Last supplement on Sep 27, 2006
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
http://preposterousuniverse.com/spacetimeandgeometry/errata.html
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:
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.
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:
- "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
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.
An example of Evans' reaction on being drawn to errors of his: On April
07, 2006 Myron wrote to me:
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.
http://www2.mathematik.tu-darmstadt.de/~bruhn/MWEsErrors.html
are not at all complete, only hints. There remains a lot of work to
do - for Myron.
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.
"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."
The above list and also my comments
http://www2.mathematik.tu-darmstadt.de/~bruhn/MWEsFurtherErrors.html
http://www2.mathematik.tu-darmstadt.de/~bruhn/ECE-CentralError.html
http://www2.mathematik.tu-darmstadt.de/~bruhn/EvansRebuttal.html
http://www2.mathematik.tu-darmstadt.de/~bruhn/EvansRebuttal230806.html
The above GCUFT Errata List will be supplemented occasionally.
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