## PS To Karel , Paper 62

Subject: PS To Karel , Paper 62
Date: Tue, 31 Oct 2006 05:55:19 EST

Paper 62 develops the Lemma and applies it to the electromagnetic and fermionic fields. In particular a cross check is given eq. (7) of paper 62, one of many cross checks given in volume two in particular. In that volume the tetrad postulate was derived or illustarted in a number of ways, and the Lemma derived in two ways. In chapter 17 of voluem one you can see teh taterad postulate at work in teh foru appendices. Without the tetrad postulate Cartan could not have developed Riemann geometry into Cartan Riemann geometry as he did in Comptes Rendues in 1922. This is all very well known. There may be other ways to derive the Lemma, it is a simple inference form the tetrad postulate, which is itself a simple statement – a complete vector field of any kind must be independent of the way it is expressed. For example, in 3-D Euclidean space a vector field in Cartesian coordinates is the same vector field as in spherical polar coordinates or any curvilinear coordinate system in Euclidean spacetime. In Cartan Riemann geometry, this basic fact is known as the tetrad postulate. You produced another cross check on the Lemma, so this is very good thinking! As you can see from section 3 of this paper the Lemma is a generally covariant wave equation, as you infer. It reduces to the Dirac equation in the limit when the fermion becomes a free fermion, (eq. (26) of paper 62. A free fermion is unifluenced by gravitation, so this is the Minkowski limit. This defines the finite volume of a particle in general relativity (volumes one – three and papers). There are no point particles or point charges or any singularities in general relativity, so the need for renormalization in q.e.d or q.c.d., or any quantum field theory, is removed by ECE theory. This is one of the major advances of the theory as you presented in your seminar. I think that this is a very good seminar, well presented and encourage the presentation worldwide of such seminars.