Classical Electromagnetism as a Consequence of Coulomb ’ s Law , Special Relativity and Hamilton ’ s Principle and its Relationship to Quantum Electrodynamics

It is demonstrated how all the mechanical equations of Classical Electromag-netism (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force in the centre-of-mass frame of two interacting charged objects, mediated by the exchange of space-like virtual photons, is predicted by QED. The interaction Lagrangian of QED is shown to be identical, in the appropriate limit, to the potential energy term in the Lorentz-invariant Lagrangian of CEM. A comparison is made with the Feynman-Wheeler action-at-a-distance formulation of CEM.