On Mon, 12 Mar 2007 02:48:40 EDT M.W. Evans once more felt it be necessary to give (repeat) a "proof" of his "Evans Lemma".

We quote the essential part of that "proof" starting with

o q^{a}_{λ} =
∂^{μ} (Γ^{ν}_{μλ} q^{a}_{ν}
− ω^{a}_{μb} q^{b}_{λ})
(8)

Now define

R = q^{λ}_{a} ∂^{μ}
(Γ^{ν}_{μλ} q^{a}_{ν}
− ω^{a}_{μb} q^{b}_{λ})
(9)

(Note that all indices here are *dummy* (or umbral) indices.)

and use

q^{a}_{λ} q^{λ}_{a} = 1
(10)

This is one of Evans' favorite errors: The left hand expression is the trace of the 4×4 unit matrix and thus has the value 4.

However, regardless if 1 or 4, what follows now is another
*wrong* step that Evans applies in hopeless situations: He wants to resolve Eq.(9) for
the expressions

Q^{a}_{λ} := ∂^{μ}
(Γ^{ν}_{μλ} q^{a}_{ν}
− ω^{a}_{μb} q^{b}_{λ})

which appear on the right hand side of Eq.(8).
So he multiplies Eq.(9) by q^{a}_{λ} hoping that so the factor
q^{λ}_{a} in Eq.(9)
would be compensated and removed due to Eq.(10).

Therefore Evans' conclusion is a fallacy.

And there is no hope to correct that error: Eq.(9) is *one* linear equation for 16 unknowns
which - as is well-known - cannot uniquely be resolved for the 16 unknowns
Q^{a}_{λ}.

(i) The Eqs. (46-47) are invalid for using a non-existing 3-index Î-tensor in 4D, see

http://www2.mathematik.tu-darmstadt.de/~bruhn/Evans3indEtensor.html

(ii) Equ.(74) falsely attributed to Bruhn can originally be found in Evans GCUFT book vol.1 as Eq.(1.59): In the first part of this book (Chap.2 - 7) Evans uses the version (1.59).

(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**