 ## Evans' New Math flaw regarding the Lorentz Transform

### Gerhard W. Bruhn, Darmstadt University of Technology

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 eo× 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 eo× i = j and k × i = j, then the difference of both equations yields (eok) × i = 0, hence eok | | i or i = λ (eok) with some number λ. However, this contradicts the basis property of the vectors eo, 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).

### References

 S.M. Carroll, Lecture Notes on General Relativity,
http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf

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

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