Sept 18, 2008

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

The story (Part 2) so far

Subject: 119(3) : Frame Invariance under the Lorentz Boost Date: Thu, 18 Sep 2008 04:24:02 EDT

Attachment: a119thpapernotes3.pdf

These are the frame invariance relations under the Lorentz boost. The Lorentz group contains three rotation generators and three translation generators. These are developed in comprehensive detail in the Omnia Opera section of this website in M. W. Evans and J. - P. Vigier , “The Enigmatic Photon” (in five volumes on this site), and in Advances in Chemical Physics volume 119 in two reviews. My 2001 edited volume 119 of “Advances in Chemical Physics” (in three parts, 35 review articles) achieved a very high journal impact index, four times higher than the average. In 4-D there are four unit vectors, which can be denoted e0, i, j, k . Frame invariance under the Lorentz boost is maintained for O(3) symmetry relations involving the timelike unit vector, e.g.: e0 x i = j et cyclicum (boost generator relations in 4-D).

This is another flaw which in certain variations goes through Evans' papers (e.g. the
3-D Î-tensor in 4-D tensor calculus).
Equations like **a** × **b** = **c** are
NOT EXTENDABLE to 4-D:
The definition of the *binary* operation × is restricted to Euclidian 3-D spaces:
Equations like **e**_{o}× **i** = **j** belong to Evans' New Math:

To see this let us remember the following property of the cross-product:
**a** × **b** = **0** for non-vanishing vectors **a**,**b** implies
the parallelity of the vectors: **a** | | **b** .

So if we would assume with Evans **e**_{o}× **i** = **j** and
**k** × **i** = **j**, then the difference of both equations yields
(**e**_{o}−**k**) × **i** = **0**, hence
**e**_{o}−**k** | | **i** or **i** = λ (**e**_{o}−**k**)
with some number λ.
However, this contradicts the *basis* property of the vectors **e**_{o},
**i**, **j**, **k** which must be linearly independent.

Frame invariance under the Lorentz rotation is maintained for the three spacelike unit vectors, i x j = k et cyclicum (rotation generator realtions in 4-D). These basic facts are well known and this is meant as an educational note. Now I will go on to the explanation of the equinox precession with gravitomagnetism, the theme of paper 119.

Because of the math flaw discussed above we need not to consider
the attachment: a119thpapernotes3.pdf
in detail where the *non-existing* 4-D-cross-product × is used essentially in
eq.(5).

[1] S.M. Carroll, *Lecture Notes on General Relativity*,

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf

[2] M.W. Evans e.a., *The Enigmatic Photon - New Directions*, Vol.4,
Kluwer 1998, ISBN 0-7923-4826-5

[3] J.D. Jackson, *Classical Electrodynamics*, John Wiley & Sons 1999,
ISBN 0-471-30932-X