Subject: Fwd: note 111(2)
Date: Wed, 30 Apr 2008 04:35:39 EDT
Good idea. In fact this is the key point, a rotation of any lien element generates torsion. For example there are torsion generators around each axis because there are rotation generators around each axis. The most general definition of tetrad is used – the matrix linking two vectors. The R parameter is related to the shell radius. In all these precision tests of general relativity there is the problem of identifying the alpha parameter of Schwarzschild (1916) with 2MG / c squared. This is actually a curve fitting exercise, not a prediction, because the alpha parameter for the vacuum comes from pure geometry as you know (the Ricci flat solution). So the purely geometrical alpha was FITTED by othe rpeople (not Schwarzschild himself) to 2MG / c squared to reproduce Newtonian dynamics. There is no prediction of Newtonian dynamics in Schwarzschild’s original 1916 vacuum solution. Similarly the commutators of two Lorentz boost generators give a torsion generator. The Christoffel connection gives zero torsion. So there is an internal contradiction in using a Christoffel connection in general relativity whenever there is rotational motion. Also in paper 93 of course we found a basic internal contradiction in the EH geometry, after an exhaustive analysis. I recall that you inferred this contradiction independently in the context of the Lense Thirring effect. If the standard modellers try to assert that rotation does not generate torsion, then they are forced back on asserting arbitrarily that a tetrad can only be used in centrally directed gravitational theory. This is counter argued by noting that the Cartan geometry is valid for any tetrad, i.e. any tensor linking any two vectors.
To the general readership: this is what I mean by an inductive discussion of a thread of thought. This is how all the ECE papers were developed. Sometimes a newspaper article or similar is useful, but the inductive approach to such an article is to apply ECE theory to it, because after all, we are developing ECE theory. Colleagueas are of course encouraged to apply ECE theory to any problem they may note in any kind of literature. At that point I can enter into an inductive discussion. It is especially important at present to apply ECE to new energy devices in a rigorously systematic manner, and this is expemplified in the papers on such devices on _www.aias.us_ (http://www.aias.us) .
In Eq. (2) which refers to the original papers of the Lense Thierring effect: Is R the radius of the rotating shell? I cannot see that this parameter should have any effect, except it defines the total mass or mass density. Consequently, your derivation does not need such a parameter. From the comparison of results (eqs. 21/22) one sees that R must be in the order of coordinate radius r, for example when looking at the poles of the sphere (sin theta = 0). If this comparison is meaningful at all depends on the interpretation of R, I think. Perhaps it would make sense to write down the general formulas for obtaining the rotational torsion from a given transformation matrix (i.e. tetrad). You did it already in part in paper 109. Or better to start with a given symmetric metric as you already proposed. The steps could be automised then.