Four-Vectors in Electromagnetism
Keywords: Four-Vectors, Electromagnetism
A new mathematical structure intended to formalize the classical 3D and 4D vectors is briefly described. This structure is evidenced to be more appropriate, for its use in Physics and the sciences in general, than any of the other mathematical structures of geometric origin, such as the Hamilton (or Pauli or Dirac) quaternions, tensors, geometric algebra (GA) and space-time algebra (STA). The application of four-vectors in electromagnetism is demonstrated, where current concepts are reproduced, in some cases, corrected, in other cases, and new concepts are discovered, such as the following: It is suggested the need of an electromagnetic scalar, the Lienard and Wiechert potentials are suggested to be incorrect and also to have an incorrect origin, new equations for the handling of energy-momentum are proposed with which it is proved that mass and momentum have to satisfy the wave equation. Several other physical variables are also proved to satisfy the wave equation, which gives a strong argument to conclude that our universe is of electromagnetic constitution. Maxwell's equations are reduced to a simple four-vector equation. As a byproduct, new values and units for the dielectric permittivity and magnetic permeability of vacuum are proposed. Then the electric and magnetic units are expressed only in terms of mechanical units so there is no need for the former.