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Equivalent Theories and Changing Hamiltonian Observables in General Relativity

Pitts, J. Brian (2018) Equivalent Theories and Changing Hamiltonian Observables in General Relativity. Foundations of Physics.

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Abstract

Change and local spatial variation are missing in Hamiltonian General Relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian-Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of first-class constraints. Kucha\v{r} waived the $0$ Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity.

Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg-Utiyama electromagnetism, one finds that the usual definition fails while the Pons-Salisbury-Sundermeyer definition with $G$ succeeds. This definition does not readily yield change in GR, however.

Should GR's external gauge freedom of General Relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Pitts, J. Brianjbp25@cam.ac.uk0000-0002-7299-5137
Additional Information: Open access. Published in topical collection Philosophical Aspects in the _Foundations of Physics_.
Keywords: Hamiltonian, problem of time, General Relativity, observables, theoretical equivalence, massive gravitons
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Fields and Particles
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Depositing User: Dr. Dr. J. Brian Pitts
Date Deposited: 04 Apr 2018 01:11
Last Modified: 04 Apr 2018 01:11
Item ID: 14528
Journal or Publication Title: Foundations of Physics
DOI or Unique Handle: 10.1007/s10701-018-0148-1
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Fields and Particles
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14528

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