Remarks on Evans' B(3) field: A self-disproval by M.W. Evans

Gerhard W. Bruhn, Darmstadt University of Technology

September 04, 2008, updated on September 12, 2008

Quotations from Evans' book [1] in black

In Chap. 2.3 of his book [1] Evans gives an equation for the B(3) field that according to his B(3) hypothesis is associated to a circularly polarized plane wave:

                B(3) = oc/h- I/ω e(3) = 5.723 × 1027 I/ω e(3)                         (137)

where [1, p.1] e is the charge of an electron, m its mass, h- is the Dirac constant and [1, p.3] e(3)=k is a unit vector in the (3) axis of wave propagation. The plane wave B is derived from its vector potential A [1, p.34]:

In S.I. units the fundamental equation linking A to the magnetic field B is in classical electrodynamics [47],

                B = Ñ×A                                                                                 (127)

So if A is a plane wave in vacuo then so is B (and its electric counterpart E). If the plane wave A is a solution of the vacuum d'Alembert equation then it may be written as

                A(1) = A(2)* = A(o)/2½ (ii+j) eiΦ                                                 (128)

From Eq. (127), the plane wave is

                B(1) = B(2)* = ω/c A(1) = B(o)/2½ (ii+j) eiΦ                                 (129)

. . .

Here Φ is the electromagnetic phase [1,2]. A(o), B(o) ... are scalar amplitudes, and i and j are unit Cartesian vectors in X and Y, perpendicular to the propagation direction Z of the wave. The following key relations then follow using elementary algebra,

                A(1)×A(2) = c/ω B(1)×B(2) = 1/ω E(1)×E(2)                                 (131)

and show that the product A(1)×A(2) is proportional to B(1)×B(2) divided by the square of the angular frequency. Expressing B(1)×B(2) in terms of the beam intensity or the power density (I in W/m)

                B(1)×B(2) = i μo/c I e(3)*                                                                 (132)

where μo is the vacuum permeability in S.I. (Chap. 1).

The most important part of Evans' B(3) hypothesis is the alleged symmetry relation [1, p.121]

                B(1)×B(2) = i B(o) B(3)* = i B(o) e(3)* ,             et cyclicum,               (357)

(see also [1, eqs.(86), (154) and (181)])

which, of course, if Evans should be right, must be fulfilled in addition.

From this hypothesis together with Evans' eq. [1,(132)] we obtain the relation

                I = c/μo B(o) ,                                                                                 (B)

(c.f. [1,eq.(183)]) which shows that at constant power density I the values of |B(3)| = B(o), i.e. the entries of the second column of TABLE 2 should be constant as well. Evans assumes I = 1 kW/m for the TABLE 2 in [1, p.37]), which due to eq. (B) yields

                B(o) = 65 microTesla                 for arbitrary frequency ω .

However, this is a contradiction to the radiation formula [1, eq.(137)] which yields the non-constant values in the second column of TABLE 2 for 7 sample values of ω in the first column.

Evans' B(3) symmetry hypothesis [1, eq.(357)]) and his radiation formula [1, eq.(137)] disagree.


[1] M.W. Evans e.a., The Enigmatic Photon, Vol.3, KLUWER 1996