How Special Relativity Determines the Signs of the Nonrelativistic, Coulomb and Newtonian, Forces

TL;DR

This paper demonstrates that the signs of Coulomb and Newtonian forces are determined by the stability conditions of photons and gravitons within special relativity, linking fundamental force signs to particle spin properties.

Contribution

It reveals a novel connection between force signs and the stability of gauge bosons, derived without static limit assumptions, emphasizing the role of relativistic field decompositions.

Findings

Signs of Coulomb/Newton forces are dictated by photon/graviton stability.

Opposite force signs are linked to the odd/even spin nature of gauge bosons.

The approach avoids reliance on static limits, emphasizing gauge-invariant decompositions.

Abstract

We show that the empirical signs of the fundamental {\it static} Coulomb/Newton forces are dictated by the seemingly unrelated requirement that the photons/gravitons in the respective underlying Maxwell/Einstein physics be stable. This linkage, which is imposed by special relativity, is manifested upon decomposing the corresponding fields and sources in a gauge-invariant way, and without appeal to static limits. The signs of these free field excitation energies determine those of the instantaneous forces between sources; opposite Coulomb/Newton signs are direct consequences of the Maxwell/Einstein free excitations' odd/even spins.