A relational approach to the Mach-Einstein question

TL;DR

This paper explores a relational theory that aims to reconcile Mach's principle with general relativity, addressing their inconsistencies and the need for a unified framework.

Contribution

It proposes a relational approach that integrates Mach's principle with general relativity, potentially resolving their conflicts and explaining cosmic acceleration without dark energy.

Findings

Identifies inconsistencies between Mach's principle and GR.

Suggests a relational framework can unify the two theories.

Addresses the cosmic acceleration issue without dark energy.

Abstract

Mach's principle is incompatible with general relativity (GR), it has not condensed into an established theory and suffers from inconsistencies. Yet, the problem is that Mach's principle is a consequence of Berkeley's notions, which are as good as irrefutable for their ontological nature. Moreover, the observed coincidence of the "preferred inertial frame" and the frame attached to the "fixed stars" is essentially Machian, while this coincidence is anomalous to both GR and Newtonian physics. Another issue is that GR needs dark energy to explain the accelerating expansion of the universe, while acceleration of receding masses is inherent to the Machian principle. So GR and Mach's principle question each other, while neither one can be falsified easily. This suggest that both are valid in their particular domain. A relational theory may reconcile the two, since it can cover both.