Evans' Concept of "Free Space"

Gerhard W. Bruhn, Darmstadt University of Technology


In [1,Chap.19.2] (see also [1, App.K.6]) M.W. Evans defines the term "free space" by the validity of

        d Ù Fa = A(o) (Rab Ù Ab − ωab Ù Fb) = o ja = 0                     (19.4)

where Fa denotes the 2-form of the electromagnetic field. Since Evans generally assumes Fa = A(o) τa and Aa = A(o) qa we obtain the free space condition

        d Ù τa = 0                                                                                 (19.4')

or by referring to the 1st Bianchi identity [3] d Ù τa + ωab Ù τb = Rab Ù qb

... Eq.(19.4) is the experimental constraint:

        Rab Ù qb = ωab Ù τb                                                                 (19.6)

or free space condition.

However, none of the eqs.(19.4) and (19.6) transforms Lorentz covariantly as can be seen from the "free space condition" written as dÙτ=0.

Evans' concept of "free space" is not Lorentz invariant.

Evans continues:

Using the Maurer-Cartan structure equations:

        τb = D Ù qb                                                                              (19.7)

        Rab = D Ù ωab                                                                         (19.8)

it is seen that a particular solution of Eq. (19.6) is:

        ωab = − ½ κ Îabc qc                                                               (19.9)

However, Eq.(19.6) is an equation of 4D where no 3-index Î-tensor can be defined [2].

Thus, Evans' particular solution (19.9) doesn't exist.

In [1,App.J, Sect. J.1] Evans once more attempts to give a proof of his "Free Space Condition" that makes use of the non-existing 3-index Î-tensor in 4D.


Reference

[1] M.W. Evans, Generally Covariant Unified Field Theory, Aramis 2005

[2] G.W. Bruhn, Evans' 3-index Î-tensor
      http://www.mathematik.tu-darmstadt.de/~bruhn/Evans3indEtensor.html

[3] G.W. Bruhn, Some Confusion in Evans' "Cartan Geometry"
      http://www.mathematik.tu-darmstadt.de/~bruhn/Cartan-geometry.html

[4] G.W. Bruhn, ECE Theory and Cartan Geometry
      http://www.mathematik.tu-darmstadt.de/~bruhn/ECE-CartanGeometry.html

[5] G.W. Bruhn, Comments on Evans' Duality
      http://www.mathematik.tu-darmstadt.de/~bruhn/EvansDuality.html



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