the other frame. In other words, the electric field in the other frame does not depend on the particular distribution of the source charges, only on the local value of the electric field in the first frame at that point. Thus, the electric field is a complete representation of the influence of the far-away charges. Alternatively, introductory treatments of magnetism introduce the Biot–Savart law, which describes the magnetic field associated with an electric current. An observer at rest with respect to a system of static, free charges will see no magnetic field. However, a moving observer looking at the same set of charges does perceive a current, and thus a magnetic field. That is, the magnetic field is simply the electric field, as seen in a moving coordinate system. Redundancy The title of this article is redundant since all mathematical theories of electromagnetism are relativistic. Indeed, as Einstein wrote, "The special theory of relativity ... was simply a systematic development of the electrodynamics of Clerk Maxwell and Lorentz". Combination of spatial and temporal variables in Maxwell's theory required admission of a four-manifold. Finite light speed and other constant motion lines were described with analytic geometry. Orthogonality of electric and magnetic vector fields in space was extended by hyperbolic orthogonality for the temporal factor. When Ludwik Silberstein published his textbook The Theory of Relativity (1914) he related the new geometry to electromagnetism. Faraday's law of induction was suggestive to Einstein when he wrote in 1905 about the "reciprocal electrodynamic action of a magnet and a conductor". 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. Such a royal route to electromagnetic understanding may be lacking, but a path has been opened with differential geometry: The tangent space at an event in spacetime is a four-dimensional vector space, operable by linear transformations. Symmetries observed by electricians find expression in linear algebra and differential geometry. 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. See also Covariant formulation of classical electromagnetism Special relativity Liénard–Wiechert potential Moving magnet and conductor problem Wheeler–Feynman absorber theory Paradox of a charge in a gravitational field Notes and references Electromagnetism Special