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Within no inertial frame can stationary charge exist. All charge, wherever itexists, experiences perpetual interaction with charge elsewhere and so can onlyexist as non-trivial current. It follows that the notion of the electrostaticscalar potential is a pragmatic idealization - it is not fundamental and isuseful simply because, in many practical circumstances, the time scales ofinterest are sufficiently small that charges can be considered stationary inappropriately chosen inertial frames. In this paper, we take the view that thesubsuming of the electrostatic scalar potential within classicalelectrodynamics raises issues of fundamental principle and consider thequestion of whether it is possible to have a relativistic electrodynamics sansthe electrostatic scalar potential - that is, expressed purely in terms of someform of relativistic magnetic potential. Surprisingly, we find that such athing can be realized in a remarkably simple way - and which is cost-free forordinary applications of electrodynamics. But the overall formalism hasfundamental ramifications for our deeper understanding of electrodynamics - forexample, a new relativistic symmetry arises which, naturally interpreted,implies that the Lorentz force must be considered as a local-action contactforce in which energy-momentum is locally conserved through the medium of anuncharged massive vector particle.

The conflict between realism and the scalar potential in electrodynamics