## Evans' Basics of the Lorentz Transform Continued

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

Sept 17, 2008
Quotations from Evans' writings in
black

Subject: Proceeding with Paper 119 Date: Wed, 17 Sep 2008 06:06:20 EDT

In note 119(2) I intend to provide another educational background note on the invariance of i x j = k under the rotational Lorentz transform. This should be quite clear to a first year undergraduate but I give the proof to counteract the deliberate misinformation published by ‘t Hooft, who published a paper in “Foundations of Physics” asserting that i x j = k (B Cyclic Theorem) is somehow “not covariant”. Thsi si why I ask for ‘t Hooft’s resignation, and non-submission of papers to FP until another editor takes over who is not associated with Bruhn. Preferably van der Merwe should bd re-instated. The B Cyclic Theorem is the basic rotation generator relation itself, and time does not enter into it (see Carroll chapter one). Then in following notes I will go on to the main theme of paper 119, which is development of gravitomagnetism, dipole dipole interaction and so on. Paper 119 will also give a plausible first approximation for the equinoctial precession and hopefully will be finished before the September equinox.

Subject: 119(2) : Invariance of the Frame of reference under Lorentz transformation Date: Wed, 17 Sep 2008 09:47:00 EDT

Attachment: a119thpapernotes2.pdf

This is the proof of the invariance of i x j = k under Lorentz transformation. It follows that the B cyclic theorem is also an invariant under the Lorentz transform. The relevant transform to take is the rotational one, because the frame relation i x j = k is one between rotation generators.

Subject: The Extent of Corruption in Standard Physics Date: Wed, 17 Sep 2008 10:09:32 EDT

It is almost unanimously agreed (evidence from feedback data and comparison of notes among scientists) that there are websites in standard physics that deliberately try to corrupt mathematics. Fortunately the interest in them is minimal, scientists have not been deceived. I have just sent over the simple proof of the Lorentz invariance of the B Cyclic Theorem. This is a school level exercise. Questions must be asked therefore why the editor of “Foundations of Physics”, G. ‘t Hooft, allowed a paper to be published in his journal stating that a frame of reference (i x j = k) is “not Lorentz invariant”. Similarly the same question must be asked of “Physica Scripta”. My answer is that it was part of a campaign of corruption in which the referees were rigged and which the editors were biased. Editors known to cite misrepresentation should be heavily criticicsed and recognized as such. This process of corruption has set in in the later twentieth century, with the result that papers in such standard journals should be read with great caution. The B Cyclic equation is the frame of reference itself, and as such is Lorentz invariant automatically. I move a vote of no confidence in editors who allow personal animosity to be published in their journals, and request the resignation of G. ‘t Hooft as editor. Similarly I request the resignation of F. Hehl as editor of Annalen for citing a website by G. Bruhn which is known to contain malicious misrepresentation. The verdict of the scientific community is again unanimously against F. Hehl. He is known not to cite my rebuttal (paper 89), which has been read by tens of thousands of scientists and accepted unanimously. This is an example of what Jeremy Dunning-Davies criticises in his book: “Exploding a Myth” (published 2007 and reviewed on this site).

Civil List Scientist

### Some Remarks on the Attachment: a119thpapernotes2.pdf

At the end of his first approach to the Lorentz transformation between two inertial frames K and K' (the latter moving with v relative to K) Dr. Evans came to the surprising result of vanishing relative velocity v=0. So Dr. Evans is lead to conventional rotations, ''such as a rotation in the x-y-plane'' (offered by S.M. Carroll in [1, p.5, eq.(1.17)] as introductory example too).

i' = i cos θ − j sin θ
(8)
j' = i sin θ + j cos θ

which indeed is a rotation of K' relative to K by the angle −θ. So Dr. Evans succeeds in calculating

i' × j' = . . . = i × j                                                 (10)

Therefore

i' × j' = k'                                                 (11)

follows from the rotational Lorentz transform of

i × j = k                                                 (12)

which nobody can doubt; therefore followed by a (boldface)

QED. The B cyclic Theorem is Lorentz invariant.

#### However, there are two objections:

(i) Evans restricted his consideration to the trivial sub-case of vanishing relative velocity v = 0. Nothing has been proven for the general case of a Lorentz transform between relatively moving frames K and K'.

(ii) Of course, in K and in K' we have i × j = k and i' ×' j' = k' with distinct binary operations × and ×' respectively. But the transformation of electromagnetic fields under a Lorentz boost cannot be discussed by that way. This must be done by referring to the well known transformation rules given in the text books e.g. in [3, eqs.(11.148)] and gives quite another result than Evans asserts with his B Cyclic Theorem.

In summary it may be said that I never read before such a helpless wrong approach to the basics of the Lorentz transform. Really, Dr Evans is not exactly an Einstein. E.g. he should attempt to compare his considerations with Carroll's introductory Chapter ''Special Relativity and Flat Spacetime'' in [1, p.6 ff.] and especially try to understand the figure on p.7 which is a visualization of the basic transformation rules [1, eqs.(1.19-21)].

### References

[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