Mach, the Universe, and Foundations of Mechanics

TL;DR

This paper discusses an approach to Mach's principle involving the universe's role in defining inertial frames, aligning with general relativity for closed universes, but emphasizes an observational, operational perspective.

Contribution

It introduces an operational approach to Mach's principle that emphasizes observational data over purely theoretical constructs.

Findings

Agreement with general relativity for finite, closed universes

Supports an observational basis for defining inertial frames

Highlights differences between theoretical and operational approaches

Abstract

Barbour's response to our recent paper on "Mach's principle and higher-dimensional dynamics" describes an approach to Mach's principle in which the universe as a whole is involved in the definition of inertial frames of reference. Moreover, Barbour's theoretical procedure is in agreement with general relativity for a finite universe that is spatially closed. However, we prefer an operational approach that relies ultimately on observational data.