Excellent Joke!
Evans confirms his New Math Equation 1 = 4

Gerhard W. Bruhn, Darmstadt University of Technology

20 Oct 2008

Text colors: Evans in black, his flaw in red, Carroll in green, my comments in blue

Use of the Kronecker Delta in Cartan Geometry

Subject: Use of the Kronecker Delta in Cartan Geometry
Date: Sun, 19 Oct 2008 05:54:30 EDT

The definition used in Cartan geometry is given by Carroll in his chapter three:

q sup mu sub a q sup a sub nu = delta sup mu sub nu ЧЧЧЧЧЦ (1)

Note that a factor 4 does not appear by definition. The notation means that the right hand side of eq. (1) is 1 when mu is the same as nu, and is 0 otherwise.

OK. Carroll's original equation is with e instead of q

e^μ_a e^a_ν = δ^μ_ν , e^a_μ e^μ_b = δ^a_b . (3.116)

which means that the matrices (e^μ_a) and (e^a_ν) are mutually inverses: The matrix products yield (e^μ_a)(e^a_ν) = I = diag(1,1,1,1) and (e^a_μ) (e^μ_b) = I = diag(1,1,1,1) as well.

Note that Eqs.(3.116) tacitly make use of the Einstein summation convention that wrt double indices (a / a and μ / μ respectively) must be summed automatically.

And now Evans continues erroneously

. . . So:

q sup nu sub a q sup a sub nu = 1 ЧЧЧЧЧЧ- (2)

i.e.

q^ν_a q^a_ν = 1 .

which is a wrong conclusion: Substituting μ with ν additionally implies Einstein summation over the double index ν:

q^ν_a q^a_ν = δ^ν_ν = δ⁰₀ + δ¹₁ + δ²₂ + δ³₃ = 1 + 1 + 1 + 1 = 4.

Evans erroneously ignores here the Einstein summation convention,
which is generally applied in tensor calculus.

Instead of applying the rules of tensor calculus according to the textbooks Evans complains about ''Bruhn's cynical lies'':

. . . that Bruhn very cynically contrives lies. The Bruhn lie-site put in a factor 4 in order to cause confusion. The fact that some standard editors are in collusion with Bruhn means that the general public must do something to stop funding these people. In GCUFT5 the correct mathematics will be given, as in GCUFT1 to GCUFT4. Every single entry in the lie-site is meant to cause confusion and to misrepresent my work or anyone who works with me. The general public is asked to pay for this lie-site. I block Bruhn and completely refuse to be drawn into any correspondence with him.
Let us call a spade a spade.
Civil List Scientist

OK. Let us call a spade a spade:

ECE ''theory'' is nonsense from GCUFT1 to GCUFT5.
That all is based on Evans' New Math,
i.e. on a long list of rather trivial but far reaching math errors that were reported on this site.

An application of Evans' above-mentioned fallacy was already criticized in that Commentary.

Complement on Oct 25 2008:

Now Evans lies himself!!! Or Carroll???

In GCUFT 5 Chap.12 we read on p.6

УEvans' Chapter12Ф Ч 2008/10/17 Ч 18:17 Ч page 6 Ч #6

. . .

derived from the tetrad normalization [13]:

q^a_νq^ν_a = 4 (12.17)

[13] is Carroll's book.

Excellent Joke! Evans confirms his New Math Equation 1 = 4

Gerhard W. Bruhn, Darmstadt University of Technology

Use of the Kronecker Delta in Cartan Geometry

eμa eaν = δμν , eaμ eμb = δab . (3.116)

qνa qaν = 1 .

qνa qaν = δνν = δ00 + δ11 + δ22 + δ33 = 1 + 1 + 1 + 1 = 4.

Evans erroneously ignores here the Einstein summation convention, which is generally applied in tensor calculus.

OK. Let us call a spade a spade: ECE ''theory'' is nonsense from GCUFT1 to GCUFT5. That all is based on Evans' New Math, i.e. on a long list of rather trivial but far reaching math errors that were reported on this site.