Quelques rêveries cosmiques cosmoquant-fr


Titre : Particules idéales, vides de Maxwell et cordes élastiques classiques.

Auteur : © Thierry PERIAT.

Immatriculation : ISBN 978-2-36923-140-0, EAN 9782369231400.

Langue : Française.

Nombre de pages : 18.

Date de parution : 22 juillet 2022.

Document : en cliquant sur le lien, un document .pdf s'ouvre dans une fenêtre externe ; uniquement sur ordinateur fixe.


Nom du fichier : Isbn 978 2 36923 140 0 periat 2022

Taille : 348.78 Ko



Ce document expose les raisons justifiant d'étudier les produits vectoriels éventuellement déformés et parfois décomposés non-trivialement.

Il le fait au travers de l'introduction de la plus simple mouture de ce concept dans un domaine se situant à l'intersection de deux disciplines physiques :

(i) l'électromagnétisme, loin des sources, et

(ii) la cosmologie.

Il démontre la compatibilité de la démarche avec le concept de filament cosmique au demeurant mis en exergue par certaines simulations du cosmos.

Vers la tête du chapitre "Cosmologie quantique".

GB/USA version

Title: Cosmology.

Author: PERIAT, T.

French matriculation: EAN 978-2-36923-128-8, EAN 9782369231288.

Language: GB/USA.

Published: 25 June 2022.

Number of pages: 40.

The document: is available in clicking on the link; only on your computer.

Nom du fichier : Isbn 978 2 36923 128 8 periat

Taille : 434.11 Ko



1. Introduction: The basic stones to work with deformed tensor products.

2. Maxwell’s classical vacuum: In writing Maxwell’s equation (EM) for empty regions of our universe (no mass and no electrical charge) in the dual space E*(3, C), and in introducing then the trivial decomposition for each cross product appearing there, I got an expression for a volumetric density of force.

The mathematical demonstration exhibits seemingly no peculiar difficulty and, in some way, is developed in a totally classical world (17th century) which would be today identified with a universe “à la ADM”; i.e.: as one of the plausible 3 + 1 slices of the full four-dimensional world. Therefore, the result may wake up the attention: “Why is there a force where nothing should happen?”

Thinking more deeply about the circumstances, we can identify two acceptable explanations: a) We intuitively and experimentally know that an observer who is “flying” in vacuum (for example inside the ISS) “feels” the influence of far situated sources (e.g.: Earth gravitation, gravitational waves, …). Hence, an empty space only is a theoretical concept and, whatever we do, (what I have called) the Maxwell’s vacuum is equivalent to a volume that is fulfilled with a tiny polarized electromagnetic field. That weak polarization is enough to induce small forces.

b) The mathematical demonstration is realized in E*(3, C), supposedly thought as isomorphic to the physical space. But: “Is the dual space really the same than the original one, or does the passage from one space to the other one introduces some not immediately visible transformation which is at the end corrupting the analysis?”

The first explanation is known and makes it acceptable to think that empty regions of our universe may be crossed by energetic streams. The second one is the starting point for quite subtler mathematical discussions that I leave for later, preferring to go a step further in that analysis.

Anyway, the resulting equation itself contains three parts:

  • a first part effectively represents the electromagnetic (EM-)polarization of Maxwell’s empty regions (These regions have a non-zero electrical permittivity, ε0, and a non-zero magnetic permeability: μ0).
  • a second one can be interpreted as being a component acting against the progression of the energetic flow. It depends on the spatial gradient of the local volumetric density of EM energy.
  • and the third one has at this stage, no clear interpretation but is related to the existence of a whirl tensor, the presence of which will be understood later when I shall explore that topic in a full four-dimensional context.

3. Algebras: Introducing a Lie algebra, the FLRW metric, a quaternionic structure and a hypothesis explaining the Koide’s formula in particles physics.

© Thierry PERIAT.

Go back to the chapter: “Quantum cosmology”.

Date de dernière mise à jour : 02/12/2022