CRA Seminar: Dr. J. Brian Pitts (University of Cambridge)

Title: Change and Observables in Hamiltonian General Relativity

Abstract: Canonical (Hamiltonian) General Relativity and the associated project in quantum gravity are said to suffer from a problem of missing change, especially in “observables”: part of the “problem of time.” This talk addresses this problem by reflecting on definitions of observables. Typically observables in Hamiltonian GR have been defined as having 0 Poisson bracket with each first-class constraint. A reforming literature has redefined gauge transformations using not separate first-class constraints, but a tuned sum thereof, the gauge generator G. G in GR changes the 4-metric by a 4-d Lie derivative. This reforming literature recovers the mathematical equivalence to the Lagrangian originally present in Rosenfeld’s and Bergmann’s school’s works on Hamiltonian GR.
The typical definition of observables can be evaluated by reflecting on the classical definition of the Lie derivative, which is like comparing 1am EDT and 1am EST. Thus demanding a 0 Poisson bracket trivially yields the absence of change. An alternative behaves better.
One can further test this alternative definition using massive photons with and without artificial gauge freedom (Stueckelberg and Proca) and massive gravitons with and without clock fields. Requiring equivalent obervables for equivalent theories, the electromagnetic comparison show the need for the gauge generator G, while the gravitational comparison shows the value of reconsidering the 0 bracket of observables with G in GR.