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In this paper we present an axiomatic, geometric, formulation ofelectromagnetism with only one axiom: the field equation for the Faradaybivector field F. This formulation with F field is a self-contained, completeand consistent formulation that dispenses with either electric and magneticfields or the electromagnetic potentials. All physical quantities are definedwithout reference frames, the absolute quantities, i.e., they are geometricfour dimensional (4D) quantities or, when some basis is introduced, everyquantity is represented as a 4D coordinate-based geometric quantity comprisingboth components and a basis. The new observer independent expressions for thestress-energy vector T(n)(1-vector), the energy density U (scalar), thePoynting vector S and the momentum density g (1-vectors), the angular momentumdensity M (bivector) and the Lorentz force K (1-vector) are directly derivedfrom the field equation for F. The local conservation laws are also directlyderived from that field equation. The 1-vector Lagrangian with the F field as a4D absolute quantity is presented; the interaction term is written in terms ofF and not, as usual, in terms of A. It is shown that this geometric formulationis in a full agreement with the Trouton-Noble experiment.Comment: 32 pages, LaTex, this changed version will be published in Found.  Phys. Let

foundations of physics letters

Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field F with an Explanation of the Trouton-Noble Experiment