Last supplement on Sep 27, 2006

A GCUFT Errata List and Other Service to the Readers

Gerhard W. Bruhn

In the past the author Myron W. Evans felt it being unnecessary to inform his readers about known bugs in his book.

Now under pressure by 'president' Widlar in his own AIAS Forum some changes seem to appear.

A good example of service to readers: Sean M. Carroll

A bad example: Myron W. Evans on his Blog:

"Yes a list of typo’s is a good idea, in fact I can only find three or four. The troll is a silly ———-."

but one day later (Fri, 22 Sep 2006) on demand:

1) Eq. (1.6), replace q by g.

2) Appendix A of chapter 1 of volume 1: Minus signs before each of the four entries of the second and fourth columns of eq. (A.4).

3) Eq. (21.20), minus sign before me, left hand side.

4) Eqs. (21.22) to (21.25), remove all occurrences of / on the left hand sides.

MWE in his Forum generously: "Don't feel that any question is too simple. ECE must be tested with Baconian principles"

However, he answers justified questions by useless hints how to read his book. One would expect: from the beginning. Not so in case of Myron's GCUFT:

"I would advise beginning volume one with appendix C, then go on to Appendix B. Appendix C defines the complex circular absis and Appendix B gives much more detail than available in most textbooks on how to reduce the tensorial representation of MH to the vectorial representation. For more advanced students proceed to the four appendices of chapter 17, where the Riemannian equivalents of the Cartan structure equations and Bianchi identities are derived through the tetrad postulate. In Appendix J, some basic mathematical proofs are collected for convenience (e.g. tetrad postulate and Lemma). The following people are now known to be biased and hostile, so are banned as referees of ECE theory: A. Lakhtakia, G. Bruhn, W. Rodrigues, and B. Flower. Any e mailing carried out by these is just personal bile. They have no credibility as scholars."

I think such advices cannot be taken seriously.

To the List of ERRATA as Myron's real service to his readers:

Typos are of minor interest only since having no further consequences. I know a lot of wrong equation labels, much more than four.

The errors in eqs. (A.4) are more serious, since most of the layman readers will not recognize the errors and hence are mislead.

Here some further serious math errors in GCUFT:

- The right hand sides of eqs. (2.8) and (2.9) cannot both equate ds˛.
- Wrong metric definition: The matrix (2.40) is not invertible since having a vanishing determinant.
    The same holds for the 4×4 matrix (2.42). A metric matrix must be invertible.
- (2.47): ω1 is no zero-form, but a symmetric two-form: *ω1 in eq. (2.47) is not defined.
- The = in the second line of (2.145) is wrong, as can be seen by writing out the suppressed indices and η, cf. (2.73).
- Wrong summation indices: Multiplication of (2.175) by qν is inadmissible: n is summation index in (2.175).
- After (2.177):
"When μ = ν, these equations become ... " is wrong: μ and ν cannot be equated here since
    ν is a summation index in (2.177).
- Wrong Hodge dual in 4-D after (3.15):
"In differential geometry the element duσ is dual to the wedge product duμÙduν." (Wrong in 4-D)
- Wrong equ. (3.15): Hodge dual only defined for antisymmetric forms. However, ω1 is not antisymmetric.
- Wrong metric definition: The matrix (3.16) is not invertible since having a vanishing determinant.
- Eq. (3.29) contains type mismatch: The left hand quantity Gμν is the electromagnetic stress tensor of type (2,0) independent of the tetrad position while the right hand side additionally has two lower tetrad indices that are merely suppressed by Evans. Thus, both sides of eq. (3.29) have different transformation behavior under changes of the tetrad field.
- Eq. (9.9) is questionable:

qcμν = qaμÙqbν.

See also (D.6): Evans assumes that the tetrad index c is somehow defined by the tetrad indices a,b, but never tells which c = c(a,b) to be used. I guess that's a relict from 3-D Euclidean space, where c could be defined by means of Hodge duality. In 4-D we have six 2-forms qaÙqb: q0Ùq1, q0Ùq2, q0Ùq3, q1Ùq2, q1Ùq3, q2Ùq1 where qa denotes the 1-form qaμ dxμ. However, we have only four 2-forms qc (A) := qc (A)μν dxμÙdxν (c = 0, 1, 2, 3). Hence eq. (D.6) cannot be true.

- "Evans Convention" in (14.20), (15.80), (B.4) and (B.25):  ... = 1 is wrong,  ... = 4 would be correct.
- Eq. (14.21) contains a lot of index errors. It should read
(Br1)                                                 R = gμν Rμν = qaμ qbν ηab Rμc qνd ηcd ,
Evans' hint:
"Multiply either side of Eq. (14.21) by qaμ" is not feasible since both a and μ are summation indices, and the multiplication would yield an invalid equation. But some simplifications of eq. (14.21) after correction, i.e. of eq. (Br1), are possible: Using qbνqνd = δbd we obtain

qbνηabqνdηcd = δbdηabηcd = ηabηcb = δca

and thus

(Br2)                                                                 R = qcμ Rμc .

As one can see from eq. (14.22) Evans aim is to resolve this equation for Rμc. However, since eq. (Br2) is one linear equation for 4×4 = 16 quantities Rμc it cannot be uniquely resolved for Rμc. Thus:

Eq. (14.22) cannot be deduced from eq. (14.21). The same holds for eq. (14.23) as well.

- The decomposition

qaμ = qaμ(S) + qaμ(A)                                                                 (14.63)

as the sum of symmetric and antisymmetric component square matrices is physically meaningless because it does not transform covariantly. The same holds for the other decompositions of Chap. 14.3 which are physically meaningless as well. The symmetric part qaμ(S) appears e.g. on p. 457.

If Evans doesn't know about these errors then he should check his book accurately and stop insulting his critics.
Better he detects his errors in good time and corrects them (if possible) than his critics.
A math oriented theory like GCUFT is very sensible against bugs. Bugs should be removed as fast as possible.
Otherwise the theory becomes unreliable and useless.

An example of Evans' reaction on being drawn to errors of his: On April 07, 2006 Myron wrote to me:
"Well Gerhard you always say that any calculation is wrong. So if you say Schneeberger is wrong you are simply behaving in the same old way. This is very boring. You have no credibility and so I request you not to send me any further absurd e mail, or any e mail. ... If you go on like this you will certainly get a haircut in the Tower. ...
Following several lines of insults and concluding with
... So why don't you do something useful and resign? British Civil List scientist."

To summarize: I've done a lot to show that Evans' GCUFT deserves a complete and careful revision. It is Myron's job to show that his theory is not FUBAR by removing all known errors and thinking precisely about the consequences of necessary changes.
The above list and also my comments

are not at all complete, only hints. There remains a lot of work to do - for Myron.

The above GCUFT Errata List will be supplemented occasionally.