Notes on ECE Lemma

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.

**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)

Thus the complete unit vector field:

e^{μ}e_{μ} = 1 - 1 -1 -1 = -2

which is a Lorentz invariant scalar, QED. 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. 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.

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

Gerhard Bruhn is a scientific fraud.

**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. 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?

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. We are then told that

q^{a}_{μ} R = q _{aμ} (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. 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. 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". 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.

British Civil List Scientist