Motto by Lar Felker:

Evans shows electromagnetism is spacetime torsion; Einstein showed gravitation is spacetime curvature.
Cartan differential geometry is sufficient to mathematically describe GR and EM together.

Oh, poor Élie Cartan, to get involved in such a horrible ECE story!

Evans assumes an analogy of electrodynamics to geometry, as described e.g. in his GCUFT book [1,App.F].

The geometry is converted to the field theory using:

                A^a = A⁽⁰⁾ q^a                                                                                                 (F.2)

                F^a = A⁽⁰⁾ T^a.                                                                                                 (F.3)

Here A⁽⁰⁾ is the fundamental potential magnitude, with units of volt s/m, A^a is the potential form and F^a the field form.

To make that agree with the usual form of the homogeneous Maxwell equation d Ù F^a = 0 Evans introduces the concept of free space:

From eqn. (F.1) to (F.3) we obtain the homogeneous Evans field equations (HE):

                d Ù F^a = R^a_b Ù A^b − ω^a_b Ù F^b = − A⁽⁰⁾ (− q^b Ù R^a_b + ω^a_b Ù T^b) .                                                 (F.4)

With the geometrical constraint <of free space>:

                R^a_b Ù q^b = ω^a_b Ù T^b                                                                                                                 (F.5)

eqn. (F.4) reduces to the homogeneous Maxwell-Heaviside field equations:

                d Ù F^a = 0                                                                                                                                 (F.6)

for each index a.

The constraint of free space is nothing but

                d Ù T^a = R^a_b Ù q^b − ω^a_b Ù T^b = 0 .                                                                                                 (3.2)

However, from (3.2) follows:

The constraint of free space is not Lorentz invariant, hence "free space" no physical property.

Evans now attempts to explain the index a (=0,1,2,3):

The superscript a is the tangent bundle index of differential geometry, and physically indicates states of polarization.

"States of polarization" is a reference to Evans' cyclical basis e^a (a=1,2,3) he had introduced in case of a circularly polarized plane wave. But he has never explained how the vectors e^a (a=1,2,3) should be defined in case of more general electromagnetic waves. And a definition of a vector e^o is totally missing.

At last Evans attempts to relate the concept of free space to a certain duality concept (of his, not Hodge! See [2,3]):

Using the structure equations:

                T^a = D Ù q^a = d Ù q^a + ω^a_b Ù q^b ,         R^a_b = D Ù ω^a_b = d Ù ω^a_b + ω^a_c Ù ω^c_b                 (F.8)

of differential geometry, eqn (F.5) becomes:

                (D Ù ω^a_b) Ù q^b = ω^a_b Ù (D Ù q^b)                                                                                         (F.9)

one possible solution of eqn. (F.9) is:

                ω^a_b = − κ Î^a_bc q^c                                                                                                                 (F.10)

                R^a_b =    κ Î^a_bc T^c                                                                                                                 (F.11)

where κ is the wavenumber (which κ in case of a general wave?).

Eqns (F.10) and (F.11) mean that in free space, ω^a_b is the antisymmetric tensor dual to the vector q^c, and R^a_b is the antisymmetric tensor dual to T^c. These equations define free space electromagnetism free of gravitation influence (mass). In this case the spin connection and tetrad are duals and the curvature and torsion forms are duals.

The free space conditions (F.5) and (F.9) give rise to the problem of fulfilling them anyhow. Therefore Evans introduces a "duality" between the forms ω and q by eq.(F.10) and between R and T by eq.(F.11). However:

The 3-index Î tensors do not exist in 4D, see [2,3].

Nevertheless the non-existing 3-index Î^a_bc tensors are used in [1,App.G] to calculate representations of the field forms F^a (a=1,2,3) from the potential forms A^c (c=1,2,3), see [1,G.29). It must be noticed that neither F^o nor A^o appear in that calculations. All index summations are running over the indices 1,2,3, the index 0 is missing:

                F¹ = d Ù A¹ + ^g/₂ (ι₂₃ A³ Ù A² + ι₃₂ A² Ù A³)
                F¹ = d Ù A¹ + g A² Ù A³                                                                                                                 (G.29)
                F² = d Ù A² + g A³ Ù A¹
                F³ = d Ù A³ + g A¹ Ù A²
                                               

Eqns. (G.29) are the fundamental definition of the field tensor of electromagnetism in objective physics.

In these equations:

                g = ^κ/_A^(o)                                                                                                                                 (G.30)

and should not be confused with the determinant of the metric.

The rest of the book [1] is proliferation of the above ECE nonsense.

As we know, motion in galaxies is torsion dominated, but in the solar system, torsional effects are very weak.

However, according to the torsion hypothesis (F.3) one should expect high torsion at places with high em radiation, so e.g. in our solar system near the sun ...