Warsaw Spacetime Colloquium: J. Brian Pitts (16 October on Zoom)

On Friday, 16 October, J. Brian Pitts (University of Lincoln, University of Cambridge, University of South Carolina) will give a talk entitled “Change in observables in Hamiltonian general relativity” (abstract below).

The meeting will take place online on Zoom (16:00-18:00 CET). If you have not registered yet, you can do so by sending a message to antonio.vassallo@pw.edu.pl.

The program for the winter semester can be found here, while the recordings of the previous meetings are available on the ICFO’s YouTube channel.

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. Change in the presence of spinors and Yang-Mills (weak & strong forces) fields is sketched. Classically, change in Hamiltonian GR is just where it should have been, at least for solutions of Einstein’s equations. Quantum imposition of the constraints is another matter.