Short comments on M.W. Evans' web-paper #116(2)

Hopeless! He will never learn it!

by G.W. Bruhn, Darmstadt University of Technology

July 15, specified on July 17, 2008

1. A New Math flaw

After just having criticized Evans' New Math rules of tensor calculus I came across Evans' most recent paper #116(2). On first glance I saw the following calculation:

. . .
                ωκμb = qκa ωaμb                                                                 (20)

Finally use:
                ωκμb T~bμν = qλb qbλ ωκμλ T~λμν = 4 ωκμλ T~λμν                 (21)

The index λ appears four times on the right hand side while at most twice is admissible. To write this flaw in ''slow motion'' and by means of brackets and avoiding four times appearing of the index λ by means of primes:

                ωκμb T~bμν = (ωκμλ qλb) (qbλ' T~λ'μν) = . . .

Now we can drop the brackets: Using qλb qbλ' = δλλ' yields

                ωκμb T~bμν = ωκμλ δλλ' T~λ'μν = ωκμλ T~λμν                                 (21')

differing from Evans' result (21) by a factor 4. This implies that the factor 4 must be dropped in the eqs. (22) and (28). And I ask you:

What is a factor 4 under friends?

However, someone who cannot distinguish between between 1 and 4 should better change his profession. Doing math is not his best ability.

2. The serious flaw

Evans' main problem and unproven claim is the validity of the dualization of the 1st Bianchi equation:

                DÙTa = RabÙqb         (1)         ?Û?         DÙT~a = R~abÙqb         (23)

What he correctly shows is not the same and hence useless:

                D Taνρ] = Ra[μνρ]         (4)         Û         Dμ T~aμν = R~aμμν         (10)

and (under unprovable assumption of the dualized Bianchi eq. (23))

                D T~aνρ] = R~a[μνρ]         (24)         Û         Dμ Taμν = Raμμν         (27)

The gap (1)?Û?(23) cannot be closed. The transition from Ra[μνρ] to R~a[μνρ] would require a common Î factor which does not exist due to the changing lower index positions. I had pointed to that flaw already in a former remark but without any effect on Dr. Evans. There are guys who do not learn from their faults.