Machian Classical and Semiclassical Emergent Time

TL;DR

This paper develops classical and semiclassical schemes based on Mach's principle that recover the concept of time from change, linking classical and quantum approaches in the context of the Problem of Time in Quantum Gravity.

Contribution

It introduces a unified Machian framework connecting classical and semiclassical schemes for emergent time in quantum gravity, emphasizing their distinct yet related roles.

Findings

Classical scheme explicitly cast as Barbour's approach.

Semiclassical scheme as a Machian variant of the Semiclassical Approach.

Both schemes are shown to be equally Machian and distinct in their treatment of time.

Abstract

Classical and semiclassical schemes are presented that are timeless at the primary level and recover time from Mach's `time is to be abstracted from change' principle at the emergent secondary level. The semiclassical scheme is a Machian variant of the Semiclassical Approach to the Problem of Time in Quantum Gravity. The classical scheme is Barbour's, cast here explicitly as the classical precursor of the Semiclassical Approach. Thus the two schemes have been married up, as equally-Machian and necessarily distinct, since quantum change is part of whence the latter's timestandard is abstracted.