Machian Time Is To Be Abstracted From What Change?

TL;DR

This paper proposes a middle-ground approach to defining time based on a sufficient totality of locally relevant change, addressing the Problem of Time in Quantum Gravity and connecting classical and quantum perspectives.

Contribution

It introduces the concept of Sufficient Totality of Locally Relevant Change (STLRC) as a new principle for understanding and resolving the Problem of Time in quantum gravity.

Findings

STLRC generalizes astronomers' ephemeris time.

Emergent Jacobi-Barbour-Bertotti time arises from STLRC.

Addresses classical and quantum Problem of Time.

Abstract

"It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things." Ernst Mach [1]. What change? Three answers to this are `any change' (Rovelli), 'all change' (Barbour) and my argument here for the middle ground of a `sufficient totality of locally relevant change' (STLRC) giving a generalization of the astronomers' ephemeris time. I then use STLRC as a selection principle on existing and new approaches to the Problem of Time in Quantum Gravity. Emergent Jacobi-Barbour-Bertotti time can be interpreted as arising from a STLRC, resolves the classical Problem of Time and has an emergent semiclassical counterpart as regards facing the QM Problem of Time.