In 1992 M.W. EVANS proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. EVANS has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published a proof of the Lorentz invariance of O(3)symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant.

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The paper (Evans 2000 Phys. Scr. 61 287–91) ‘On the nature of the B(3) field’ essentially refers to a hypothesis that was proposed in 1992 by M W Evans: Evans claimed that a so-called O(3)-symmetry of electromagnetic fields should exist due to an additional constant longitudinal ‘ghost field’ B(3) accompanying the well-known transversal plane em waves. Evans considered this symmetry, a fixed relation between the transversal and the longitudinal amplitudes of the wave, as a new law of electromagnetics. In the paper (Evans 2000) in this journal the authors claim ‘that the Maxwell–Heaviside theory is incomplete and limited’ and should be replaced with Evans' O(3)-theory the centre of which is Evans' O(3)-symmetry law. Later on, since 2002, this O(3)-symmetry became the centre of Evans' CGUFT which he recently renamed as ECE theory. A law of physics must be invariant under admissible coordinate transforms, namely under Lorentz transforms. A plane wave remains a plane wave also when seen from arbitrary other inertial systems. Therefore, Evans' O(3)-symmetry law should be valid in all inertial systems. To check the validity of Evans' O(3)-symmetry law in other inertial systems, we apply a longitudinal Lorentz transform to Evans' plane em wave (the ghost field included). As is well-known from SRT and recalled here the transversal amplitude decreases while the additional longitudinal field remains unchanged. Thus, Evans' O(3)-symmetry cannot be invariant under (longitudinal) Lorentz transforms: Evans' O(3)-symmetry is not a valid law of physics. Therefore it is impossible to draw any valid conclusions from that wrong O(3)-hypothesis. The paper (Evans 2000) has no scientific basis.

A few years ago a hopeful article (Evans 2000 Phys. Scr.61 513–7) appeared in this journal promising that according to its 15 authors' opinion the pending energy crisis could be solved by ‘extracting energy from the vacuum’. However, in the past years the energy price has grown to unthinkable heights: a reason for having a look at the promised ‘energy from the vacuum’ in (Evans 2000). So we shall do so below and shall arrive at a great disappointment: the 15 authors were in error; their vacuum energy stems from a simple flaw of thinking by misinterpreting the well-known Lorenz term of the classical Maxwell gauge theory. Their miraculous conclusion should have made the authors suspicious, that just the Lorenz term should yield a vacuum current. Surely, its a pity that vacuum currents and vacuum energy in (Evans 2000) have their origin merely in a simple flaw of thinking, and all further speculations for a vacuum energy density are in vain. However, better to return to reality. Quote: Abstract of [1]: Great announcements…It is shown that if the Loren(t)z condition is discarded, the Maxwell–Heaviside field equations become the Lehnert equations, indicating the presence of charge density and current density in the vacuum. The Lehnert equations are a subset of the O(3) Yang–Mills field equations. Charge and current density in the vacuum are defined straightforwardly in terms of the vector potential and scalar potential, and are conceptually similar to Maxwell's displacement current, which also occurs in the classical vacuum. A demonstration is made of the existence of a time dependent classical vacuum polarization which appears if the Loren(t)z condition is discarded. Vacuum charge and current appear phenomenologically in the Lehnert equations but fundamentally in the O(3) Yang–Mills theory of classical electrodynamics. The latter also allows for the possibility of the existence of vacuum topological magnetic charge density and topological magnetic current density. Both O(3) and Lehnert equations are superior to the Maxwell–Heaviside equations in being able to describe phenomena not amenable to the latter. In theory, devices can be made to extract the energy associated with vacuum charge and current.

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