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.