Please, send your email contributions to

bruhn@mathematik.tu-darmstadt.de

Polemics are not welcome.

**To last contribution:**
**click here**

**Alexandre Szames**

*I have forwarded yesterday your posting and it seems to me that Myron's message below
should be interpreted as a reply. I am just a science writer but I have my limits and this
has become a little too complicated for me to follow - thus I appreciate counterpoints and
debates.*

** Gerhard W. Bruhn** replied:

at first many thanks for your support.

It's a pitty that MWE refuses to discuss with me directly.
I shall wait a week whether MWE sends further mails and then reply
to all together. MWE's mail below gives no new point of view.

. . . With (*) MWE claims an equation with two different types of quantities on
both sides, i.e. a type mismatch, as if he would claim
apple = pear,
or if one would claim scalar = vector.

What Evans replies in his mail is not helpful. The only help would be
if he could explain why an apple is a pear or reversely.
But nobody is able to do that: The definitions of the two
(mathematical) fruits are different.

Now, Evans is a scholarly man who claims the Nobel prize for his
scientific work on his website. So he should help himself if possible.
Even if I could help him (but as explained above nobody can change
apples to pears) he would reject me with a lot of further polemics.
So there is no remedy for MWE, since, of course, only a real
magician could help him.

**Lar Volker** wrote on Saturday 13 November 2004 16:25:

*
Hello,
Fine. One dispute. Go back to it later.
This man has done a tremendous amount of work that is consistent. He
is sick with a post traumatic stress disorder and needs help, not
strife at the present.
The fact remains that both Einstein and Cartan knew that the metric
needed torsion to allow for electromagnetism. Evans has found several
methods to add it. Help him, do not attack. Eventually you will find
common ground.
Write a supporting analysis article. Regardless of one detail that
can be cleared up, there are 20 places where agreement can be found.
Dig into it and show the antisymmetric metric exists. Ride coattails.
*

**Gerhard W. Bruhn** replied:

I do not know your educational background, so let it me say it at first very
simply:

Evans' theory lacks from a very essential point where it is
i n c o n s i s t e n t
, comparable with a three-legged chair
one legg of which is rotten: That chair looks like a chair,
but you cannot use it as a chair.

That rotten leg is the statement that

*
"if there exists a symmetric metric, then there must exist an
antisymmetric metric"*

exemplified on the top of p.23 of

http://www.aias.us/book01/chap2-cr3.pdf

by the special **R**^{3} case where he claims the validity of the equation

(*)
− [dx_{1}^{2} + dx_{2}^{2} + dx_{1}^{2}]
= ds^{2} = dx_{1}^dx_{2} + dx_{2}^dx_{3} + dx_{3}^dx_{1}

which is wrong due to type mismatch.

The only help that I can give MWE is to let him know that (*)
is erroneous. As you know his replies contain a lot of polemics.

What he should do is remove that equation and the statement about
the existence of the «antisymmetric metric», which is wrong already
in the well-known simple **R**^{3} case.

What else? That is Evans' problem, not mine! I do not know how to
close the gap. My opinion: It's impossible.

But again: Evans refuses to accept that truth.

So tell me what could I do else? Shall I accept an erroneous equation
(*) since Evans is sick???

And, I have already checked another article of his as you can see on
my website,

http://www2.mathematik.tu-darmstadt.de/~bruhn/PHYSICAL_OPTICS1.htm

that contains essential calculation errors. I have corrected
the wrong calculations, but then I get contradictions to his main
statements in that article. Hence the statements are erroneous.

Shall I cover that tacitly, or what? Probably the situation is the same
in the other 20 or more articles.

What counts is not quantity but quality!

**Dave Feustel** wrote
on Sunday 14 November 2004 04:49 am:

refering to:

«What else? That is Evans' problem, not mine! I do not know how to
close the gap. My opinion: It's impossible.»

*
Derive some impossible results or results not produced
or even contradicted by lab experiments with non-linear optics.
Dave Feustel
1-260-422-5330*

**Gerhard W. Bruhn** replied:

MWE uses mathematics as an essential tool to derive his "theory".
You will admit that without mathematics no GUFT would exist.
Therefore the validity of GUFT cannot be reduced to its experimental
evidence:

**A necessary condition for its valitity is its formal
mathematical correctness.**

So it's sufficient to point out examples of essential abuse of
mathematics in MWE's book-preprint. Evans is kindly requested to remove these monita (if
he can).

You have some knowledge of math (though - as I guess - you have no sufficient
knowledge about differential forms), therefore I can give you an example
closer to Evans' claim (*), which is of mathematical type, or what
do you think?

The type mismatch in (*) is closely related to an equation that claims

scalar = vector (in **R**^{3})

ω_{1} is a differential scalar while ω_{2} is of vector type.
ω_{1} = ds^{2} is the squared line element of a curve
(in Euclidean **R**^{3}),
hence a number (=scalar).
The differential 2-form appears as the **vectorial** surface element of a surface in **R**^{3}
normal to the direction (1,1,1) and hence is of vector type.

For that you should have a look at chap.5 (Vector Integration) of the
book "Vector Analysis" in Schaum's Outlines Series. Surface integrals
are treated with examples in the subsection SURFACE INTEGRALS.
The surface element is there denoted by dS (with CAPITAL S) not to be
mixed up with the line element ds that appears already at the end of
chap. 3. (I recommend to read chap.8 (Tensor Analysis) also, which will help a lot to
keep you away from mathematical errors.)

You can see the problem with MWE's equation (*) also from Carroll's book

http://arxiv.org/pdf/gr-qc/9712019

ω_{2} is another writing of the skew symmetric matrix

0 1 −1

−1 0 1

1 −1 0

which is the (0,2)-tensor ε_{ik} in **R**^{3} that belongs to the "space"
Λ^{2} (Carroll p.21) while the line element (Carroll p.25) does not.

Concerning other errors of MWE's:

Did you ever read my criticisms on Evans' phaselaw paper in

http://www2.mathematik.tu-darmstadt.de/~bruhn/PHYSICAL_OPTICS1.htm
?

I doubt that. Otherwise you would have observed that the necessary condition of correct
calculations is
essentially violated also in that article on the level of elementary integration
calculus. Hence that article should have been withdrawn by Evans.

That's a realistic description of the present state of Evans' GUFT.

**MWE** to Lar Felker on Sun, 14 Nov 2004 19:30 +0100:

1) g

2)

Is this guy thick or just trying to be funny?

MWE

**Gerhard W. Bruhn** replied:

I guess MWE has problems with reading or understanding texts accurately.
I neither denied

1) g^{μν} g_{μν} = 4 (for the 4-dim. case)
nor
2) **e**^{(1)} × **e**^{(2)} = i **e**^{(3)}*
(or where???).

My argument is simply:

**ω _{2} is a differential 2-form that cannot be equal to the scalar square
of the line element ds, i.e. to ω_{1} = ds^{2}**.

The equation (*) written in the terminology of Schaum's Outlines Series (Vector Analysis)means

ds

which is evidently erroneous!

However, we have some progress: We have limited the disagreement to

MWE claims

(*) − [dx

to be true while I have argued that (*) in invalid due to type mismatch (see my remarks to Dave Feustel above).

g

hence by equating the indices of δ

MWE's equation 2) holds for a cyclic complex basis in 3-dimensional space, since the cross-product yielding vectors again cannot be extended to higher dimensions.

**MWE** to Franklin and Dave on Tuesday 16 Nov 2004 14:31:

*These notes are for a second appendix to the book and for posting on
www.aias.us. They prove straightforwardly that the existence of the well known tetrad
(vierbein) implies the existence of the symmetric and antisymetric metrics and the general
tensor metric. This is the eighth Bruhn rebuttal. (I have rebutted him five times, David
Hamilton once and, indirectly, Corneliu Ciubotariu once). In this case Bruhn made another
very trivial error which is corrected in my eqns. (17) and (18) of the attached.
In my opinion Bruhn is deliberately misrepresenting my work to this
group and to the world, because his errors are so trivial that no genuine professor of
mathematics would ever make them. This is why I feel that the appropriate disciplinary
action should be taken against Bruhn by his Chair and Dean. In other words these are not
genuine errors, but deliberate harassment. In my experience many appointments to academia
are made internally on a who you know basis, so are uncompetitive. The genuine scientists
are often left out in the cold, so must make their own wisdom.
"........................................ for now I see
Peace to corrupt no less than war to waste."
John Milton, "Paradise Lost", 1667.*

*
Attachment: antisymmetricmetric.pdf (handwritten, title THE ANTISSYMMETRIC METRIC)
*

**Gerhard W. Bruhn** replied:

The attachment antisymmetricmetric.pdf deals with the 4-dimensional spacetime.
Therefore MWE has left now the **R**^{3}-problem (*)
of p.23 of his preprint

http://www.aias.us/book01/chap2-cr3.pdf

without having given any satisfying reply.

**Thus, the objection against (*) is not refuted.**

**MWE** to all on Wednesday 17 Nov 2004 12:21:

*
Alejandro Buchmann,
Dean,
Informatics,
Technical Univeristy of Darmstadt,
Dear Dean Buchmann,
I wish to register a strong formal complaint against Dr. G. Bruhn and
request appropriate disciplinary action to be taken against him.
1) Dr Bruhn has made several trivially erroneous attacks against my work and in my opinion
this is defamatory. The repeated attacks amount to first degree harassment. This conduct
brings your University into disrepute becasue first degeree (or aggravated) harassment is a
felony. Any member of staff of a reputable university that commits a felony is normally
dismissed for misconduct.
2) Dr Bruhn has comandeered the e mail listing of the Alpha Foundation for Advanced Study
(AIAS), of which I am Director, and has spread this defamation to my colleagues. This has
annoyed and disturbed several of them.
3) Dr Bruhn has posted this defamation on websites and has approached scientific editors
in efforts to defame me. He has also approached one colleague at CERN, Dr Caspers, with the
same intent.
The work of AIAS has attracted one and a half million hits this year and
is rigorously correct, being based on differential geometry. Others and myself have
corrected Bruhn on several occasions, but his harassment and defamation continues. His
conduct reveals that he is technically not able to assess scientific work. We at AIAS find
his repeated defamation offensive and unscientific.
Appropriate disciplinary action would be dismissal, loss of salary,
benefits and pension.
Cordially Yours,
Myron W. Evans,
AIAS Director.
*

**Gerhard W. Bruhn** replied:

A remarkable contribution of MWE to scientific discussion, really!

After that intermezzo back to science:

You'll find the **GAP** in
http://www.aias.us/book01/chap2-cr3.pdf

on p.22 between the eqns. (2.7) and (2.8). The statement

«
*Because ε _{k} is dual to ε^{ij} by geometry,
then q^{kr(S)}ε_{r}
must be dual to q^{ij(A)}.*

Of course, the 2-form − ½ q

MWE is kindly asked to close the gap by a convincing calculation - if possible.

The **4-dimensional case** is treated by MWE with the eqns. (2.16) and (2.17).
While (2.16) is correct equ. (2.17) shows the analogous type mismatch: Writing out (2.17)
by using the matrices (2.14) and (2.15) we obtain as Evans' claim here

(**)
dx_{0}^{2} −
dx_{1}^{2} −
dx_{2}^{2} −
dx_{3}^{2}
= ^{1}/_{3}
[dx_{0}^dx_{1} + dx_{0}^dx_{2} + dx_{0}^dx_{3}
+ dx_{1}^dx_{2}
+ dx_{2}^dx_{3}
+ dx_{3}^dx_{1}] .

No matter how, this **type mismatch** cannot be removed by
aposteriori explanations as in MWE's article antisymmetricmetric.pdf .