In [1; (11b)] V.V. Dvoeglazov displays a transformation formula for the longitudinal component B⁽³⁾ of Evans' hypothetical B⁽³⁾-field:

B⁽³⁾' = B⁽³⁾ + ^γ−1/_β² (β·B⁽³⁾)β − γβB⁽⁰⁾                                                 (11b)

where β = ^v/_c, β = |β| and γ = ¹/_{sqr(1−β²)}. For sake of simplicity we may assume c=1.

In the special case of longitudinal motion v = v k, v > 0, using B⁽³⁾ = B⁽⁰⁾k Dvoeglazov's equation yields

B⁽³⁾' = B⁽⁰⁾ sqr(^1−β/_1+β) k ,                                                                

which means B⁽³⁾' = B⁽³⁾ sqr(^1−β/_1+β) , i.e. due to Dvoeglazov the longitudinal component of the B-field is decreased by the longitudinal Lorentz transform.

Since B⁽³⁾ is merely the longitudinal component of a field B that has an additional transversal component B_^ Dvoeglazov's result contradicts the well-known Lorentz transform of the electromagnetic field where the longitudinal component remains unchanged. We quote here the transformation rules from the "classical" book of A. Sommerfeld [2; p.245-246]

E_{| |}' = E_{| |} ,                                 B_{| |}' = B_{| |}                                 (| | = longitudinally),
E_^' = ¹/_γ (E + v×B)_^ ,                 B_^' = ¹/_γ (B − v×E)_^                 (^ = transversally).

In Equ.(6) Dvoeglazov shows us the transversal B-field components

B_x = − sqr(2) B⁽⁰⁾ sin Φ ,                 B_y = + sqr(2) B⁽⁰⁾ cos Φ .                                 (6)

which yields the transversal B-field

B_^ = B_x i + B_y j = ¹/_sqr(2) B⁽⁰⁾ [(i i + j)e^iΦ + (− i i + j)e^−iΦ]                                 cf. (2)

where Φ = ω(t−z) for a wave propagating in z-direction with velocity c=1. The Maxwell equation Ñ ×B_^ = ^{∂E_^}/_∂t leads to a corresponding transversal E-field

E_^ = ¹/_sqr(2) B⁽⁰⁾ [(i − i j)e^iΦ + (i + i j)e^−iΦ] = E_x i + E_y j .

Together with the longitudinal B-component

B_{| |} = B⁽³⁾ = B⁽⁰⁾ k                                                                 (3)

we have all required field components to perform the above mentioned Lorentz transformation of B to obtain (note β=v due to c=1):

B_{| |}' = B_{| |}         and         B_^' = ¹/_γ (B_^ − β k×E_^) = sqr(^1−β/_1+β) B_^

This result proves that V.V. Dvoeglazov's Equ. (11b) cannot be true.

More, we obtain an important conclusion concerning M.W. Evans O(3)-hypothesis [4; Chap.1.2]: Dvoeglazov's wave (2-3) fulfils Evans' Symmetry Relation relative to the original coordinate frame (x,y,z,t):

B⁽¹⁾ × B⁽²⁾ = iB⁽⁰⁾ B⁽³⁾* ,                                                                 (1)

which is obviously equivalent to

½ |B_^|² = ½ (|B_x|² + B_y|²) = B_z|² = |B_{| |} |²

However, seen from the new coordinate frame (x',y',z',t') after the longitudinal Lorentz transform we obtain

½ |B_^'|² = ½ (|B_x'|² + B_y'|²) = ^1−β/_1+β |B_z|² = ^1−β/_1+β |B_{| |}|² = ^1−β/_1+β |B_{| |}'|²   <   |B_{| |}'|² .