Modified Inertia as Nonconservative Newtonian Dynamics

TL;DR

This paper presents a simplified non-conservative Newtonian framework for Milgrom's Modified Inertia theory, enabling observable predictions and analyzing its non-conservative gravitational effects on binary systems.

Contribution

It introduces a tractable Newtonian dynamics equivalent to MI, incorporating non-conservative forces and dark matter, and explores conservation restoration attempts.

Findings

Modified inertia is equivalent to a Newtonian theory with non-conservative gravity.

Tidal forces in this framework are non-conservative and affect binary systems.

Discussion on restoring conservation in MI.

Abstract

Modified Newtonian dynamics by Milgrom is a paradigm for explaining the rotation curves of spiral galaxies and various other large scale structures. This paradigm includes several different theories. Here we present Milgrom's modified inertia (MI) theory in terms of a simple and tractable non-conservative Newtonian dynamics, which is useful in obtaining observable predictions of MI. It is found that: 1) Modified inertia theory is equivalent to a Newtonian theory, with a non-conservative gravitational field, and dark matter density; 2) The tidal force in the equivalent Newtonian dynamics is non-conservative, and its effect on a binary system in free fall in the gravitational field of a spheroid is addressed. We also discuss attempts to restore conservation in MI.