[1] The requirement that the equations remain consistent when viewed from various moving observers led to special relativity, a geometric theory of 4-space where intermediation is by light and radiation.
An effort to mount a full-fledged electromechanics on a relativistic basis is seen in the work of Leigh Page, from the project outline in 1912[3] to his textbook Electrodynamics (1940)[4] The interplay (according to the differential equations) of electric and magnetic field as viewed over moving observers is examined.
[8] Rosser's book Classical Electromagnetism via Relativity was popular,[9] as was Anthony French's treatment in his textbook[10] which illustrated diagrammatically the proper charge density.
Indeed, as Einstein wrote, "The special theory of relativity ... was simply a systematic development of the electrodynamics of Clerk Maxwell and Lorentz".
[15] Nevertheless, the aspiration, reflected in references for this article, is for an analytic geometry of spacetime and charges providing a deductive route to forces and currents in practice.
Using exterior algebra to construct a 2-form F from electric and magnetic fields, and the implied dual 2-form ★F, the equations dF = 0 and d★F = J (current) express Maxwell's theory with a differential form approach.