Progress in paper 439 – Overall path through Cartan geometry

paper439 Draft.

I finished the basic calculations of paper 439. When putting all parts of Cartan geometry together, we obtain a calculation scheme starting from a potential and ending in electric and magnetic fields of a given physical problem. That is within a framework of general relativity, therefore a novel approach. This is a great progress in ECE theory. Such a complete path had not been carried out before. One reason was that we had not compiled the Cartan formulas in this way so that (at least I myself) did not see that it is possible so straightforwardly. I had looked for this method for years
Another reason is that the Gamma connections can only be computed by computer algebra, and there is the ambiguity of how to choose the appearing constants. Setting them to zero gave an astonishing success in most cases I investigated.
(There remain some problems for complicated potentials. This has to be investigated further and is not addressed in the paper).

One result of the paper is that the B(3) field comes out for e-m waves in a quite natural way. It is lastly a consequence of the fact that the tetrad has to be a non-singular matrix in 4 dimensions. Myron would be delighted
There remains the problem that the Lambda spin connection is not antisymmetric. Either there is still an error in the calculations, or it has to do with the charge density. For e-m waves, which correspond to the e-m free field, all connections are antisymmetric.

I separated the Maxima code in a way that a library for all operations of Cartan geometry needed has been built. This should also be usable for the text book. In addition, this seems to be the begin of a generally usable code which Sean MacLachlan requested a long time ago.

I think we make progress in theory now. I appended the draft version of paper 439. The conclusion is still missing. I will give a perspective for the next papers where the new code path through Cartan geometry could be modified for solving new questions. For example,
1) when the e-m fields are given, what are the connections, and what is the potential (or tetrad)?
2) how can a resonant spin connection be obtained from a given e-m field?

Horst Eckardt

The work of Burkhard Heim

There was a German physicist, Burkhard Heim (1925-2001). Interestingly, he was first a chemist like Myron Evans, but later he turned to theoretical physics. He independently developed a unified field theory on basis of Einstein’s general relativity. Heim started with Einstein’s field equation and added an electromagnetic tensor to the gravitational field tensor. In this way he postulated a gravito-magnetic field. He tried to perform an experiment for proofing its existence but never got the funding for it. In ECE theory we¬† went a different way. We calculated the gravitomagnetic field of the earth and the angle of precession for a gyroscope carried in an orbiting satellite. This was a re-interpretation of a NASA expermint carried out with big financial effort. The results were in good agreement with the experiment. The gravitomagnetic field is effective only in planetary and cosmic dimensions.

Heim struggled with the problems of Einstein’s theory inferred by the approach that the energy-momentum tensor enters the theory as a given, external source. In ECE theory there are no sources, only fields. What appears as sources, are dense, localized fields. Therefore ECE theory solves this problem elegantly. There is no external energy-momentum. Heim also introduced torsion in his theory, which is not there when sticking at Einstein’s equations.

The quantization of Heim’s theory of general relativity was a main achievment. He quantized the theory by introducing a quantum of action. This is connected with a geometrical minimal area element. Heim succeeded in computing all masses of elementary particles, classifying their internal symmetries as observed in expensive accelerator experiments. He did not use adjustable parameters and developed analytical expressions which he inferred from geometrical conditions of the tensors he had developed. However, he had to use six dimensions to be succesful. His formulas were programmed at the German Electron Synchrotron in Hamburg and astonished the scientists: all masses were predicted very precisely. In recent times, only Ulrich Bruchholz succeeded in such computations; he used the Einstein-Rainich theory and a numerical method which is also parameter-free.

Heim’s late work concentrated on investigating the effect of the higher dimensions. The basic dimensions are three space dimensions plus one time dimension which are used in four-dimensional relativistic spacetime. These are quantitative in the sense that physical laws can be formulated mathematically and give numbers as results which can be compared with experimental findings. The 5th and 6th dimension are of different character. Their coordinates are time-like so that the six-dimensional space has three space-like and three time-like coordinates. The 5th and 6th coordinate are not quantitative in the usual sense. They describe structural and organisatotional processes that obey an abstract logic. This is the entry point of a non-material, mental, even spiritual world. Matter within three dimensions has emanations into these invisible dimensions so that it is impacted by these higher-level processes. This field transcends today’s science by far.

Dimensions higher than four can be described by Cartan geometry. This is a point where Cartan geometry merges with Heim theory and could be used to better understand the mathematical background, which Heim had to acquire by hard work and by applying complicated structural logic reasonning. For example, Heim used antisymmetric (or Hermitian) tensors, and antisymmetry is also a fundamental property of Cartan geometry and was investigated in great detail in the context of ECE theory.

Let’s look a bit closer to some details. Cartan geometry can be formulated for any dimension. Taking into account its physical interpretation (ECE theory), we have to consider the role of the Hodge-dual operator. This derives a Cartan form from another Cartan form. In four dimensions, the Hodge dual of a 2-form is a 2-form, therefore there is a certain symmetry in four dimensions, manifesting in Maxwell’s equations. When rising the dimension, a 2-form in 5 dimensions would give a Hodge-dual 3-form and in 6 dimensions a Hodge-dual 4-form. To understand the meaning of this asymmetry, we have to know that matter density is described by the Hodge dual of 2-forms. Therefore, if we stay at this description of matter in higher dimensions, matter obtaines additional degrees of freedom, in accordance with Heim’s theory.

The last point is an example how results of ECE theory could be useful to understand Heim’s ideas. He was so far ahead of contemporary science that he was not accepted by academia, a fate that also Myron Evans suffered.