PSA2016: The 25th Biennial Meeting of the Philosophy of Science Association

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

Change seems missing in Hamiltonian General Relativity’s observables. The typical definition takes observables to have 0 Poisson bracket with each first-class constraint. Another definition aims to recover Lagrangian-equivalence: observables have 0 Poisson bracket with the gauge generator G, a 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.

Author Information:

J. Brian Pitts    
Faculty of Philosophy
University of Cambridge

 

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