Pitts, J. Brian (2016) What Are Observables in Hamiltonian Theories? Testing Definitions with Empirical Equivalence. In: UNSPECIFIED.
|
Text
PSA2016ObservablesArtificialGauge.pdf Download (129kB) | Preview |
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}