Some remarks on paper #93 by M.W. Evans e.a.

August 20, 2008

Evans on his blog on 2008/08/11 praising the merits of the authors:

''. . . In paper 93 of the AIAS unified field series Stephenís suspicions were proven to be correct and the Einstein-Hilbert field equation was found to be mathematically incorrect. . . . ''

And on his blog on 2008/08/19:

''. . . A more thorough understanding of geometry was given by Cartan and is obtainable from the action of the commutator of covariant derivatives (papers 93 onwards). I proved the ECE dual identity in great detail in these papers, and it is this dual identity that finally disposes of any doubts that Einsteinís version of relativity is incorrect because torsion cannot be arbitrarily neglected in geometry. This amounts to disposing of half the geometry, and with hindsight is bound to go badly wrong. The dual identity sharply exposes the way in which it does go wrong. The great problem is that contemporary physics has lost its basic integrity to such an extent that it will not admit that it is pure mythology. . . .''

As mentioned already several times with regard to other Evans' papers the common paper #93 by Evans e.a. lacks from the following Evans' basic flaws:

(i) Evans asserts in Appendix 1 the ''dual transform'' of his field equation

                d Ù Fa = μo ja = Ao (Rab Ù qb − ωab Ù Tb)                                 (4)

to give

                d Ù F~ a = μo Ja = Ao (R~ ab Ù qb − ωab Ù T~ b)                      (7)

This assertion is ''proven'' in some detail in Appendix A of paper #93. We shall have a closer look at that Appendix below.

(ii) The ansatz of eqs.(2) and (3) for the electromagnetic field Fa in analogy to the Bianchi identiy (1) yields four fields F0, F1, F2, F3 since a=0,1,2,3 while in physics only one electromagnetic field F is observed. Evans never explained how the physical 2-form F could be connected with the vector valued 2-form Fa (a=0,1,2,3). This is an inadmissible type mismatch.

(iii) Erroneous use of a non-existing Î-tensor:

. . . A solution of Eq.(10) is:

                Rab = − ½ κ Îabc Tc,         ωab = − ½ κ Îabc Tc                      (13)

The eqs.(13) are 4-dimensional tensor equations. However, the tensor Îabc cannot be defined in 4-dimensional tensor calculus. Hence the eqs.(13) are null and void.

Comments on Appendix 1 of paper #93,
see also Evans' Duality Experiments:

Hodge dual transformation

. . .

The Bianchi identity

                d Ù Ta + ωab Ù Tb = qb Ù Rab         (wrong sign, index b missing)                             (A12)

is an identity between two-forms. So it remains true for:

                d Ù F~ a = A(o) (R~ ab Ùqb missing + ωab Ù T~ b)         (two signs wrong)             (A13)

because F~, R~, T~ are two-forms, antisymmetric in their last two indices (the suppressed indices μ,ν)

The wrong eqs. should read:

                d Ù Ta + ωab Ù Tb = qb Ù Rab = Rab Ù qb ,                                             (A12')

                d Ù F~ a = A(o) (R~ ab Ù qb − ωab Ù T~ b) .                                             (A13')

The above red marked errors are removable. However, not so Evans' misunderstandings of elementary differential geometry: Evans apparently believes that he could substitute the forms Ta and Ra in eq.(A12) by F~ a = A(o) T~ a and by R~ a instead of Ra. This argumentation is wrong:

Eq. (A12') is NOT an identity between arbitrary 2-forms Ta and Rab.

Evidently Dr Evans has not understood the basic idea of the 1st and 2nd Bianchi identity of differential geometry, which shall be repeated here for the reader's information:

The forms Ta and Rab have to be generated from arbitrarily given 1-forms qa and ωab by

                Ta := d Ù qa + ωab Ù qb                                 (Def I)


                Rab := d Ù ωab + ωac Ù ωcb,                         (Def II)

Then the defined 2-forms Ta and Rab fulfil the identities

                D Ù Ta = Rab Ù qb                                         (Id I)


                D Ù Rab = 0.                                                 (Id II)

Proof of (Id I)

                D Ù Ta = d Ù Ta + ωab Ù Tb
                            = d Ù (d Ù qa + ωab Ù qb) + ωab Ù (d Ù qb + ωbc Ù qc)
                            = 0 + d Ùab Ù qb) + ωab Ù d Ù qb + ωab Ù ωbc Ù qc
                            = (d Ù ωab + ωac Ù ωcb) Ù qb = Rab Ù qb .

Proof of (Id II)

                d Ù Rab = d Ù (d Ù ωab + ωac Ù ωcb) = 0 + d Ùac Ù ωcb) = ωcb Ù d Ù ωac − ωac Ù d Ù ωcb

                ωac Ù Rcb = ωac Ù (d Ù ωcb + ωcd Ù ωdb)   \
                                                                            Þ   ωcb Ù d Ù ωac − ωac Ù d Ù ωcb = ωcb Ù Rac − ωac Ù Rcb ,
                ωcb Ù Rac = ωcb Ù (d Ù ωac + ωad Ù ωdc)   /


                d Ù Rab = ωcb Ù Rac − ωac Ù Rcb ,


                D Ù Rab := d Ù Rab + ωac Ù Rcb − ωcb Ù Rac = 0 .