**Authors:** H. J. Spencer

A new algebraic representation is used to immediately recover all the major results of classical electromagnetism. This new representation (‘Natural Vectors’) is based on Hamilton’s quaternions and completes the original attempt by Maxwell to use this powerful, non-commutative algebra in the final presentation of his theory in his Treatise. The foundational hypothesis here is that the principal electromagnetic variables are best represented by Natural Vectors, rather than the conventional 3D vectors defined by ‘real numbers’. The present results avoid all use of the field concept and validate the retarded scalar and vector potentials approach first introduced by L. V. Lorenz, who combined Gauss’s 1845 suggestion of the finite speed of interaction with Newton’s action-at-a-distance model of physics into a charge-potential model of electromagnetism in 1867. This new approach demonstrates the primacy and physical significance of the ‘Lorenz gauge’. Not withstanding Maxwell’s aether theory, the present results are based on the artificial continuous charge-density substance model of electricity that is used today to develop and teach Maxwell’s Equations for classical electromagnetism. The present analysis also demonstrates that Helmholtz’s ‘fluid’ model of electricity is one of the few that can result in an electromagnetic ‘explanation’ for the phenomenon of light. Unlike algebraic Minkowski 4-vectors, the more powerful 4-dimensional covariant 'Natural Vectors' used here generate all the differential equations normally found in classical electro-magnetism in an immediate and direct algebraic manner. This new theory focuses on the remote interaction between charges, which then appears both as variations in the charge-density and the potentials “traveling at light-speed across space”. Surprisingly, this same result also appears for the current-density; this suggests that the conventional interpretation of this major symbol in Maxwell’s Equations needs to be questioned further. * SPSI, Surrey, B.C. Canada (604) 542-2299 spsi99@telus.cnet © H. J. Spencer Version 2.3 25-07-2012 Version 1.0 16-06-2007

**Comments:** 74 Pages. Unlike algebraic Minkowski 4-vectors, the more powerful 4-dimensional covariant 'Natural Vectors' used here generate all the differential equations normally found in classical E/M in an immediate and direct algebraic manner.

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