Universal Harmonic Inertia and Harmonic Momentum: A Harmonic Formulation of Gravitation and Electrostatics

Abstract I propose that harmonic behaviour is fundamental in conservative physical interaction and correlation, and that inertia is a property of the relations between entities rather than of entities in isolation. I give the inverse-square force laws, gravitation and electrostatics, in a harmonic, relational form, isomorphic to the classical ones. I name the conserved quantity of the pairwise harmonic motion the harmonic momentum, and I note, without developing, that the reading has implications beyond the two laws reformulated here. About this document This document is a four-page foundation note. Rewriting Newton's inverse-square law by substituting the attracting body's mean density over the sphere of the separation, the two-body interaction becomes harmonic about the other body, with the spring constant set by that density. The same description applies at the barycentre, where it yields Kepler's third law directly, and the conserved quantity of the motion is the Laplace-Runge-Lenz (eccentricity) vector, named here the harmonic momentum. The claim is an exactly equivalent description, isomorphic to Newton, with the same predictions. The note is deliberately fenced, and implications beyond the reformulated laws are reserved for a companion paper in preparation. The principle and conjecture are first recorded in the author's notes of July 2005. The density form is set out in a solely authored draft of August 2013. The identification of the conjectured conserved quantity with the Laplace-Runge-Lenz (eccentricity) vector was made in September 2026. The paper was developed in collaboration with a Mistral AI research assistant, based on the author's original ideas, drafts and archive materials. Citation and related work This note is deposited to establish priority and date of record. It is intended that a version will also be submitted to arXiv (physics.class-ph) and to the Journal of the British Interplanetary Society. A companion paper extending the reading and developing the implications is in preparation.