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

]]>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.

]]>I myself tried out tetrad matrix examples which have diagonal form. This means that the coordinate systems of the base manifold and tangent space are collinear. In terms of Cartan geometry, this means that there is a 1-to-1 correspondence between Greek and Latin indices. As a next step, I will develop the e-m field from torsion (which is simply a re-numbering of torsion tensor elements). The tetrad is the e-m potential, and a diagonal tetrad means that there is exactly one scalar potential and one vector potential. We will see if meaningful results will follow from this approach. ]]>

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Many thanks. To give a rough first answer to the question on why a central mass evolves, these data show that a mass m is captured by a dark star, so over time the mass of the dark star becomes larger and larger as it captures more and more objects. It is possible to use the same set of equations to study the trajectory of a photon of mass m captured by a dark star, or in orbit around a smaller mass M than that of a dark star. In the next note I will develop the theory of the trajectory of a photon of mass m in the vicinity of a dark star of mass M. In that problem m << M, for any M. Horst’s code is so powerful that it can be applied to any problem with the production of many new results. He plans toput it in the public domain with instructions on how to use it. The standard dogmatists have not advanced in fifty years. In fact, according to Hawking’s rejection of black holes in 2013 / 2014, they have gone backwards. The photon mass m is very tiny but as I showed in 1991 with the discover of the B(3) field, is identically non zero. Vigier pointed out the connection between B(3) and photon mass.

Fascinating results – congratulations both!!

Sent from my Samsung Galaxy smartphone.

]]>Coming too near a dark star is like stepping in to a coal pit. Any self consistent numerical method can be used and your method looks very promising.

Constant m Orbits

I like the name "dark star". There was a Russian SciFi film in the sixties where a spaceship came near to a dark star. The star was only visible by hiding the view to other stars and nebulae behind the object. Unfortunately the star had a devastating effect on the crew…

Coming back to notes 438(1,2): I found that with the parameters of the S2 star it is quite difficult to keep closed orbits when changing the central mass. One has to search new initial conditions for each parameter set, and numerical stability limits are quickly reached when increasing the central mass. Since we are planning to study different effects as

– relativistic vs. Newtonian theory

– constant and non-constant m functions

it seems to make more sense to use a model system with unified parameters. This will also give more numerical stability.

Am 23.04.2019 um 12:35 schrieb Myron Evans:

]]>Constant m Orbits

These are defined by Eqs. (1) and (2) and when solved give a precessing orbit. In the particular case m = 1 they give the precessing orbits of special relativity. It would be very interesting to investigate the properties of the precession as M becomes infinite and the dark star is formed. I use Michel’s appellation "dark star" (1783). For different values of constant m the orbit departs more and more from special relativity because it is an orbit of generally covariant m theory. The complete orbit equations are Eqs. (7) and (8) of Note 438(1). It would be very interesting to investigate what happens to the orbit as M approaches infinity and the dark star is formed. It is already known that the complete orbit equations spark off new physics of many different kinds. In order not to waste the astronomical data on the fictitious "black holes" they can be reinterpreted in terms of the dark star and m theory. The unhealthy obsession or fixation on black holes is due to the fact that funding depends on finding them, even though they do not exist. The same type of idee fixe is present in the obsessions about the Higgs boson and gravitational radiation. This is the age hold habit of forcing nature into anthropomorphic preconceptions – the opposite of Baconian science.

These are defined by Eqs. (1) and (2) and when solved give a precessing orbit. In the particular case m = 1 they give the precessing orbits of special relativity. It would be very interesting to investigate the properties of the precession as M becomes infinite and the dark star is formed. I use Michel’s appellation "dark star" (1783). For different values of constant m the orbit departs more and more from special relativity because it is an orbit of generally covariant m theory. The complete orbit equations are Eqs. (7) and (8) of Note 438(1). It would be very interesting to investigate what happens to the orbit as M approaches infinity and the dark star is formed. It is already known that the complete orbit equations spark off new physics of many different kinds. In order not to waste the astronomical data on the fictitious "black holes" they can be reinterpreted in terms of the dark star and m theory. The unhealthy obsession or fixation on black holes is due to the fact that funding depends on finding them, even though they do not exist. The same type of idee fixe is present in the obsessions about the Higgs boson and gravitational radiation. This is the age hold habit of forcing nature into anthropomorphic preconceptions – the opposite of Baconian science.

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