[Paper Review] Machian Time Is To Be Abstracted From What Change?

Edward Anderson|arXiv (Cornell University)|Sep 6, 2012

Quantum Mechanics and Applications27 references19 citations

TL;DR

This paper proposes that Machian time should be abstracted from a sufficient totality of locally relevant change (STLRC), generalizing ephemeris time to resolve the Problem of Time in Quantum Gravity. It shows that emergent Jacobi-Barbour-Bertotti time arises from STLRC, offering a semiclassical counterpart and serving as a selection principle to reject approaches based on 'any' or 'all' change, thereby advancing relational timekeeping in quantum gravity.

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.

Motivation & Objective

• To resolve the Problem of Time in Quantum Gravity by reinterpreting Machian time as emerging from locally relevant change.
• To challenge the 'any change' and 'all change' interpretations of timekeeping, proposing instead a middle-ground approach based on a sufficient totality of locally relevant change (STLRC).
• To provide a conceptual and physical foundation for emergent time in quantum gravity that aligns with astronomical practice and semiclassical consistency.
• To evaluate and reject alternative time-keeping schemes—hidden times, matter times, unimodular time—by showing they fail to fully exploit relational principles.

Proposed method

• Introduces the concept of generalized local ephemeris time (GLET) as a physical realization of Machian time derived from a sufficient totality of locally relevant change (STLRC).
• Applies the STLRC framework to emergent Jacobi-Barbour-Bertotti (JBB) time, showing it resolves the classical Problem of Time and has a semiclassical counterpart.
• Uses GLET as a selection principle to evaluate and reject time-keeping strategies based on 'any' or 'all' change, including hidden times, matter times, and unimodular time.
• Reinterprets existing approaches—such as conditional probabilities, records schemes, and Histories Theory—within the STLRC framework to ensure compatibility with relational time.
• Demonstrates that the semiclassical approach to time in quantum gravity is aligned with GLET and that combined histories-records-semiclassical schemes are consistent with STLRC.
• Argues that Ashtekar variables and Loop Quantum Gravity have so far only partially realized relationalism, favoring 'any change' over the full potential of 'STLRC'.

Experimental results

Research questions

• RQ1 How can Machian time be rigorously abstracted from physical change in a way that resolves the Problem of Time in quantum gravity?
• RQ2 Why is the 'any change' or 'all change' interpretation of time insufficient for a consistent relational time in quantum gravity?
• RQ3 Can generalized local ephemeris time (GLET) based on a sufficient totality of locally relevant change (STLRC) serve as a viable and foundational time concept in quantum gravity?
• RQ4 How does emergent Jacobi-Barbour-Bertotti time relate to GLET and what does this imply for the semiclassical regime?
• RQ5 To what extent can existing time-keeping schemes in quantum gravity be reinterpreted or rejected based on the STLRC criterion?

Key findings

• The paper establishes that time is best abstracted from a sufficient totality of locally relevant change (STLRC), which generalizes ephemeris time and avoids the extremes of 'any' or 'all' change.
• Emergent Jacobi-Barbour-Bertotti (JBB) time arises naturally from STLRC and resolves the classical Problem of Time, with a semiclassical counterpart that matches known results to high accuracy.
• The GLET framework rejects 'hidden times', 'matter times', and 'unimodular time' as incomplete, since they rely on specific, non-universal changes rather than a sufficient totality of locally relevant change.
• The semiclassical approach to time in quantum gravity is found to be compatible with GLET, and combined histories-records-semiclassical schemes are shown to be consistent with STLRC, enhancing their foundational viability.
• The paper identifies that current formulations in Ashtekar variables and Loop Quantum Gravity only partially realize relationalism by favoring 'any change' over the full relational potential of STLRC.
• For certain reduced phase space models (RPMs), the combined approach based on GLET and semiclassical beables accounts for 6/8 of the Problem of Time solutions, demonstrating strong explanatory power.