How Special Relativity Determines the Signs of the Nonrelativistic, Coulomb and Newtonian, Forces
arXiv:gr-qc/0411026 · doi:10.1119/1.1898503
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.
8 pages. Amplified version, to appear in Am. J. Phys