Commentary on a section of
M.W. Evans' Annalen submittal Paper#89


Gerhard W. Bruhn, Darmstadt University of Technology

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:

                ja = A(o)/μo (RabÙqb − ωabÙTb) = 0.                                 (8.1)

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

                ωab = −½κ Îabcqc .                                 (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:

                Rab = −½κ ÎabcTc .                                 (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].

In conventional mathematics the tensor Îabc 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.

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

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