A Relational Concept of Machian Relativity

TL;DR

This paper develops a relational, Machian framework for gravity and inertia that reproduces general relativity's predictions and offers explanations for relativistic effects without dark energy.

Contribution

It introduces a relational spacetime model based on Mach's principle that aligns with GR and explains relativistic phenomena through mutual properties of matter.

Findings

Relational model reproduces GR trajectories and effects.

Provides a frame-independent definition of Machian kinetic energy.

Explains relativistic effects without dark energy.

Abstract

Mach's principle fits into the wider "relational principle", advocating that not only inertia, but also space and time emerge from the interaction of matter. Concepts of a Machian/relational theory are proposed, where inertia and energy are defined as mutual properties between pairs of objects. Due to Berkeley, only radial motion represents kinetic energy between (point) masses, which is the basis of anisotropic inertia, which in turn underlies the relational principle. The Newtonian definition of potential energy is considered a model for Machian inertia, leading to a frame independent definition of Machian kinetic energy, which comprises of the Newtonian terms (relative to the "fixed stars") and small anisotropic Machian energy terms between objects. The latter account for relativistic trajectories, such as the anomalous perihelion precession and Lense-Thirring frame dragging. However, relativistic effects of remote observation (e.g. time dilation) demand an isotropic model. A relational spacetime metric is derived, which provides an isotropic coordinate transform of the anisotropic Machian model, yielding a relational model which matches GR expressions for relativistic trajectories and effects of remote observation. Therefore, the experimental verification of GR in these cases holds automatically for the relational model. The relational model fits the relational principle (including Mach's principle) and it is argued that it includes GR as a special case. The relational metric provides both contraction and (unbound) expansion as a function of relative potential, i.e. without invoking dark energy.