Dear all,
The CamPoS (Cambridge Philosophy of Science) seminar continues this
Wednesday, 20th February, 1-2:30pm in HPS Seminar Room 2. Brian Pitts
(Philosophy, Cambridge) will give a talk entitled “Real Change Happens in
General Relativity, Even in Hamiltonian Form”. The abstract is below.
All are very welcome, and we hope to see many of you there.
Best wishes,
Vashka
--
From time to time natural philosophers have argued that there is no real
change, despite manifest appearances. A recent powerful claim to this end
has been made from Einstein’s General Relativity (GR), the standard theory
of gravity, as expressed in Hamiltonian form. Hamiltonian mechanics employs
not coordinates q and their velocities, but coordinates q and their
conjugate momenta p: more fields but fewer derivatives. Various physicists
and philosopher Earman have questioned objective change due to Hamiltonian
GR, while common sense has been defended by Kuchař and Maudlin, yielding a
stand-off.
Fortunately confusion dissipates when one insists on the golden
principle, employed by Salisbury, Pons, and Shepley, that Hamiltonian
General Relativity be equivalent to General Relativity in more familiar
Lagrangian or 4-dimensional differential geometric form. In GR in more
familiar form, there is change for solutions that are not stationary, that
is, that lack a time-like Killing vector field: no matter how one labels
space-time, the metric depends on time. Hamiltonian change thus must be the
Hamiltonian form of lacking a time-like Killing vector field. Castellani’s
distinction between the 4-dimensional gauge (coordinate) transformation
generator (t)G(t) and the Hamiltonian H clarifies matters.
Pace Dirac and Bergmann, a first-class constraint in
Dirac-Bergmann constrained Hamiltonian dynamics typically does not generate
a physically equivalent configuration. In Maxwell’s electromagnetism, a
first-class constraint generates an (anti)-physical change in the electric
field, spoiling equivalence to Gauss’s law. First-class constraints in GR,
working together, not separately, appear both in the Hamiltonian to
generate time evolution and in the gauge transformation generator to
generate coordinate transformations. Gauge (coordinate) equivalence in GR
must be understood in terms of histories, not instantaneous states as Dirac
envisaged. More confusion is avoided by not introducing primitive point
identities into mathematical physics. There is no reason that “observables”
should be spatially changeless constants of the motion, especially if
observables have something to do with observations (as Bergmann held). He
developed the notion of observables in GR by analogy to Hamiltonian
electromagnetism while neglecting equivalence with Lagrangian GR.
_____________________________________________________
Sent by the CamPhilEvents mailing list. To unsubscribe
or change your membership options, please visit the list
information page: http://bit.ly/CamPhilEvents
Posts are archived here: http://bit.ly/CamPhilEventsArchive
