Scale-Invariant Gravity: Particle Dynamics

TL;DR

This paper introduces a scale-invariant, relational gravitational dynamics method called best matching, which predicts zero total energy and angular momentum for the universe and links fundamental constants to matter distribution.

Contribution

It presents a novel scale-invariant approach to gravity using best matching, extending relational dynamics and deriving new predictions for cosmological constants.

Findings

Energy and angular momentum of the universe are zero.

Gravitational constant and cosmological force strength are determined by matter distribution.

The model predicts redshift from inhomogeneity, not expansion.

Abstract

A new and universal method for implementing scale invariance, called best matching, is presented. It extends to scaling the method introduced by Bertotti and the author to create a fully relational dynamics that satisfies Mach's principle. The method is illustrated here in the context of non-relativistic gravitational particle dynamics.. It leads to far stronger predictions than general Newtonian dynamics. The energy and angular momentum of an `island universe' must be exactly zero and its size, measured by its moment of inertia, cannot change. This constancy is enforced because the scale invariance requires all potentials to be homogeneous of degree -2. It is remarkable that one can nevertheless exactly recover the standard observed Newtonian laws and forces, which are merely accompanied by an extremally weak universal force like the one due to Einstein's cosmological constant. In contrast to Newtonian and Einsteinian dynamics, both the gravitational constant G and the strength of the cosmological force are uniquely determined by the matter distribution of the universe. Estimates of their values in agreement with observations are obtained. Best matching implements a dynamics of pure shape for which the action is a dimensionless number. If the universe obeys such scale invariant law, steadily increasing inhomogeneity, not expansion of the universe, causes the Hubble red shift. The application of best matching to geometrodynamics is treated in a companion paper.