 ## Remark on Evans' Defense of the Covariance of his B Cyclic Theorem

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

In a blog reply on my article to appear in Foundations of Physics Evans complains that the journal has accepted "an identical manuscript" of mine for publication that had already appeared in Physica Scripta. This shows that he has not read the manuscript or not understood that the new FoP article is just a commentary on two publications of his in APEIRON 2000 and in The Enigmatic Photon vol.4, (Kluwer Academic Publishers 1997), where former errors of his were corrected to yield the NON-covariance of his B Cyclic theorem.

Instead of a direct defense of his APEIRON article Evans attempts to defend his theorem by pointing to a formal rebuttal we'll discuss now.

We quote from this "formal rebuttal":

The B Cyclic Theorem is {2}:

B(1)×B(2) = i B(o) B(3)*                                                 (1)
et cyclicum

where the plane wave magnetic flux densities are:

B(1) = B(2)* = B(o)/sqr(2) (iij) eiΦ,
(2)
B(3) = B(3)* = B(o) k

The first equation (2-1) describes the transversal components, while the second equation (2-2) is Evans' assumption of an additional constant longitudinal field. As is well known [J.D.Jackson, Classical Electrodynamics, 3rd ed. Eq.(11.148)] for a Lorentz boost in z-direction the (longitudinal) z-component B(3) = B(o)k of the magnetic flux remains invariant:

B(3)B(3)'                                                             (17)

(where a prime was missing and added on the right hand side) hence due to Evans' Eq. (2-2)

B(o) = B(o)'                                                                 (17')

However, Evans tells us to have shown the transformation rule

B(o)' = (1−v/c/1+v/c)½ B(o)                                             (19)

(which is indeed correct as a consequence of the Lorentz transformation of the transversal field components). Therefore now Evans has a problem caused by his assumption (2-2): The factor 1−v/c/1+v/c must be 1, and that requires v=0.

Evans solves this problem in his typical way, by another mistake: He now surprisingly argues that v should be

"zero because the fields are already propagating at c and cannot propagate any faster"

a dubious remark since v is the relative velocity of two inertial frames K and K' as pointed out by Evans himself in The Enigmatic Photon vol.4 under consideration here and nothing else, especially no relative propagation velocity of any fields.

### Thus with this "formal rebuttal" Evans has rebutted himself.

The remainder of Evans' "formal rebuttal" is irrelevant.