Ubi materia, ibi geometria. | Lle mae 'na fater, mae 'na geometreg. |

Wo Materie ist, dort ist Geometrie. | Where there is matter, there is geometry. |

By John Surbat, A.I.A.S., Sept. 25, 2023

For much of the last century, almost no chemists or physicists possessed the mathematical skills (like knowledge of differential geometry) that are required for development of general relativity, so this task was left to mathematical physicists. There is an important difference in methodology between mathematicians and physicists. Mathematics deals with abstractions, while the physical sciences (physics, chemistry, and so on) ultimately need to maintain a connection to the physical world through experiment.

Mathematical physicists are mathematicians by formal education who have learned a bit of physics, but often without full understanding, so their perspective tends to be different from those whose academic education was in physics. Consequently, they failed to notice that the limitations of general relativity were due to the neglect of torsion, and even went as far as inventing dark matter as a fudge to prop up a failing theory.

Einstein was a physicist by nature, and (reluctantly) had to learn the mathematics needed for general relativity by seeking out the help of the greatest mathematical minds of the time.This took a great toll on him, as can be seen in the photos take around 1915, and he also developed lifelong stomach problems from the stress.

However, this mathematical environment started changing around the time when Myron Evans embarked on his early research, because progress in the analysis of infrared spectra now demanded advanced mathematics, and Myron relished this challenge!

However, when he started his journey toward understanding the nature of light and electromagnetism, Myron did not realize that the mathematics used to describe the translation and rotation of molecules caused by the electromagnetic fields of photons in the far infrared would find use in unifying gravitation with electromagnetism.This did not become clear until he was two thirds of the way through his research career!

Unlike mathematical physicists playing around with Einstein’s field equation, Myron was not free to invent new forces and unfounded interactions, like those with dark matter, because chemistry and chemical physics are explored by experiment, according to Baconian Principles (which were a first formulation of the modern scientific method). The Royal Society of Chemistry was founded on these principles in 1660.

Myron’s chemistry research, which included the use of far infrared spectroscopy, mathematical analysis, computer simulation and animation, and the use of the most powerful Control Data and IBM supercomputers, all in collaboration with the greatest teams of scientists in the world, is described in great detail in Introduction to the complete scientific works of Myron Evans.

Myron’s use of modern methods continued during the development of ECE theory, when the advent of powerful computer algebra systems allowed rapid evaluation of mathematical approaches, and their immediate integration into physical theories. Furthermore, computer methods were more than just a tool for integrating fundamental mathematics into the theory. They were also invaluable in enabling better visualization and interpretation of output data.

This was a continuation of Myron’s use of supercomputers for data analysis, simulation and animation in his early research. For example, while he was working on Modern Techniques in Computational Chemistry (MOTECC) at IBM Kingston, Myron had an opportunity to assess the newer and smaller computers, which were then starting to be able to cope with such computations.This was the dawn of the microcomputer era, when significant computing capabilities were becoming available at the local level. As ECE theory was being developed, personal computers and computer algebra systems were bringing this new third pillar of physics, computer analysis and simulation, into direct play. In particular, Maxima was used to enhance the integration of differential geometry, and to demonstrate the internal consistency of the geometric basis of ECE theory. By the time computer algebra started being used in ECE theory, the old IBM code had had its day and it was time to consign it to history.However, the new approach was much more adaptable and would now show its worth.

Horst Eckardt’s early experience with computers resembled that of Myron in certain ways. When Horst was pursuing his Ph.D. in the early 1980s, at the Institute of Theoretical Physics of the University of Clausthal-Zellerfeld, there were two kinds of theoretical physicists. One group thought that, for a reasonable theory, paper and pencil were sufficient, and abhorred automated numerical computations. The other group, which could be found in the department of theoretical solid-state physics, based its work on extensive numerical computations and used the most advanced computers. Both groups cultivated a certain mutual distance. Nevertheless, this was the time when effective numerical studies became possible using supercomputers, which established a third pillar of theoretical physics: computational physics. The first books on this subject also appeared around the same time.

The first calculations that Horst carried out were done on a TR440, a German mainframe, and on the same type of CDC machine that Myron used. The calculations in solid state physics were used effectively to compare theory with experimental data, for example photo electron emission experiments on bulk materials and surfaces, as well as X-ray photoelectron spectroscopy (XPS) data for higher-energetic excitations of core states. All of these computer programs were numerical codes based on an elaborate adaptation of solid-state physics to the requirements of numerical algorithms.

Computer algebra, which goes back to the sixties and seventies, enabled a quite different approach, since it allowed computations to be done symbolically. One of the first systems was developed under the name Macsyma at MIT, on behalf of the US Department of Energy (DOE). As it evolved, there was a branch that remained open source, called Maxima, and another branch that became a commercial product, called Mathematica. Both had identical initial components, but Mathematica has benefited from continuous development, and can perform functions that are not available in Maxima.

Maxima has been used in nearly all UFT papers, beginning with Paper 85. For early computations, Horst wrote extra Fortran code for solving equations, but this soon became unnecessary as built-in capabilities overtook requirements. Maxima offers a number of built-in numerical algorithms that allow, for example, Lagrange equations (including their relativistic forms, which were developed in ECE theory) to be solved and the results graphed.

The use of computer algebra increased the efficiency of ECE theory development enormously, and allowed hand-computation errors to be avoided completely. During their most productive period, Myron and Horst were able to publish a new paper (with new content) nearly every two weeks.

Mathematica has been used for calculations that were not possible with Maxima, for example, Douglas Lindstrom used it to solve the ECE vacuum equations in UFT Paper 292. In addition, fluid dynamics equations have been solved numerically using the finite element method (FEM) program FlexPDE (from PDE Solutions).

To aid in understanding the historical development of ECE theory, computer algebra code has been provided for a number of important UFT papers as well as for the ECE textbooks, and this code can be found on the “UFT Papers” page (by following the link under the “Scientific Work” tab on the main menu) of the AIAS website.