## Myron's New Questionable Developments of Cartan Geometry

### Gerhard W. Bruhn, Darmstadt University of Technology

Evans wrote on his blog Key Difference between now and 2003 Date: Tue, 18 Dec 2007 09:30:30 EST

Maxima shows that R~ Ù q is not zero in general for a Christoffel connection. This is the result of computer algebra for several line elements (see paper 93 onwards). This result is incompatible with the fact that for a Christoffel connection T~ vanishes. In 2003 it was thought that given the Bianchi identity:

D Ù T := R Ù q

one could get EH simply by assuming T = 0, giving R Ù q = 0. The latter is what we call the Ricci cyclic equation, almost always mis-named the first Bianchi identity. Maxima gives R Ù q = 0 for all valid line elements, but gives R~ Ù q not zero in general.

No miracle, Myron!
In 2003 you were right: T = 0 implies 0 = D Ù T = R Ù q .
However, in 2007 you "proved"

D Ù T = R Ù q         Þ         D Ù T~ = R~ Ù q

which is WRONG [3], [4]. Correctly you may conclude

T = 0         Þ         T~ = 0         Þ         D Ù T~ = 0 .

However, since your assertion D Ù T~ = R~ Ù q is wrong, you CANNOT conclude

### D Ù T~ = 0         Þ         R~ Ù q = 0.

Hence R~ Ù q ≠ 0 in general in accordance with your Maxima computer result.

So EH theory has collapsed due to this result of the computer.

### Of course, NOT! Myron, YOU have disproved yourself − by Maxima and computer!!!

The rest of Evans' blog note is irrelevant as starting from wrong assumptions:

Progress can only be made with a theory such as ECE that correctly uses a NON Christoffel connection. I continue to hope for elementary scientific conduct from the standard model crowd. Unfortunately anthropomorphic unpleasantry occurs when a well known theory is developed. After all, we are developing EH, not discarding it or trying to make a mess of it. To translate into tensor notation:

R~ Ù q         translates to         Rκμμν         (???)

which is essentially impossible (or at best extremely laborious) to work out by hand. It is seen that it is related to the EH Ricci tensor, but is not the same as the EH Ricci tensor. Maxima found that it disappears self consistently in Ricci flat spacetimes. So with all these checks one can have great confidence in one’s work, especially with the help of Maxima, introduced to us by Tom Widlar and meticulously coded by Horst Eckardt and his research group at the Siemens Company. We now have plans to make Maxima available on the _www.aias.us_ (http://www.aias.us) website.

Civil List Scientist

### Myron's dilemma

Evans is here in a certain dilemma: In his blog note [2] he announces a "New Approach to General Relativity", based on the "dualized" Bianchi identity. However, that dualization is wrong, see [3], [4]. Thus, this announced new approach to GR is pure nonsense. And if his conclusion in [3] were true then the approach could not yield any new results on GR since then the dualized Bianchi identity were no independent equation that could change the GR.

### References

[1] M.W. Evans, Key Difference between now and 2003

[2] M.W. Evans, New Approach to General Relativity

[3] G.W. Bruhn, Evans' Central Claim in his Paper #100

[4] W.A. Rodrigues, Differential Forms on Riemannian (Minkowskian) and Riemann-Cartan Structures
and some Applications to Physics
, arXiv