Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field F with an Explanation of the TroutonNoble Experiment
Abstract
In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a selfcontained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinatebased geometric quantity comprising both components and a basis. The new observer independent expressions for the stressenergy vector T(n)(1vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1vectors), the angular momentum density M (bivector) and the Lorentz force K (1vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the TroutonNoble experiment.
 Publication:

Foundations of Physics Letters
 Pub Date:
 August 2005
 DOI:
 10.1007/s1070200575337
 arXiv:
 arXiv:physics/0412167
 Bibcode:
 2005FoPhL..18..401I
 Keywords:

 Physics  General Physics
 EPrint:
 32 pages, LaTex, this changed version will be published in Found. Phys. Lett