A magnetic clock for a harmonic oscillator

Abstract

We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone, or by both the clock and the evolving system. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it. This allows us to analyze and discuss the relations that must hold between quantities that characterize system and clock separately, in order for the resulting overall picture be that of a physical dynamics as we mean it.