The oldest version of the textbook I have is from 2017, containing chapters 1 and 2. So I probably began writing in 2016. I took longer breaks in-between, because ECE theory made great progress during that time and I concentrated on working for new articles with Myron.
When you want to explain a subject in an understandable way, you have to have a full understanding of the content first. Otherwise your arguments will not be convincing. I decided that the book should give a self-contained introduction to ECE theory. So I had to begin with Cartan geometry and studied the book of Carroll on differential geometry first. Although Carroll’s book is not written in a strict formal manner for mathematicians, It was still too verbose for my purpose. Therefore, I condensed from it the content that was actually important for ECE theory. This took a longer time.
For the single chapters, I went through the AIAS papers and was surprised at the number of details we had found out. For many subjects, there was a development until the final structure and content was evident. I had to evaluate that and tried to concentrate on the final results. For some subjects, for example the rotation of relativistic line elements, there was no final conclusion. I had to select a final result for each subsection and bring them together under a common view. But this was an exception.
In other cases, I found some additional results by re-thinking the problems that Maron and myself had solved in the AIAS articles. Among them are some break-throughs:
– improved unified description of fluid gravitation
– the intrinsic structure of fields (aether theory)
– self-consistent, parameter-free description of light deflection by matter
– a final consolidation of photon mass with the theory of relativity
– cosmology by aether density effects, different behaviour of matter and radiation
– new examples for the gravitomagnetic field
– new method of energy from spacetime by momentum transfer
Viewd from a retrospective, we have extended the spectrum of using methods of classical physics a lot. In particular, Lagrange theory has turned out to be applicable in fields nobody had suspected, for example cosmology. Perhaps this is the greatest break-through, althoug energy from spacetime is more practically important, as soon as viable technologies have been developed.
I am thinking on an improvement of m theory. Maybe that the velocity vector is used in the gamma factor in an uncomplete form. This would lead to a modification of the equations of motion. If this gives meaningful results, I will describe this in a new paper.
Currently I am working out the intrinsic structure of fields in more detail, as Kerry had proposed. There are some ambiguities about which I have to think further.
I hope to start Volume 2 of the textbook early next year.
Horst