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Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity

Pitts, J. Brian (2017) Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity. Classical and Quantum Gravity, 34. 055008. ISSN 1361-6382, Print ISSN 0264-9381

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Abstract

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables.

The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries.

The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Pitts, J. Brianjbp25@cam.ac.uk0000-0002-7299-5137
Keywords: quantum gravity problem of time Hamiltonian formulation General Relativity Parmenides Zeno observables gauge symmetry theoretical equivalence empirical equivalence
Subjects: Specific Sciences > Physics > Cosmology
General Issues > Experimentation
Specific Sciences > Physics > Fields and Particles
General Issues > Logical Positivism/Logical Empiricism
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Depositing User: Dr. Dr. J. Brian Pitts
Date Deposited: 03 Mar 2017 17:59
Last Modified: 03 Mar 2017 17:59
Item ID: 12870
Journal or Publication Title: Classical and Quantum Gravity
Official URL: http://iopscience.iop.org/article/10.1088/1361-638...
DOI or Unique Handle: doi.org/10.1088/1361-6382/aa5ce8
Subjects: Specific Sciences > Physics > Cosmology
General Issues > Experimentation
Specific Sciences > Physics > Fields and Particles
General Issues > Logical Positivism/Logical Empiricism
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
General Issues > Theory/Observation
Date: 2017
Page Range: 055008
Volume: 34
ISSN: 1361-6382, Print ISSN 0264-9381
URI: http://philsci-archive.pitt.edu/id/eprint/12870

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