Intrinsic time geometrodynamics

Tuesday, Sept 12th
Eyo Eyo Ita, University of South Africa
Title: Intrinsic time quantum geometrodynamics: emergence of General Relativity and cosmic time 
PDF of the talk (1.5M)
Audio+Slides [.mp4 8MB]

By Jorge Pullin, LSU

Usual Newtonian mechanics describes the motions of systems with respect to an absolute time variable usually called t. Already special relativity introduces the idea that time is not absolute and that it ticks at different rates for different observers. General relativity goes beyond that: one can pick any variable to play the role of time. The result of that is that if one tries to understand the dynamics of the theory as an "evolution in time" one runs into difficulties. This is important because many of our ideas of how to quantize theories are implemented dynamically. One needs what is known as a "Hamiltonian formulation" of the theory in order to implement what is known as "canonical quantization". In the Hamiltonian formulation there is a quantity known as the Hamiltonian that is responsible for time evolution. If one attempts to construct a Hamiltonian formulation for general relativity one discovers that the Hamiltonian vanishes. This reflects the fact that if one is allowed to pick any time variable one essentially can get any evolution one wants. This was the source of quite a bit of confusion and explains why a suitable Hamiltonian formulation took almost 50 years to emerge, being general relativity from 1915 and the Hamiltonian formulation only finally understood in the early 60's. Today we know that if one wants to have a defined Hamiltonian and evolution one needs to choose a time variable. The intrinsic geometrodynamics essentially chooses the volume of space as time variable. This seminar discussed the details and its implications for quantization in particular in the so-called "path integral quantization". Among the results a natural vacuum for the theory is found that involves the well known mathematical invariant related to the Chern-Simons form, suggesting perhaps that general relativity could be turned into a renormalizable quantum field theory.