E. B. Christoffel revisited
© Thierry PERIAT : Texts, ideas and photos
The search for unity inside theoretical physics, especially between the general theory of relativity (GTR) and the quantum approach is soon a hundred years old fundamental quest. It has occupied many brilliant brains and it does occupy them yet. Therefore, my tittle on the homepage may sound a little bit pretentious. Did I really discover the missing path?
I am not sure because, as Descartes has teach it centuries ago, the doubt is a good guide for the rationalistic and scientific ways of thinking. If I did, my presentation is the most simplified and caricatural one. What is the main idea?
W. Heisenberg has indicated to us that positions and speeds form two separate and independent sets of observables. He also suggested that energies and lapse of times were following a similar logic. There is for now, no operator representing the time, and, at least at a technical level, this absence is blocking the progression.
Therefore, I decided to consider the simplest transposition of that suggested interdependence: delta energy. Delta lapse of time must be at least equal to a fraction of the Planck constant. The situation realizing the exact equality is labelled as “quantum limit”. After that, considering the physical units involved in such a relation, I realized that it was possible to inject any force and especially the Lorentz force density into it. I also understood that that Heisenberg’s relation was able to yield a polynomial of degree two allowing both, the simultaneous intervention of my extrinsic method and the one of E. B. Christoffel’s historical work on the preservation of these polynomials. This is the central skeleton of my toy-approach.
For sure, it must be fine tuned and generalized. But if it is the right way connecting the two main pillars of the modern theoretical physics, this is already a scoop and an essential stone for future progressions. We may say that Heisenberg was born a little bit too late. If he could have confronted his thoughts with the calculations of Christoffel’s, he would certainly have suggested a similar idea. The preservation of elements of lengths appear to be a consequence of the preservation of the quantum limit (see definition above in that text). This conclusion will certainly not receive any positive echo in the scientific community; just because it is not academic, not politically correct and contradicting the main stream. Or because it is simply false? You are deciding. Just let me know your opinion in me. Thanks.
Everybody knows Einstein's master work (The general theory of relativity - GTR). Only few specialists remember exactly how it has been built. In that document I exhume E. B. Christoffel's work [ (1869)] which is (i) continuing Riemann's work (1864) and (ii) one of the mathematical pillars of the GTR. I demonstrate that that work can be applied either for the preservation of the ds2 (the historical case) or for the invariance of Planck's limit (see def.4.1) as well, without being obliged to be in contradiction with the solutions of the GTR. It turns out that, in doing so, I just preserve the inverse of a non-degenerated 4D metric. The bonus of that demonstration is a new family of electromagnetic fields (see equ.22) depending on that metric and on its variations (see further developments on the next page).
The v5, 16 September 2018 is on www.researchgate.net/profile/Thierry_Periat
The v4 has been proposed to the review General Relativity and Gravitation but not approved for publication
© Thierry PERIAT, 02 December 2018.
 By the way, you may want to discover more on this difficult thematic in exploring the and its diverse consequences step by step (another exploration extending the GTR).