I have taken the advice of colleagues and will trash any incoming
garbage from Bruhn and Jadczyk, but after making a rebuttal of each point.
Here Jadczyk attempts to assert that the Riemann form cannot be defined. He
apparently attempts to assert that a tensor valued two-form is not covariant.
This is deceptive nonsense put across in mathematical language that is
designed specifically to be obscure, in order to give the impression of being
correct. The Riemann form is defined by:

R = D Λ ω

as in Carroll, chapter three. Here ω has two indices *a* and *b*
and one index μ.
It is not a tensor but the quantity D Λ ω
is a tensor valued two form as is very well known. It is the Riemann or
curvature form. Mysteriously we find that Carroll is never criticised,
although he uses the exact same standard differential geometry as I do. No
one else ever critcises differential geometry. It mysteriously began to be
criticised only when I started using it. This alone is enough to show that
trash is trash. I conclude that Jadzcyk is a pseudo-scientific non-entity, a
conclusion which apparently has also been arrived at by John Baez, who has
removed all reference to "Ark" as Jadzyk calls himself.
Additionally we have also shown at AIAS that the Alcubierre warp drive metric
does not obey the Ricci cyclic equation

R Λ q = 0

and so talk of time travel is complete nonsense. Similarly, talk of Kerr and charged Kerr black holes is garbage, because these metrics do not obey the Ricci cyclic relation. Stephen Crothers has trashed other ideas in the black hole fantasy world. Talk of gauge invariance is irrlevant, it has been replaced in ECE by the invariance of the tetrad postulate under the general coordinate transform.

Anyone who immediately resorts to wild abuse and theft of e-mail listings, as Jadczyk does, is hiding an inability to treat his fellow scientists with respect. Looking at his work, no wonder. This is intellectual cowardice and dishonesty, an unwillingness to recognize merit in others, to whom he attributes his own opiate dreams.

Evans intentionally misunderstands what was said: The point is that the eq.

D Λ ω^{a}_{b} = d Λ ω^{a}_{b}
+ ω^{a}_{c} Λ ω^{c}_{b}

cannot be taken as a pattern for the exterior covariant derivation of a (1,1) valued
2-form X^{a}_{b}. The general rule for the exterior covariant
derivative of a covariant (1,1) valued 2-form X^{a}_{b}
is

D Λ X^{a}_{b} =
d Λ X^{a}_{b}
+ ω^{a}_{c} Λ X^{c}_{b}
+ X^{a}_{c} Λ ω^{c}_{b}

An example is X^{a}_{b} = R^{a}_{b}. The reason
for the exception for ω^{a}_{b} is its non-covariance.

More: A. Jadczyk proved by counter example that the expression
d Λ X^{a}_{b}
+ ω^{a}_{c} Λ X^{c}_{b}
is NOT COVARIANT in general.

Bruhn has posted two further abusive messages on 30th Sept. where he resorts openly to gutter abuse once again. I simply repeat the fact that a unit vector in 4-D is

e^{μ} = (1, 1, 1, 1)

The term (1, 1, 1, 1) is no vector, only a quadruple of numbers, since the corresponding basis vectors are missing. And if Evans should have thought of the vector

e^{μ}∂_{μ} =
1 ∂_{o} +
1 ∂_{1} +
1 ∂_{2} +
1 ∂_{3}

then the question arises why that should be a unit vector.

Thus the complete unit vector field:

e^{μ}e_{μ} = 1 −1 −1
−1 = −2

which is a Lorentz invariant scalar, QED.

That's not QED but NONSENSE: The quantity e^{μ}e_{μ}
(where e_{o}=1, e_{1}=−1, e_{2}=−1,
e_{3}=−1
due to
Evans' original "rebuttal") , is no **vector**.
Evans has confused the quantities e_{μ} with the basis vectors
∂_{μ} (in usual notation
∂_{1}=**i**,
∂_{2}=**j**,
∂_{3}=**k**.
∂_{o}=**h**)

In vector notation one may write a unit complete vector field

**
V** = 1 **k**

where *1* is a scalar and **k** is a unit vector.
The complete vector field is invariant, *1* is invariant, **k**
is invariant under ANY transformation.

No! Again nonsense! A vector is defined by

V = V^{μ} ∂_{μ}

where V^{μ} and ∂_{μ} transform contragrediently
according to their index positions:

∂_{μ'} =
^{∂xμ}/_{∂xμ'} ∂^{μ},
V^{μ} =
V^{μ'} ^{∂xμ}/_{∂xμ'}

see Carroll p.43, eqs. (2.11-12).
Hence, if the eq. **V** = 1 **k** holds in one frame, i.e.
V^{o} = 0,
V^{1} = 0,
V^{2} = 0,
V^{3} = 1,
then the V^{μ} transform by
V^{μ} = V^{μ'} ^{∂xμ}/_{∂xμ'}
and are by no means invariant. The same holds for the basis vector **k** = ∂_{3}
which due to [Carroll (2.11) transforms to
^{∂xμ'}/_{∂x3} ∂_{μ'},
which differs from **k**' = ∂_{3'} in general.

We now see that Bruhn has accepted that the B Cyclic theorem is the frame of reference itself. This is done quietly so that no one notices.

**Nonsense !!! Where?**

A scalar *R* such as that used by Einstein is uniquely defined
by summation over repeated indices. QED.

QED? *What* has been proven here?

For example:

R = g^{μν} R_{μν}

is the usual scalar curvature. According to Bruhn this would have sixteen different values.

In fact it has only one value because it is the double sum over μ and ν. Similarly the ECE R is a sum over repeated contravariant covariant indices and has only one value.

That's not the point.
The point is, that in case of the ECE Lemma there are 16 (sixteen) simultaneous equations that determine the
*one* scalar R: **R is 16-fold overdetermined.** The sixteen different equations
for the scalar R are displayed
here
.

Gerhard Bruhn is a scientific fraud.

Thank you. Because of showing *your numerous shortcomings*, Myron?

**Correction of
Bruhn 16.08.2007
**

Here Bruhn asserts subjectively that I have "given up" my complex Euler transform method, and asserts that the well known Euler transform method is "dubious". News to all textbooks.

**See
Consequences of a complex Euler transform**

He then asserts that:

ω_{r} = 2 (β - 1 /
r)

is "incorrect". On the contrary, this is just simple algebra
in which ω_{r}
is DEFINED as constant, so the relation between the varying β and 1 / r is
also defined by the DEFINED constant ω_{r}. Here our
friend tries to give another false impression, in fact two false impressions.
How will he wriggle out of this one?

In their paper 92 Evans & Eckardt start with the ODE

^{∂²Φ}/_{∂r²} +
(^{2}/_{r}+ω_{r}) ^{∂Φ}/_{∂r} +
(2rω_{r} + r² ^{∂ωr}/_{∂r})
^{Φ}/_{r²} = − ^{ρ}/_{εo}
(1)

If ω_{r} is chosen as a constant C, then the coefficients
2β = ^{2}/_{r} + C
and
2rω_{r} + r² ^{∂ωr}/_{∂r} =
κ_{o}² = ^{2C}/_{r}
are **both NOT constant**.

So what now, Myron? My advice: **Think twice!**

**Correction of
19.06.2007**

Here Bruhn is his usual deceptive self. It is apparently asserted that

R = q^{μ}_{a}
R^{a}_{μ}

occurs in the proof of the ECE Lemma. This is not the case.

**Then, please, have a look at
YOUR own blog site.
Or do you employ ghost writers?**

We are then told that

q^{a}_{μ} R = q^{a}_{μ}
(q^{μ}_{a} R^{a}_{μ})

is "inadmissible". On the contrary, summation over repeated indices is carried out inside the bracket on the right hand side, making it a scalar.

The above formula is misleading due to the *triple* use of the same indices a and μ,
and you get caught by your own trap when continuing

q^{a}_{μ} R =
q^{a}_{μ}
(q^{μ}_{a} R^{a}_{μ})
**
=
(q ^{a}_{μ}
q^{μ}_{a}) R^{a}_{μ}
= 4 R^{a}_{μ}**

a step that could *not be executed if you avoid the triple use of indices*:

q^{a}_{μ} R =
q^{a}_{μ}
(q^{ν}_{b} R^{b}_{ν})
**
= ???**

My use of such summation is rigorously proven in the appendices of chapter 17 of volume one, which friend Bruhn predictably ignores. Gerhard Bruhn is indeed an old donkey, as he describes himself to Bo Lehnert.

**Thus, you should check your appendices once more. Who is the donkey then, friend Myron???**

The tone adopted to Lehnert is far more polite. A German saying is quoted, so here is a Celtic saying: "Nid da lle gellir gwell".

That's the usual friendly tone between colleagues, Myron, unlike your polemics.

It is known that Bruhn also approached Dr Eckardt's employers Siemens and was ignored entirely, i.e. trashed. In this incident the address of the Darmstadt police was found. Dr Eckardt's abilities vastly exceed those of Dr Bruhn's.

**
Then, Myron, repeat reading the previous debate until you have understood the objections
against
your
usage of dummy indices.**

British Civil List Scientist

Posted: 2007-10-01