Electromagnetic fields

Three consequences of a meeting

Document ISBN-978-2-36923-031-1 see below, after the comments; provisory v3, 17 September 2020, 10 pages.

The context

My previous work “A. Einstein versus W. Heisenberg”, recently retitled “When Christoffel meets Heisenberg” (for now, only in the French language), represents the first step in a global new approach.

The theory of deformed tensor products starts its analysis with a peculiar point of view on what should be preserved (syn: invariant) for observers living in separate frames. The Planck' limit is added to the prerequisites on which A. Einstein' theory of relativity is built. The two requirements are mathematically and simultaneously compatible with the help of a specific constraint.

Following that way of thinking I explore in an unprecedent manner the links between E. B. Christoffel’ work [01; 1869], A. Einstein’ theory [02; 1916], W. Heisenberg’ uncertainty principle [03; 1927] and E. Cartan’ approach on metrics [04; 1933].

It is known that E. Cartan’s considerations on the preservation of elements of length (the ds2) [05; 1922] follow a different logic than A. Einstein’ ones. Focusing attention on the concept of exterior product, they nevertheless yield the same field equations, in automatically including a “cosmological constant”.

My alternative analysis is maybe of importance since both known approaches (Einstein’s theory and Cartan’s approach) are yet in competition when one tries to determinate which one describes the reality with the best accuracy. Short said: until now, the experiments reveal no drastic differences between both intellectual approaches and this fact suggests a question: “Are these theories the two sides of the same glove?”

The electromagnetic fields.

My analysis brings a new generic formulation for any EM fields in a context where particles are moving in respecting the Lorentz-Einstein law of motion “at the quantum limit”. These fields have remarkably interesting and, sometimes strange, properties which I am exploring here and in diverse documents.

Discussion.

The validity of my theory depends directly on the one of the covariant versus of the Lorentz law. A relatively recent analysis of that law has been done in [06]; it should guide the critics concerning my work.

Bibliography:

[01} Christoffel, E. B. : Über die Transformation der homogenen Differentiale Ausdrücke zweiten Graden; Journal für die reine und angewandte Mathematik, pp. 46-70, 3 Januar 1869. This document can be studied at the University of Göttingen (Germany).

[02] (a) Einstein, A. : Die Grundlage der allgemeinen Relativitätstheorie; Annalen der Physik, vierte Folge, Band 49, (1916), N 7. (b) Einstein, A. and Minkowski, H.: The principle of relativity; translated in English by Saha, M.N. and Bose, S.N. published by the university of Calcutta, 1920; available at the Library of the M.I.T.

[03]Heisenberg, W.: (1927), "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik".

{04] Cartan, Elie. Les espaces métriques fondés sur la notion de d'aire dans ``Actualités scientifiques et industrielles'', numéro 72, exposés de géométrie publiés sous la direction de monsieur Elie Cartan, membre de l'institut et professeur à la Sorbonne; Paris, Hermann et Cie, éditeurs, 1933.

[05] Cartan, E. : Sur les équations de la gravitation d'Einstein ; extrait du journal de mathématiques, 1922, Fasc. numéro 2, 74 p. édité par Gauthier-Villars et Cie, libraires du bureau des longitudes de l'école Polytechnique, Paris (1922).

[06] The motion of point particles in curved spacetime, arXiv:1102.0529 [gr-qc].

 

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event Date de dernière mise à jour : 18/10/2020

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