Unifying the Galilei and the Lorentz Electromagnetism: The magnetic model

We examine two models for electromagnetism, the usual Lorentz invariant electromagnetism and the Galilei invariant version represented by the magnetic model proposed in [1]. For every inertial frame we define two coordinate systems: the Galilei and the Lorentz systems, that accommodate both models. We show that the Lorentz transformation for the fields and the 4-current are induced from the corresponding Galilei transformation, which does not arise as the low velocity limit of the Lorentz transformation. In addition we show the Maxwell equations for the electromagnetic fields and the 4-current induce a family of Galilei invariant equations depending on a parameter β such that in the limit β → 0 they become the Maxwell equations.