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:

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

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.

Further Correction of Bruhn

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^μe_μ = 1 −1 −1 −1 = −2

which is a Lorentz invariant scalar, QED.

That's not QED but NONSENSE: The quantity e^μe_μ (where e_o=1, e₁=−1, e₂=−1, e₃=−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' = ^{∂x^μ}/_∂x^μ' ∂^μ, V^μ = V^μ' ^{∂x^μ}/_∂x^μ'

see Carroll p.43, eqs. (2.11-12). Hence, if the eq. V = 1 k holds in one frame, i.e. V^o = 0, V¹ = 0, V² = 0, V³ = 1, then the V^μ transform by V^μ = V^μ' ^{∂x^μ}/_∂x^μ' and are by no means invariant. The same holds for the basis vector k = ∂₃ which due to [Carroll (2.11) transforms to ^{∂x^μ'}/_∂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?

On the ECE Lemma.

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.

No! Distortion of facts! For details see Comments on Evans' note2 on the ECE Lemma.

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?

^∂²Φ/_∂r² + (²/_r+ω_r) ^∂Φ/_∂r + (2rω_r + r² ^∂ω_r/_∂r) ^Φ/_r² = − ^ρ/_{ε_o} (1)

If ω_r is chosen as a constant C, then the coefficients 2β = ²/_r + C and 2rω_r + r² ^∂ω_r/_∂r = κ_o² = ^2C/_r are both NOT constant.

Comments on the web-article

Scientific Refutation of Jadczyk on the Bruhn Site , etc.

by Gerhard W. Bruhn

Scientific Refutation of Jadczyk on the Bruhn Site

Further Correction of Bruhn

On the ECE Lemma.

No! Distortion of facts! For details see Comments on Evans' note2 on the ECE Lemma.

HOME