An equivalence principle for electromagnetics through Clifford's geometric algebras

As already pointed out by several authors, a given electromagnetic medium creates an effective geometry and a given geometry creates an effective medium—what we call the equivalence principle for electromagnetics. This bears some resemblance to the kinematic aspects of the interaction between masses and the spacetime metric of general relativity. In this article, using Clifford's geometric algebras defined over the tangent and cotangent bundles of spacetime, we generalize the topological interpretation of this equivalence principle: introducing a transformation that we call the vacuum form reduction, we are led to a fictitious spacetime corresponding to a special class of bianisotropic media (in the materials interpretation) and which reduces to spacetime vacuum as a particular case (in the topological interpretation). We illustrate our theoretical approach with two examples: transformation and moving media.