 ## 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  in black

In Chap. 2.3 of his book  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 ,

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) = /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.

### References

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