Wikipedia Entry on Spacetime Torsion

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In this case wikipedia incorrectly describes spacetime torsion and curvature as being equivalent. This is incorrect, as shown in a textbook such as S. P. Carroll, “Spacetime and Geometry: an Introduction to General Relativity” (Addison Wesley, New York 2004), chapter three. Many of the papers in the attached overview deal with the precise definition of curvature and torsion. These are the same definitions as used by Prof. Carroll, whose book is based on graduate courses at Harvard, UC Santa Barbara, and Chicago. The torsion and curvature are both generated by the commutator of covariant derivatives acting on a tensor of any rank in any spacetime. In the elegant notation of differential geometry they are denoted R for curvature and T for torsion. As has been known since the nineteen twenties, they are defined by the Cartan Maurer structure equations:

T = D ^ q
R = D ^ omega

where D ^ is a certain type of operator, q is the Cartan tetrad, and omega is the spin connection of Cartan. It is seen immediately that R and T are not equivalent. They are related by the Cartan Bianchi identity:

D ^ T := q ^ R

and the Cartan Evans identity

D ^ T tilde := q ^ R tilde

where tilde denotes Hodge dual. The operator D ^ is defined as:

D ^ := d ^ + omega ^

where d ^ is the exterior derivative of differential geometry. These basic definitions and theorems are very well known, but Wikipedia attributes them to a kind of Russian fraud of the nineteen eighties. The truth is that wikipedia is itself well known by now to be organized, abusive fraud organized by non-scientific elements who hide behind anonymity. It is well known to indulge in personal animosity, and to try to destroy reputations. I advise that concerned readers construct their own blogs and their own anti-wiki’s over the next few years. At present this blog is among the most powerful in theoretical physics, as the attached feedback demonstrates. The attached measure of intense interest in ECE is a unique data set, no other theory has been tested with such meticulous precision over such a length of time. So we know clearly adn with accuracy that the false authority of standard physics (in all its manifestations) has been rejected overwhelmingly by professional scientists. The same should happen to wikipedia, otherwise we have an ugly electronic dictatorship corrupting science.

OVERVIEW_OF_ECE_THEORY.doc

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