# What Are Observables in Hamiltonian Theories? Testing Definitions with Empirical Equivalence

Pitts, J. Brian (2016) What Are Observables in Hamiltonian Theories? Testing Definitions with Empirical Equivalence. In: UNSPECIFIED.

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## Abstract

Change seems missing in Hamiltonian General Relativity's observables. The typical definition takes observables to have $0$ Poisson bracket with \emph{each} first-class constraint. Another definition aims to recover Lagrangian-equivalence: observables have $0$ Poisson bracket with the gauge generator $G$, a \emph{tuned sum} of first-class constraints.

Empirically equivalent theories have equivalent observables. That platitude provides a test of definitions using de Broglie's massive electromagnetism. The non-gauge Proca'' formulation has no first-class constraints, so everything is observable. The gauge Stueckelberg'' formulation has first-class constraints, so observables vary with the definition. Which satisfies the platitude? The team definition does; the individual definition does not.

Subsequent work using the gravitational analog has shown that observables have not a 0 Poisson bracket, but a Lie derivative for the Poisson bracket with the gauge generator $G$. The same should hold for General Relativity, so observables change locally and correspond to 4-dimensional tensor calculus. Thus requiring equivalent observables for empirically equivalent formulations helps to address the problem of time.

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Item Type: Conference or Workshop Item (UNSPECIFIED)
Creators:
CreatorsEmailORCID
Pitts, J. Brianjbp25@cam.ac.uk0000-0002-7299-5137
Keywords: observables, problem of time, quantum gravity, particle physics, empirical equivalence
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Fields and Particles
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: 05 Nov 2016 19:38
Item ID: 12595
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Fields and Particles
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: 2 November 2016
URI: http://philsci-archive.pitt.edu/id/eprint/12595