**Authors:** H. J. Spencer

This research programme continues with its fundamental analysis of the electromagnetic interaction. In contrast to the continuous charge model of electricity that is today used as the foundation for presentations of classical electro-magnetism (CEM), this paper now analyzes the continuous interaction of pairs of charged point particles that better reflects the known basis of electricity – electrons. This analysis first demonstrates that all continuous theories of interaction between point particles that exhibit inertial resistance to changes in their motion are inconsistent with all asynchronous action-at-a-distance forms of interaction or equivalently, interactions limited to points on their ‘light-cone’. This research programme is an extension of the Newtonian scheme of classical mechanics that represents the locations of point particles, not by standard algebraic vectors but by a more powerful, non-commutative complex algebra, based on Hamilton’s quaternions, called here ‘Natural Vectors’. This NV representation is extended here from representing a single location (the ‘field point’) to representing the differences between pairs of point objects; this automatically advances the idea that even ‘classical’ electrons must be treated as ‘fermions’ (as this is an anti-symmetric algebraic representation). Adding the assumption of separability of the electromagnetic momentum to the previous single-time version now reproduces Planck’s 1907 infamous proposal (not Einstein’s) for defining relativistic forms of single particle momentum and energy but now in terms of EM electro-kinetic momentum between two particles, in contrast to Planck’s original but unphysical assumption of a constant, mechanical force on a single particle that required the Lorentz transformation. This paper also extends this new two-electron viewpoint to many-body situations involving myriads of pair-wise interactions by showing that classical electromagnetism is a consequence of the statistical effects of very many of these interactions arising from multiple, remote electrons moving within metallic conductors on one or many ‘target’ electrons. A new discrete, many-body approximation model (“Mesoscopic Electrodynamics”) is developed here that is shown to be a covering theory for the standard (continuum) model of CEM. The emphasis here is shifted back from empty space to the actual experiments involving electrical currents in metallic wires that were the real foundation for CEM’s integral and differential equations, which only summarized these effects mathematically but never provided any physical justification or insights. This theory now extends the rival, forgotten (‘continental’) approach to CEM to directly include radiation, as just a long-range induction effect, removing the only advantage previously associated with Maxwell’s field theory. It also links directly to Newtonian mechanics to provide a seamless unity to all of classical physics. These results now demonstrate that, contrary to the orthodox consensus, Maxwell’s Equations (as a field theory) are not a fundamental model for understanding the basic interaction between any types of elementary particles. This view challenges the last 150 years in theoretical physics that has been constructed only on the mathematics of continuous fields, leading to quantum field theories. This approach eliminates the force densities (electric and magnetic fields), the ‘instant’ Coulomb potential and the single-time (‘God-like’) view of nature that have dominated physics for 300 years, only because these ideas could use the simplified (but well-studied) mathematical representation of differential equations. *Surrey B.C. Canada (604) 542-2299spsi@shaw.ca © H. J. Spencer Version 2.180 29-04-2011 Version 1.0 21-10-2007 [123 pp;94Kw]

**Comments:** 121 Pages. This is the next paper in the EM series building on earlier Natural Vectors.

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