1983Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsRequires access

Evolution without evolution: Dynamics described by stationary observables

Don N. Page, William K. Wootters

Open publisher page 591 citations

Abstract

Because the time parameter in the Schr\"odinger equation is not observable, energy apparently obeys a superselection rule in the same sense that charge does. That is, observables must all commute with the Hamiltonian and hence be stationary. This means that it is consistent with all observations to assume that any closed system such as the Universe is in a stationary state. We show how the observed dynamic evolution of a system can be described entirely in terms of stationary observables as a dependence upon internal clock readings.

About this research paper

What this paper is about

Because the time parameter in the Schr\"odinger equation is not observable, energy apparently obeys a superselection rule in the same sense that charge does. That is, observables must all commute with the Hamiltonian and hence be stationary. This means that it is consistent with all observations to assume that any closed system such as the Universe is in a stationary state. We show how the observed dynamic evolution of a system can be described entirely in terms of stationary observables as a dependence upon internal clock readings.

Why it matters

OpenAlex reports 591 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Because the time parameter in the Schr\"odinger equation is not observable, energy apparently obeys a superselection rule in the same sense that charge does. That is, observables must all commute with the Hamiltonian and hence be stationary. This means that it is consistent with all observations to assume that any closed system such as the Universe is in a stationary state. We show how the observed dynamic evolution of a system can be described entirely in terms of stationary observables as a dependence upon internal clock readings.

Key concepts: Observable, Superselection, Physics, Stationary state, Hamiltonian (control theory), Time evolution, Statistical physics, Classical mechanics

Related papers

Back to paper searchBrowse research topicsOriginal source
Evolution without evolution: Dynamics described by stationary observables — Research Paper | ScholarLens