## On the Non-Lorentz-Invariance of M.W. Evans O(3)-Hypothesis

### Gerhard W. Bruhn

February 28th, 2009

Surely a math based theory like Evans' theory should be mathematically consistent: A theory that contains a lot of mathematical inconsistencies is like the weather forecast in the times a century ago: No reliable conclusions can be drawn from it, it is only a "theory".

However, a very important example of my interests in the PHYSICS of ECE "theory" should be mentioned here also: Dr. Evans' O(3) theory, the basis of the later ECE theory, is based on the physical assumption that a circularly polarized plane electromagnetic wave in vacuo is always accompanied by a "ghost field", a constant magnetic B-field in longitudinal direction. Hereby a certain ''O(3) symmetry'' condition must be fulfilled in addition: The transversal amplitude must agree with the (constant) longitudinal amplitude. That is a suggestion that must be examined carefully:

FIRST of all: Evans' hypothesis is compatible with the homogeneous Maxwell equations, since the additional constant longitudinal B(3) field fulfils the Maxwell equations separately.

HOWEVER, what about the O(3) symmetry? A plane wave appears as such in all inertial systems due to the invariance of the Maxwell equations under Lorentz transformations, while the electric and magnetic fields are subject to a mixed linear transformation, the Lorentz transfomation of the electromagnetic fields.

Dr. Evans felt correctly obliged to check the invariance property of his O(3) hypothesis. In 2000 he wrote a paper titled "On the Application of the Lorentz Transformation in O(3) Electrodynamics", APEIRON Vol 7

where he gave a positive answer:

The O(3) hypothesis is Lorentz-invariant.

However, in 2007 I came across that paper. It turned out that Dr. Evans had erroneously assumed the invariance of wave number and frequency while from the Doppler effect it is well-known that both change under Lorentz transformations. The simple correction of that physical flaw lead to the result of NON-invariance of the O(3)-hypothesis which could have been obtained already by Dr. Evans himself if he had correctly used the transformation properties of wave number and frequency. This result was published in my note ''On the Non-Lorentz-Invariance of M.W. EVANS' O(3)-Symmetry Law'', Foundations of Physics (2008), Vol. 38, 1, pp.3-6