Date: Wednesday 27th of January 2021, 13:30.
Location: Online (MS Teams meeting).

‘Change and Observables in Hamiltonian General Relativity’

by Dr Brian Pitts, School of History and Heritage, University of Lincoln, Lincoln, UK.

Abstract:

Since the 1950s it has been claimed that change is missing in the formulation of General Relativity most straightforwardly quantized, the Hamiltonian (“canonical”) formulation. In particular, “observables” are said to be constants of the motion and to require integration over the whole universe. This talk gives a technical evaluation of that claim and a sketch of the trajectory of canonical GR co-founder Peter Bergmann’s thoughts on the topic. Technically one finds that the typical notion of observables (as having 0 Poisson bracket with each first-class constraint) contains 2 suspect ingredients. One is the use of first-class constraints separately rather than as a team, the Rosenfeld-Anderson-Bergmann-Castellani “gauge generator” G, which preserves Hamilton’s equations. Use of separate constraints violates Hamiltonian-Lagrangian equivalence, a principle that Bergmann claimed to uphold. The second suspect ingredient, having 0 Poisson bracket (as opposed to a suitable nonzero Lie derivative) under coordinate gauge transformations, in its usual form contradicts daily experience and the principle that equivalent theories have equivalent observables. A reformed definition of observables uses the gauge generator G and takes them to be invariant under internal gauge transformations but only covariant under coordinate transformations. This definition makes the metric and the electromagnetic field strength observables for Einstein-Maxwell: observables are local fields that vary spatio-temporally. Change is essential time dependence, cashed out technically as the lack of a time-like Killing vector field or (with matter) an analogous condition. Quantum imposition of the constraints is another matter.