Bruhn Disinformation Site

with comments by G.W. Bruhn

Evans' "rebuttals" give the only opportunity to critically discuss aspects of his ECE-theory with the author. This recent rebuttal is, aside from some gaffes, of remarkably moderate tone and therefore a good opportunity to show where Evans goes astray with his ECE-theory. Recently he wrote on his blogsite that he sees "friend Bruhn" sitting on the wrong tree. Yes, it's true: We both are sitting on

Meanwhile Evans has issued another note "Correct Method for Lorentz Transform" the correctness of which will be discussed in my next commentary. In advance the reader could have a look at the section "Lorentz transform of a z-boost K → K' " of my note Commentary on Evans' Key Derivation 6 .

The deliberate disinformation (D???) occurs he??

is the assertion that the speed of light can be

exceeded. If the original frame is moving at

c, then there is no physical meaning to a frame

moving at c + v . Thus v = 0 .

That's a distortion of facts: Evans falsely considers a frame K' of velocity c
where two frames K of velocity 0 and K' of velocity v would be correct.
Besides, even if K' had the velocity c then,
due to the well-known *relativistic addition theorem of velocities*,
a motion of velocity v relative to K' would
appear as ^{c+v}/_{1+cv/cē} = c when seen form the frame K.

The standard of English is very poor. The

general rule for coordinate of basis

sets is given by Carroll and is actually

reproduced in Bruhn's (L2.0) to (L2.3).

Bruhn gives:

** i' = i , j' = j**
(1)

so:
[ ** i' × j' = k = i × j** ]
(2)

**This is what I proved.**

It should be noticed here that the previous line (2) is *Evans'* conclusion, not mine.
And that conclusion is wrong since Evans erroneously assumes that the Lorentz
transform L commutes with the cross product ×: The **Evans-rule**

L(**a** × **b**) **=** L**a** × L**b**

is **wrong** in general.

Bruhn now concludes that the B Cyclic Theorem is the frame of reference.

Unclear formulation: A theorem is no frame of reference, so what is meant by Evans?

Here Bruhn admits that my definition

R q^{a}_{λ} :=
∂^{μ}(Γ^{ν}_{μλ}q^{a}_{ν}
− ω^{a}_{μb}q^{b}_{λ})
(3)

is correct.

Not at all!
As everybody, who knows to count to three, can see that Evans' equ. (3) consists of
4 × 4 = sixteen scalar equations due to a=0,1,2,3 and λ=0,1,2,3.
So we have sixteen
different equations for the one unknown value of R. Hence R is **16-fold
over-determined** and therefore eq. (3) is **no valid definition** of R.
That is the statement in the article Evans referred to.
It seems that Evans has problems with his eyes and should take medical help.

In this equation (3) there ??

summation over repeated ν and μ indices and

over repeated b indices, on the right hand side. So R

is a scalar. ...

To become concrete we consider an example: Take (a,λ)=(0,0) and compare with (a,λ)=(1,0). >From equ.(3) we obtain the equations

R q^{o}_{o} :=
∂^{μ}(Γ^{ν}_{μo}q^{o}_{ν}
− ω^{o}_{μb}q^{b}_{o})
(3')

R q^{1}_{o} :=
∂^{μ}(Γ^{ν}_{μo}q^{1}_{ν}
− ω^{1}_{μb}q^{b}_{o})
(3'')

Why should these equations agree, Myron? TELL US, WHY???

... Multiply both sides by q^{λ}_{a} ...

This is not allowed, if you don't know the agreement of all sixteen values of R given by the sixteen equations (3), Myron.

... and use:

q^{a}_{λ}q^{λ}_{a} = 4
(4)

to find:

R = ¼ q^{λ}_{a}
∂^{μ}(Γ^{ν}_{μλ}q^{a}_{ν}
− ω^{a}_{μb}q^{b}_{λ})
(5)

This result does not become more valid by repetition: It is only true, if one knows the
*agreement* of all sixteen R-values given by the sixteen equations (3).

One can use the normalisation:

(q^{a}_{λ}q^{λ}_{a})_{n} = 1
(6)

Evidently the value
(q^{a}_{λ}q^{λ}_{a})_{n} (=1)
differs from the value q^{a}_{λ}q^{λ}_{a} (=4),
and therefore the first value is no substitute for the second one, at least in *traditional*
math.

This just repeats 9.04.07 which I have answered many times before. In 9.04.07 Bruhn admits that the Lemma is correct, he accepts

D^{μ}(D_{μ} q^{a}_{ν}) := 0
(7)

This is an identity because

D_{μ} q^{a}_{ν} = 0
(8)

This means that Bruhn also accepts the tetrad postulate (8).

In
9.04.07
I do NOT admit that the Lemma is correct, **just in the contrary**:
Some attempts to prove Evans' lemma are rejected:
The first attempt is invalid due to the use of undefined expressions.
The second one is that one considered above.
Evans' "proofs" don't become better by repetition.

He now attempts to d???ate

by setting up his own error, and then attributes

it to me. He then falsely asserts, that I give

a second proof to correct his contrived error.

I need not repeat my above criticsms of Evans' proof of the Lemma in detail.
The definition of the scalar R by a system of 16 independent equations
is *not a contrived but a real error* of someone who has only a very
poor knowledge of the mathematics to be applied here.

Here Jadczyk asserts that Cartan geometry is not generally covariant. This is completely erroneous, the very reason for Cartan geometry is its general covariance.

A. Jadczyk had pointed to an ambiguous formulation in Evans' ECE book vol.1: The rule

D Ù ω^{a}_{b} =
d Ù ω^{a}_{b}
+
ω^{a}_{c} Ù ω^{c}_{b}
(17.16)

cannot be generalized to general covariant (1,1)-valued forms X^{a}_{b}
like e.g. R^{a}_{b}. The general rule is

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

An example is the identity
D Ù R^{a}_{b} =
d Ù R^{a}_{b}
+
ω^{a}_{c} Ù R^{c}_{b}
+
ω^{c}_{b} Ù R^{a}_{c}
(D)

The reason for the exception of rule (17.16) against (D) is
that the form ω^{a}_{b}
does **not transform covariantly**
while its covariant exterior derivative
D Ù ω^{a}_{b}
(which is =R^{a}_{b}) does so.

It must be added that the term "Cartan Geometry" is Evans' invention which is used nowhere else.

For some bizarre reason he reproduces the 1857 Act reforming the Civil List.

Some information about the Civil List. Where is the problem, Myron???

The meaning of the index a has been discussed since 1992. Here Bruhn sets up his own eq. (2.1) and proceeds to rebut his own error. This is his usual method.

The meaning of the hypothetical index a, attached to the usual field form F,
was *under discussion* for 15 years. That shows its problematic nature.
More, a usual index must run over 0,1,2,3. What
is the meaning of F^{o}?
And what is the relation of the forms F^{1}, F^{2}, F^{3}
in relation to the fields that are measured by experiments?

In that context a totally antisymmetric 3-index Î^{abc}
occurs in the ECE theory, as listed in my article
Comments on Evans' Duality,
see e.g. the eqs. (F.10-11) in the GCUFT-book vol.1.
However, such a tensor cannot be defined covariantly in the 4-dimensional case, see
Evans' "3-index, totally antisymmetric unit tensor".

The tensor F^{a}_{μν} is generally covariant as discussed by Carroll.

That's a completely misleading remark: Carroll does not define or discuss
a vector-valued electromagnetic 2-form
F^{a}, only the usual *scalar*-valued 2-form F of electromagnetism
(p.86-87 of his textbook) is treated.