A remark on Evans' recent web article on the ECE Lemma

Gerhard W. Bruhn, Darmstadt University of Technology

There is some little progress but a fatal error left in


and its attachment


For the first time the former "Cartan Convention" is displayed correctly:

                                qλa qaλ = 4                                 (12)

But any remark about the wrong former version qλa qaλ = 1 (e.g. in the GCUFT book vol.1) is missing, and no word about the designation "Cartan Convention", it's a "normalisation" now.

However, already "Definition" (11)

                                R qλa = ∂μνμλqνa − ωaμbqλb)                                 (11)

is inadmissible : Equ. (11) is to be satisfied for all pairs of indices a,λ = 0,1,2,3. Therefore Equ. (11) represents 4×4 = 16 (sixteen) definitions of R, and nobody tells us

why these different definitions of R should agree.

Thus, the conclusion

. . . and multiply both sides of eq. (11) by qaλ to obtain

                                R = ¼ qaλμνμλqνa − ωaμbqλb)                                 (13)

is inadmissible. This value of R cannot fulfil the 16 equations (11) in general. Myron should check that by plugging the expression (13) into the definitions (11) (by hand *) or by computer algebra). He should tell us the result.

There is no ECE Lemma.

Part 2 of Evans' paper is based on the existence of the (non-existing) value of R and is obsolete therefore.

*) Applying his New Math (handling of Eqs. (22 - 23)) Evans would probably execute the following "self check" by hand:

Plugging R (eq.(13)) into eq.(11) yields

                                R qλa = [¼ qaλμνμλqνa − ωaμbqλb)] qλa

                                          = [¼ qaλqλa]μνμλqνa − ωaμbqλb)

                                          = [¼ 4] ∂μνμλqνa − ωaμbqλb)

                                          = μνμλqνa − ωaμbqλb)

and so he feels fully justified.

Really! So he did!!! In the handwritten document http://www.atomicprecision.com/blog/wp-filez/acheckpriortocoding5.pdf we read

. . .


                o qαa = ∂μνμλqνa − ωaμbqλb)                                                       (8)

Now define

                R = qaλμνμλqνa − ωaμbqλb)                                                       (9)

and use the famous EC (= Evans Convention)

                qλaqaλ = 1 (!!!)                                                                                 (10)

to find by using the eqs. (8-10)

                o qλa =(8) 1 · ∂μνμλqνa − ωaμbqλb)
                                =(10) [qλaqaλ] · ∂μνμλqνa − ωaμbqλb)
                                =(?) qλa · [qaλμνμλqνa − ωaμbqλb)]
R qλa                                                         (11)

Remarkably, really! I don't know more than two Doctores who are able to do New Math in such a perfect way.


(25.06.2007) The consequences of the invalidity of the Evans Lemma

(19.06.2007) A Lecture on New Math given by Dr Horst Eckardt and Dr Myron W. Evans

(27.05.2007) Commentary on Evans' recent remark on the ECE Lemma

(09.04.2007) Review of the Evans Lemma

(12.03.2007) Evans "proves" the Evans Lemma again