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

[Antonio Vassallo]

(With apologies for cross-posting)

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 at pw.edu.pl.

The Colloquium is organized by the Philosophy of Physics Group
<https://icfo.ans.pw.edu.pl/en/?page_id=3168> at the International Center
for Formal Ontology (Warsaw University of Technology). The program for the
winter semester can be found here
<https://icfo.ans.pw.edu.pl/en/?page_id=3389>.

The recordings of the previous meetings are available on the ICFO's YouTube
channel
<https://www.youtube.com/playlist?list=PLM-1yNCyvJJAfiq7LDFjfYc1I5OOxhJ1A>.

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.
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