I was asked how charge and mass of matter is handled in Heim’s generalized field theory.

Heim uses Einstein’s field equation and defines a (generalized) energy-momentum tensor for this purpose, which contains electromagnetic and gravitational components. The gravitational components are defined in analogy to the electromagnetic components and contain the gravito-magnetid field, for example. The problem, however, is that the energy-momentum tensor contains charge and mass density terms. In this way, Einstein’s field equations become dependent on explicit sources. This leads to problems of several kinds, in particlular a physical interpretation problem of sources in general relativity, and, as far as I know, abolition of energy conservation.

Heim tries to avoid these problems by assuming that sources are nothing else than “compacted” fields. I cannot say how he treats this formally. Evans avoids this problem in his ECE theory in the same way, but Evans does not use Einstein’s field equations, he uses the geometry equations of Cartan instead. This approach avoids all the problems that Einstein had. There are no sources a priori but only fields, as Heim assumed. In ECE theory, the equations of Cartan geometry can be written in a form equivalent to Maxwell’s equations, for electrodynamics as well as for gravitation. By comparing with Maxwell’s original equations with chages and currents, one can define charge and current terms, which consist of field terms mixed with curvature and torsion terms. The same can be done for gravitation. Unification happens via geometry. If a charge is there, we have electromagnetism, if not, we have gravitation only.

Heim and Evans agree in the point that they do not need sources in their theories. Matter is a “condensed field” of general relativity and spacetime itself may be interpreted as a vacuum or aether field being everywhere. To my understanding, Heim’s theory could be put on a much clearer ground if it would be based on Cartan geometry rather then Einstein’s field equations.

Considering matter as condensed fields leads to quantum mechanics in a straight line, avoiding extra concepts like quantum electrodynamics and similar. According to Evans, all physics is geometry.