# Algebra - Physics - Cosmology

## The Theory of the (E) Question.

My scientific quest:

A new cosmology in which the geometries and the algebras

are intimely connected.

Aknowledgement:

Thank you very much to all authors (articles, books, courses, photographies) who have tried to indirectly help me along the way (2003 - 2021).

This website exposes the main ideas of a personal vision revisiting some basic topics on which the modern physics is built.

It participates, at a modest level, to the general discussion looking for the real nature of empty regions paving the universe (nothing, electromagnetic and gravitational fields, perfect bosonic fluids, etc...).

The initial kick having motivated this research is a peculiar utilization of the concept of rotation inside Maxwell's equation describing the behavior of electromagnetic fields in vacuum.

## News

You are encouraged to visit the French part of this website to get a better overview of my work.

If you have a remark, a comment or the need to communicate with me, just use the contact form

The Theory of the (E) Question has now:

• A method allowing the construction of a curvature tensor connecting it with E. Cartan's work on area metrics.
• A better understanding of the concept of aera.
• A more detailed calculation of the strategic discriminant for the treatment of the (E) question in a four-dimensional space.
• Two very original propositions:
• one connecting a Thirring-lense effect with the electromagnetic polarisation in vacuum and another
• one concerning a quantification of the geometry in any three-dimensional space.

## The element of length.

A crucial element in mathematics and in physics as well is re-analyzed with the binoculars of the intrinsic method.

Why the Euclidean three-dimensional space in which we live is not so easy to understand as it may look at the first glance.

Or how E. Cartan's spinors enter into the discussion.

## Introducing strings into the discussion.

The premisses are inducing the next question: "Can we introduce the concept of string into that new vision?"

Once again, the answer is: yes!

Have a look on this investigation: "Vacuum and strings" (extern link - zenodo.org)

## A personal vision - What the filaments are teaching us on the structure of the Universe.

The existence of filaments inside the set of large-scale structures is now a certitude; see an enumeration of proofs starting as soon as 2002 in [a; §1.] but also recall that the (citation) “the first filaments were detected in the mid-1970s in the three-dimensional survey of bright galaxies CfA Redshift Survey” [b; p.2] (end of citation).

The main topic of reference [a] is to furnish a plausible method describing these structures conveniently. Explaining first why the MST (i.e.: minimal spanning tree, Martinez & Saar 2002) and the notion of skeleton (Novikov et al. 2003) are not really the optimal procedures, the usefulness of the Candy model and of its extrapolations is then exposed.

As explained in [b], the challenge which the ΛCDM model is facing, consists of proving that filaments are a consequence of some ad hoc interaction involving the hypothetical dark matter halos at some convenient period in the universal chronology.

Now, since -up to 2017 [c]-  there was no direct proof of the existence of dark matter, doubts are invading a part of the scientific communities and I propose the first stones for a renewed analysis of our cosmology through the (so-called) © Theory of the (E) Question. My goal is, in a first step, to prove that basic considerations on the concept of material strings in contraction (or in elongation) are compatible with the presumable equation of state describing the universe in average and with the very classical Maxwell’s laws concerning electromagnetism in empty spaces.

Bibliography:

[a] Detection of cosmic filaments using the Candy model; HAL Id: hal-02675764, submitted on 31 May 2020. Already published in Astronomy and Astrophysics”, by EDP Sciences, © ESO 2005.

[b] On the nature of filaments of the large-scale structure of the Universe; HAL Id: hal-01962100, preprint submitted on 20 Dec. 2018.

[c] Current status of direct dark matter detection experiments. Nature Physics, 13, 212-216, 2017 (arXiv:astro-ph/1709.00688v1).

## Mathematical methods for the decomposition of deformed tensor products.

Mathematical methods are systematic procedures, the purpose of which is to reach a given goal.

The theory which is exposed on this website is (i) studying the deformation of tensor (resp. Lie) products and (ii) is comparing them with a generic type of decompositions. Because of that, it is mainly a set of thoughts and of mathematical manipulations developed around the concept of “division”.

In extenso, that theory is looking for mathematical methods allowing the discovery of decomposition for these products.

The mathematical part of that theory started in 2003 with a simple remark during the redaction of the document “Maxwell’s vacuum” (visit the page explaining this fact on this website).

## The dispersion relation in vacuum.

This document explains why and how a second order surface can be associated to the dispersion relation of light in vacuum within a mathematical context involving the existence of deformed cross products (The Theory of the (E) Question - TEQ).

## The principle of less action and the Bowen-York-Lichnerowicz black holes.

The next important question is: "How is the light propagating?"

In that second part, I bet that the principle of less action works and that a very classical Newtonian force of gravitation tells to the light in which direction it should propagate.

That is, I impose a coincidence between that force and the direction minimizing the slopes of the second order surface.

In doing so, I state that (i) the singular vector of that surface must be a position in the space of that theoretical discussion and, quite amazingly, that (ii) the surface is related to the decomposition of some (eventually) deformed cross product signaling the presence of a Bowen-York-Lichnerowicz black hole.

Hence, that document (extern link - vixra.org) suggests that the light propagating in vacuum might be living on a surface surrounding such a black hole.

## The Hubble law

The third document of that exploration is analyzing if the Hubble's law is compatible with the proposition?

And yes, it is formally compatible.

The three documents are sketching the skeleton of a new cosmology indicating that the galactic filaments are the visible part of elastic strings evolving at the surface of giant voids.

## Building a link between the Klein-Gordon equation and the covariant formulation of the Lorentz law.

The Thirring-Lense effect is a mathematical consequence of Einstein's master work.

Its effective existence has been checked with the Gravity Probe B experiment.

The Theory of the (E) Question studies the decompositions of deformed tensor products, deformed exterior products and deformed Lie products with the help of diverse mathematical methods which have been classified in: intrinsic and extrinsic.

The intrinsic method has been involved previously in studying the dispersion relation.

It can also be involved in an analysis of the Klein-Gordon equation describing the propagation of massive waves. This way of doing allows the introduction of a vector g playing a very crucial role in the formulation of the Thirring-Lense effect.

In a four-dimensional context, the extrinsic method can be involved for the study of the Klein-Gordon equation describing the propagation of massive waves (extern link - vixra.org).

That way of doing allows (i) a recovering of the dispersion relation (see above) and (ii) a link with the covariant formulation of Lorentz law in electromagnetism.

## Lumine naturae.

Can we relate the Thirring-Lense effect to the electromagnetic polarization in vacuum?

Please visit the French part of this website to discover how.

## A scenario explaining the (energetic) generations (leptons): a proposition.

The topic can be discovered on the French part of this website.

## A new hypothesis in cosmology: the role of gravitational term in the covariant formulation of the Lorentz law.

The universe is expanding; well, but why, and what is the mechanism explaining that? The academic literature proposes diverse scenarios.

## Are you lost? Then ...

Last edited: 25/09/2021