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It is demonstrated how all the mechanical equations of classicalelectrodynamics (CEM) may be derived from only Coulomb's inverse square forcelaw, special relativity and Hamilton's Principle. The instantaneous nature ofthe Coulomb force in the centre-of-mass frame of two interacting chargedobjects, mediated by the exchange of space-like virtual photons, is predictedby QED. The interaction Lagrangian of QED is shown to be identical, in theappropriate limit, to the potential energy term in the Lorentz-invariantLagrangian of CEM. A comparison is made with the Feynman-Wheeleraction-at-a-distance formulation of CEM.

physica scripta

Classical electromagnetism as a consequence of Coulomb's law, special relativity and Hamilton's principle and its relationship to quantum electrodynamics