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

S. Deser
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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.

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S. Deser. 2005-02-24. How Special Relativity Determines the Signs of the Nonrelativistic, Coulomb and Newtonian, Forces. https://doi.org/10.1119/1.1898503

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