Some Further Rebuttals of the
Bruhn Disinformation Site

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.

25.05.2007 (88 Hits since June)

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) = La × Lb

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?

27.05.2007 (145 Hits since June)

Here Bruhn admits that my definition

        R q^a_λ := ∂^μ(Γ^ν_μλq^a_ν − ω^a_μbq^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_μoq^o_ν − ω^o_μbq^b_o)                 (3')

        R q¹_o := ∂^μ(Γ^ν_μoq¹_ν − ω¹_μbq^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_λq^λ_a = 4                 (4)

to find:

        R = ¼ q^λ_a ∂^μ(Γ^ν_μλq^a_ν − ω^a_μbq^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_λq^λ_a)_n = 1                 (6)

Evidently the value (q^a_λq^λ_a)_n (=1) differs from the value q^a_λq^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.

29.01.2007

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.

14.03.06

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

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

20.08.07

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 F¹, F², F³ 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.