**Subject:** Paper 93 Appendix 4 : Meaning of the a index

**Date:** Thu, 30 Aug 2007 05:15:40 EDT

Attachment: a93rdpaperappendix4.pdf

This appendix develops the meaning of the a index, one of the mathematical advances of ECE is the realization that the electromagnetic field is a vector valued two-form, not a scalar valued two-form as in Maxwell Heaviside field theory. This advance is necessary before Maxwell Heaviside field theory can be unified with the theory of gravitation and the whole theory made generally covariant as needed by general relativity. The a index has a simple and clear meaning, it represents the superimposition of a coordinate system on another, for example the complex circular on the cartesian, thus describing a plane wave. See also Donald Reed in ACP, vol. 119(3) (2001) or Brian Silver, “Irreducible Tensorial Methods” (Academic, 1976). The complete field in this case superimposes ((1), (2), (3)) on (X, Y, Z). One can also impose a coordinate system on itself, in spherical polar this is (1, 2, 3) on (1, 2, 3).

Readers are no doubt aware of the attempts by F. W. Hehl to deliberately confuse and obscure this simple deduction.

Now I am ready for the final Appendix 5, which works out the non-vanishing Christoffel symbols, Riemann elements, etc of the general spherically symmetric metric in four dimensions, giving full details not easily available in the literature. These are needed for the precise Coulomb law (see previous notes for paper 93).

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