Mechanics, cosmology and Mach's principle

TL;DR

The paper explores how recent cosmological data support Mach's principle, suggesting that the universe's mass/energy distribution influences inertial frames, with implications for general relativity and cosmology.

Contribution

It provides a precise formulation of Mach's principle and shows its realization under specific cosmological conditions using an approximation to general relativity.

Findings

Mach's principle is supported by cosmological data.

Inertial frames are influenced by the universe's mass/energy distribution.

The specific density value for the universe is twice the critical density.

Abstract

It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames as originally suggested by Mach. The background concepts of inertial frame, Newton's second law, and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then an approximation to general relativity discovered by Einstein, Infeld, and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result is put into context.