Gerhard W. Bruhn, Darmstadt University of Technology

Sept 13, 2008

see also Counter examples (Dec 4, 2008)

_{Quotations from Evans' writings in }**black**

In his note #112 Evans complains that the validity check of his 'dualized' 1st Bianchi identity fails. He writes: Eq.(1), the 1st Bianchi identity

D ^ T^{a} = R^{a}_{b} ^ q^{b}
(1)

implies that there exists the identity

D ^ T^{~a } = R^{~a}_{b} ^ q^{b} .
(2)

where the tilde denotes Hodge duality in four dimensions. Eq.(2) is the inhomogeneous field equation of dynamics in ECE theory. It is seen that the equations of dynamics in ECE theory are duality invariant, a fundamental symmetry property.

Surely a nice property, which even the famous Maxwell equations fail to have. Evans' conclusion:

All solutions of the Einstein field equation in the presence of finite canonical energy momentum density give the result:

D ^ T^{~ a } = 0 .
(4)

and the result

R^{~ a }_{b} ^ q^{b} **≠** 0 .
(5)

and so the Einstein field equation violates the Bianchi identity in its form (2). ...

Which means: All these examples are torsion-free, T^{a} = 0,
and fulfil the 1st
Bianchi, reduced to
R^{a}_{b} Ù q^{b} =
D Ù T^{a} = 0.
But then from T^{a} = 0 we *trivially* obtain in addition

T^{~ a} = 0
and
D Ù T^{~ a} = 0

while
R^{~ a}_{b} Ù q^{b} = 0
fails to hold in general. See the listing in Chap. 5 of
Evans' web paper #117.
In addition Evans gives his *counter-examples* at
kruskal.pdf ,
spherical.pdf ,
a-r.pdf .

**Postscript on 05.10.2008:** Meanwhile the aias-team has compiled a large amount of evidence
against their own duality hypothesis and published in a
metric-tests.zip.

All these examples fulfil
the original 1st Bianchi identity (Sect. 1.1.9), but are
*counter-examples* for the alleged validity of the 'dualized' 1st Bianchi
identity (2) (Sect. 1.1.11):

To all who think logically this means:

Therefore it is *impossible* to prove that ''implication'' (2) from eq.(1).
Not so for
the British Civil List Scientist who creates ''proof'' after ''proof'' for this
''implication''.

Recently Evans attempts to falsly attribute his wrong ''dual identity'' to É.Cartan by naming it
''the **original
Cartan** identity''.
**This is an impudent attempt to deceive unsuspecting readers.** Cartan has nothing to do with Evans'
unqualified assumptions.

Subject: Generalized FLRW Metric Date: Tue, 30 Sep 2008 07:05:07 EDT

I have found one of these in a paper by Portugal in about 1995. It is:

ds squared = c squared dt squared - a dx squared - b dy squared - c dz squared

where:

a = t squared / (m - n ) squared

b = 1 / (t power 2(m +n) exp (2x))

c = exp (2x) / (t power (2 (m + n)))

Our code will again show this to be completely incorrect geometrically,
again violating the dual identity of geometry. It may be worth trying out this one,
but as Horst mentions, we are now able to shred any standard lien element like a
production line.

So it is quite clear that the standard scientists amount to a small and obsolete group with cynical intentions on power and money. In our system it is up to the politicians to clean up this mess. The easiest way is to turn off the public funding.

This appears in Jeremy’s book, and Horst tested it against the dual identity. It was found to be a complete fiasco, not even obeying the Ricci cyclic (so called “first Bianchi identity”). I think we could also show this in paper 120. I don’t know what Dirac was trying to do here, I think it was also to do with the singularities. So this subject area is a mess, and I recommend students to go into other subject areas of physics, chemistry, engineering or similar, i.e. to do something useful for society. Do not swallow pronouncements as if they come from marble. I have never been impressed by reputation or the fact that someone works somewhere which is proclaimed to be terribly important.

September 30th, 2008

Subject: Source of the Incorrectness of Standard Gravitational Physics Date: Tue, 30 Sep 2008 07:36:31 EDT

This can be traced to the use of the symmetric connection. The idea of connection was intorduced by Christoffel in the nineteenth century, but the symmetric connection seems to have been developed by T. Levi-Civita, the co-founder with G. Ricci-Curbastro of tensor calculus in 1900 in:

“Methods de Calcul Differential Absolu et Leurs Applications”

This was the source used by Einstein, whose many errors in tensor calculus were corrected by Levi-Civita during 1915 to 1917. Therefore it is necessary to find the above document from a library or lending library and to se whether the connection used is symmetric. I am fluent in written French so can read it. If so, this would pinpoint the source of the present fiasco, in which the whole of cosmology and gravitational physics is being shown to be incorrect because of its use of this symmetric connection. There is a classic book by Levi-Civita:

“The Absolute Differential Calculus”

and there is a need to go through this to find whether Levi-Civita ever used anything different from a symmetric connection (i.e. zero torsion). If he did not then it shows why torsion has been incorrectly eliminated from gravitational theory, rendering it meaningless, and violating the dual identity. Levi-Civita died in isolation in 1941 after having been ostracized by the scientific community because of his ethnic background. This may also have contributed to the fact that torsion was not properly taken account of. It is clear that Einstein never properly grasped the meaning of torsion in correspondence with Cartan. Now we know that torsion is central to all physics.