01.01.2008
(Quotations from Evans' papers are displayed in
With the introduction to his paper #100 . Evans announces a review of major themes of his ECE theory. We shall start reviewing paper #100 with its section 2 finding a collection of older and recent flaws of that "theory". All these errors are beyond repair.
We read on p.9 of Evans' paper 100 [1.2]:
. . . The second advance in basic geometry is the inference {1-12} of the Hodge dual of the Bianchi identity. In short hand notation is:
D Ù T~ = R~ Ù q
(9)
The proof of this assertion as given by Evans in his
papernote 100(16)
[1b] is wrong as was shown in [5].
In addition Evans writes on p.9/10 of
paper #100 - Section 2 [1.2]:
. . . that the Bianchi identity and its Hodge dual are the tensor equations
Dμ Tκμν = Rκμμν (13)
and
Dμ T~ κμν =
R~ κμμν
(12)
Both equations have (due to summation over the index μ)
2-tensors on both sides, while the tensor equivalents of the 1st Bianchi identity
and its alleged dual Eq.(9) must have 4-tensors. Thus, the eqs. (13) and (12)
cannot be the tensor duals of the 1st Bianchi identity and of Eq.(9) respectively.
. . .
Therefore the neglect of torsion makes EH theory internally inconsistent, so standard
model general relativity and cosmology are also internally inconsistent at a basic level.
As was pointed out above the author Evans failed to prove the existence of
internal inconsistencies in EH theory.
We read on p.6 of Evans'
paper [1a]:
2. Concerning the 2nd Bianchi identity
. . . Similarly the "second Bianchi identity" of standard model general relativity is:
D Ù R = 0 (8)
and in tensor notation this becomes
Dρ Ù Rκσμν + Dμ Ù Rκσνρ + Dν Ù Rκσρμ = 0 . (9)
Again this neglects torsion arbitrarily, and . . .
And in Evans'
paper #100/2 [1.2]:
In the course of development of ECE theory a similar problem was found with what is referred to in the standard model literature as "the second Bianchi identity". In shorthand notation this is given {13} as:
D Ù R = 0 (15)
but again this neglects torsion. . . .
The reader should have a look in Evans' standard textbooks
[2, p.93, Eqs.(3.139-141] and [3, p.488 f., Eqs.(3.28)-(3.32)]
where Equ.(8)/(15) is proven in case of non-vanishing torsion.
We follow here [2] applying slight modifications of notation.
The reader is also recommended to read the more systematic
and deeper book by F.W. Hehl [4, p.208].
S.M. Carroll writes
Rab =
d Ù
ωab +
ωac
Ù
ωcb
[2,(3.138)]
to apply d Ù which yields
d Ù
Rab =
d Ù
d Ù
ωab +
d Ù
(ωac Ù
ωcb) = 0 +
(d Ù
ωac) Ù
ωcb −
ωac
Ù
(d Ù
ωcb)
where d Ù
ω.. can be eliminated by means of Equ. [2,(3.138)]
to obtain
d Ù
Rab =
d Ù
d Ù
ωab +
d Ù
(ωac Ù
ωcb) = 0 +
(d Ù
ωac) Ù
ωcb −
ωac
Ù
(d Ù
ωcb)
or
d Ù
Rab +
ωac
Ù
Rcb −
ωcb
Ù
Rac = 0
[2,(3.140)]
However, from
Dμ Xab
=
∂μ Xab +
ωμac Xcb
−
ωμcb Xac
[2,(3.128)]
we obtain by left multiplication by dxμÙ due to
dxμDμ = D,
dxμωμac =
ωac,
dxμωμcb =
ωcb,
the result
D Ù Xac =
d Ù Xac +
ωac Ù
Xcb
−
ωcb Ù
Xac
valid for arbitrary tensor valued forms Xab
= Xab μν
dxμ
Ù
dxν
By applying this to [2,(3.140)] we obtain the second Bianchi identity
[1.1] M.W. Evans, A Review of Einstein-Cartan-Evans (ECE) Field Theory
(Introduction of Paper #100),
[1.2] M.W. Evans, Geometrical Principles (Section 2 of Paper #100:
[1.3] M.W. Evans, The Field (Section 3 of Paper #100:
[1.4] M.W. Evans, Aharonov Bohm and Phase Effects in ECE Theory (Section 4 of Paper #100:
[1.5] M.W. Evans, Tensor and Vector Laws of Classical Dynamics and Electrodynamics
(Section 5 of Paper #100)
,
[1.6] M.W. Evans, Spin Connection Resonance (Section 6 of Paper #100)
,
[1a] M.W. Evans, Development of the Einstein Hilbert Field Equation . . .,
[1b] M.W. Evans, Proof of the Hodge Dual Relation,
[1c] M.W. Evans, Some Proofs of the Lemma,
[1d] M.W. Evans, Geodesics and the Aharonov Bohm Effects in ECE Theory,
[2] S.M. Carroll, Lecture Notes on General Relativity,
[3] S.M. Carroll, Spacetime and Geometry,
[4] F.W. Hehl and Y.N. Obukhov, Foundations of Classical Electrodynamics −
[5] G.W. Bruhn, Consequences of Evans' Torsion Hypothesis,
[6] G.W. Bruhn, Remarks on Evans' paper #100 - Section 2,
[7] M.R. Spiegel, Vector Analysis,
[8] G.W. Bruhn, Evans' "3-index Î-tensor"
,
[9] G.W. Bruhn, Comments on Evans' Duality,
[10] G.W. Bruhn, F.W. Hehl, A. Jadczyk , Comments on ``Spin Connection Resonance
[11] G.W. Bruhn,
Remarks on Evans/Eckardt’sWeb-Note on Coulomb Resonance,,
(08.01.2008)
An Editorial Note by G. 't Hooft in Found. Phys.
(29.01.2008)
Remarks on Evans' Web Note #100-Section 7: The Sagnac Effect
(25.01.2008)
Remarks on Evans' Web Note #100-Section 6: SCR
(16.01.2008)
Remarks on Evans' Web Note #100-Section 5: EM field
(08.01.2008)
Remarks on Evans' Web Note #100-Section 4: The Aharonov Bohm effect
(05.01.2008)
Remarks on Evans' Web Note #100-Section 3: Field and Wave equation
(01.01.2008)
Remarks on Evans' Web Note #100-Section 2: Torsion and Bianchi identity
(27.12.2007)
Remarks on Evans' Web Note #103
(19.12.2007)
Myron now completely confused
(14.12.2007)
Evans' Central Claim in his Paper #100
(10.12.2007)
How Dr. Evans refutes the whole EH Theory
=
(Rac −
ωas
Ù
ωsc)
Ù
ωcb −
ωac
Ù
(Rcb −
ωcs
Ù
ωsb) =
Rac
Ù
ωcb −
ωac
Ù
Rcb
D Ù
Rab = 0
valid without any assumptions on torsion.
References
http://www.atomicprecision.com/blog/2007/12/27/introduction-to-paper-100/wp-filez/a100thpaperintroduction.pdf .
A Review of Einstein-Cartan-Evans (ECE) Field Theory,
http://www.atomicprecision.com/blog/wp-filez/a100thpapersection2.pdf .
A Review of Einstein-Cartan-Evans (ECE) Field Theory,
http://www.atomicprecision.com/blog/wp-filez/a100thpapersection3.pdf .
A Review of Einstein-Cartan-Evans (ECE) Field Theory,
http://www.atomicprecision.com/blog/wp-filez/a100thpapersection4.pdf .
http://www.atomicprecision.com/blog/wp-filez/a100thpapersection5.pdf .
http://www.atomicprecision.com/blog/wp-filez/a100thpapersection6.pdf .
http://www.aias.us/documents/uft/a103rdpaper.pdf .
http://www.atomicprecision.com/blog/wp-filez/a100thpapernotes16.pdf .
http://www.atomicprecision.com/blog/wp-filez/acheckpriortocoding5.pdf .
http://www.aias.us/documents/uft/a56thpaper.pdf .
http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf, 1997.
http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf, 1997.
Charge, Flux and Metric,
Birkhäuser 2003, ISBN 0-8176-4222-6, ISBN 3-7643-4222-6
ECEcontradictions.html .
onMwesPaper100-2.html .
in Schaum's Outline Series, McGraw-Hill.
Evans3indEtensor.html .
EvansDuality.html .
in Gravitational General Relativity''
, ACTA PHYSICA POLONICA B Vol. 39/1 (2008)
pdf .
html
RemarkEvans61.html .
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