution of three-dimensional geometry?
- What are the implications of the holistic relational structure of classical general relativity for the quantization of the theory?
- Shapes (local conformal geometry in three dimensions) play the dominant role in the dynamics of general relativity. Work on Shape Dynamics is currently the most active and promising line of research with which I am involved with collaborators.
- In my The End of Time I argue that the wave function of the universe is static and that the appearance of the flow of time emerges because the wave function of the universe is concentrated on configurations of the universe that we recognize as records. Edward Anderson and I are currently trying to develop this idea and create a theory of records. If successful, this work promises to explain the origin of the arrow of time at a fundamental level.
FQXi grant on the Nature of Time and the Structure of Space
In 2008 I received funding from the Foundational Questions Institute (fqxi.org) for my two-year research proposal Machian Quantum Gravity. The detailed proposal is here (pdf). In January 2011 I received further research funding for another two-year period for the project The Nature of Time and the Structure of Space (pdf). This new project follows on naturally from the first project, bulding on results obtained in it.
Perimeter Institute seminars
A seminar ("The case for geometry") from my visit to the Perimeter Institute in May 2010 is available on their site.
Videos of three seminars from a previous visit in September 2008 are also on the same site. These talks cover much of my research programme.
My collaborator Brendan Foster also gave a talk about our reevaluation of Dirac's theorem on constraints and gauge transformations.