M.W. Evans' Annalen submittal Paper#89

July 20, 2008

_{(Quotations from Evans' original text in }black,
comments in **blue**)

Hehl has entirely failed to understand the basis and by now well known and accepted mathematical advances made in ECE theory {1-12}. . . .

When the tetrad describes spin motion of spactime (Appendix 5) unaffected by curving of spacetime the homogeneous current of ECE theory vanishes:

j^{a} = ^{A(o)}/_{μo}
(R^{a}_{b}Ùq^{b} −
ω^{a}_{b}ÙT^{b}) = 0.
(8.1)

It has been shown in Appendix J of ref.(1) that this condition implies:

ω^{a}_{b} =
−½κ Î^{a}_{bc}q^{c} .
(8.2)

The spin connection becomes dual to the tetrad through a wave number. Furthermore, the Riemann form becomes dual to the torsion form through the same wave-number:

R^{a}_{b} =
−½κ Î^{a}_{bc}T^{c} .
(8.3)

This is a fundamental mathematical advance of ECE theory. The ECE duality equations define a hitherto unknown rotational part of the Riemann form . . .

In *conventional*
mathematics
the tensor Î^{a}_{bc} used in eqs.(8.2-3) does not
exist in *four*-dimensional tensor calculus [2].

[1] M.W. Evans, *Appendix 8: Mathematical advances made by ECE theory*,

Part of the web-paper #89 p.43 ff.

http://www.aias.us/documents/uft/a89thpaper.pdf

[2] G.W. Bruhn, *Evans' ''3-index, totally antisymmetric unit tensor''*,

http://www.mathematik.tu-darmstadt.de/~bruhn/Evans3indEtensor.html

[3] G.W. Bruhn, *M.W. Evans' New Math in Full Action*,

http://www.mathematik.tu-darmstadt.de/~bruhn/EvansEvolution.html