Comments on an Article of L. Felker on MWE's GCUFT

by Gerhard W. Bruhn, Darmstadt University of Technology

Recently L. Felker broadcasted an article "Einstein Was Right!?" to the AIAS fellows to be submitted to SCIENTIFIC AMERICAN. This article (quoted here by [1a]) is a revised version of the web article [1]. Both are excerpts from Felkers book manuscript [2] where he tries to "explain" MWE's GCUFT.

A letter of recommendation from EMyrone@aol.com followed on We, July 6 2005 09:12

Subject: for AIAS Sites : Article by Lar Felker
for AIAS Sites
This is a well written and comprehensible article by Lar Felker and with his permission I think it deserves a box of its own on the www.aias.us and www.atomicprecision.com websites. I see no reason for rejection, rejection would show that the editor is being unreasonable and censorious in view of the fact that the whole physics world has accepted the theory. This should be unsurprising because the whole physics world has accepted Cartan and Riemann. I am not saying that the unified field theory is everything. Far from it, but its mathematical structure gives the mathematical structure of all the major equations of classical and quantum mechanics. There is plenty of room for interesting debate about the meaning of the tetrad wavefunction and many other topics.
In humour, from Wilde's "The Importance of Being Earnest": "I dislike argument, argument is vulgar and often convincing."

MWE

A similar recommendation from MWE exists for Felker's book. Thus, we may consider L. Felker as MWE's authorized speaker:

L. Felker's errors are MWE's errors.

Confirming this L. Felker tried to defend his master in [3], where a critical review by Chronostalker on the mathematical prerequisites of MWE's GCUFT had appeared.

Following Oscar Wilde's advice from above we shall be so vulgar as to discuss here two parts of L. Felker's article:

Felker, [1a; p.14] (cf. also [1; p.13] and [2; p.78]):

The tetrad is a matrix defined qaμ where qaμ = Va/Vμ is built of 16 elements which are ratios of vectors. Va is a vector in the moving frame and Vμ is a vector in the real spacetime of our universe.

Comment Bruhn:

The author

(a) has neither understood the tetrad and vector concepts
(b) nor knows the elements of vector algebra.

ad (a): A tetrad is a basis of four (tetra) vectors ea of the tangent space at some point P of a manifold, not to be confused with the coefficient scheme (qaμ). It's a substitute of the coordinate tangent vectors ∂μ := ∂/∂xμ at P. The coefficients qaμ appear in a linear representation of the basis vectors ∂μ relative to the vectors ea; the representation of a given tetrad {ea} by a matrix (qaμ) depends on the coordinate system:

(1)                 ∂μ = qaμ ea .

This requires that the coefficients qaμ form a nonsingular matrix (qaμ), the inverse of which is denoted by

(2)                 (qμa) := (qaμ)−1.

A given vector V of the tangent space at P can be represented relative to the basis {ea}

(3)                 V = Vaea

and relative to the basis {∂μ} as well

(4)                 V = Vμ∂μ .

From eqns. (1), (2) follows immediately

(5)                 Vμ = qμaVa

and

(6)                 Va = qaμVμ .

By calling Va and Vμ "vectors" Felker confuses vectors with their components. The same holds for calling the coefficient scheme (qaμ) a tetrad: The tetrad is the system of vectors

(7)                 ea = qμa ∂μ .

ad (b): Felker's "equation" qaμ = Va/Vμ ignores that the equation (6) cannot be resolved for qaμ by division by Vμ since its right hand side

(8)                 qaμVμ = qa0V0 + qa1V1 + qa2V2 + qa3V3 .

is - due to summation convention - a sum of four summands and not a single term.

Remark A quite similar error can be found in one of Evans' "proofs" of the tetrade postulate reviewed in [4].

Felker, [1a; p.21] (cf. also [2; p.76]):

Any asymmetric matrix can be broken into its symmetric and antisymmetric parts.

                                qaμ = qaμ(S) + qaμ(A)

                          qaμ = (symmetric) + (antisymmetric)
                                = gravitation + electromagnetism
                                = curvature + torsion
                                = distance + turning

Comment Bruhn:

This rule does not hold if both indices, here a and μ, are of different type: The index a refers to the tetrad basis {ea}, while μ refers to the coordinate basis {∂μ} as is indicated by latin and greek letters and their different positions (up and down): Let Q:=(qaμ) and denote Q' the transposed matrix. Then, as is well-known, the matrices Q(S) := ½(Q + Q') and Q(A) := ½(Q − Q') are the symmetric part and the antisymmetric part of Q respectively. However, Q(S) and Q(A) fail to be tensors in general. Hence the above physical conclusions are complete nonsense.

Conclusion

L. Felker has proven to be mathematically unable for defending his master's GCUFT. So MWE himself is challenged to intervene, e.g. by giving a contribution in Chronostalker's Forum [3].

References

[1]        John B. Hart and Laurence G. Felker: The Tetrad and Symmetry in the Evans Unified Field Theory
                http://www.aias.us/Comments/Art%202%20of%20X%20Tetrad%20and%20Sym%20in%20Evans%20UFT.ZIP

[2]        Laurence G. Felker: The Evans Equations of Unified Field Theory
            Descriptive Book for All Audiences (2.8 MB)
                http://www.atomicprecision.com/new/Evans%20Equations%20of%20Unified%20Field%20Theory%20Rev%203.pdf

[3]        Chronostalker Forum:
                http://opensys.blogsome.com/2005/07/01/

[4]        G.W. Bruhn: M.W. Evans' New Proof for the Tetrade Postulate
                http://www2.mathematik.tu-darmstadt.de/~bruhn/New_Tetrad-Proof.htm