New Transformation Equations and the Electric Field Four-vector

Abstract

Lorentz introduced a set of coordinate transformation equations that revolutionized our perception of space and time. These equations assured that Maxwell's equations of the electromagnetic field have covariant form under transformation between inertial reference frames. It has become apparent that a set of transformation equations exist which replace the Lorentz equations while still satisfying the requirement that the spacetime interval remains invariant under transformation. However, in order that Maxwell's equations remain covariant under this transformation, new terms must be added to the existing equations. In addition, the magnitude of the charge is no longer invariant, but charge density is. The electric field is described by a four-vector and the antisymmetric electromagnetic field tensor is replaced by the electric field tensor.

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