APPENDIX 8: MATHEMATICAL ADVANCES MADE BY ECE THEORY.

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_bÙq^b − ω^a_bÙT^b) = 0.                                 (8.1)

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

                ω^a_b = −½κ Î^a_bcq^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_bcT^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 . . .

Apparently the math progress described here belongs completely to NEW MATH [3].