The intrinsic method

 

The document: ISBN 978-2-36923-084-7 (extern link).

The intrinsic method

It is a mathematical tool to get answers to the so-called (E) question in any three-dimensional space: “Consider a deformed cross product (DCP) in E(3, K) where, usually, K represents either R or C. Consider the image of that DCP in the dual space E*(3, K) of E(3, K). How can I divide it and get a pair ([P], z) in M(3, K) x E(3, K)?”

Applications

In mathematics

  • Alone, this method is incomplete. It does not give indications on the residual part of the decomposition (see the semantic). Therefore, it must be confronted with the results of the extrinsic method. This work has been done and can be read on the French part of the website: Entre les produits.
  • The main part resulting from the intrinsic method differs from the trivial decomposition and the hiatus is per se motivating a discussion.
  • A part of that discussion is exposed in “Introducing a new vision for the cosmology”.
  • In fact, I have pushed the investigation further in the document “Einstein-Rosen revisited”. It turns out that the discussion around the hiatus is a mathematical and technical discussion asking our manner to measure differences.

In physics

Despite of its incompleteness, I have applied this method in diverse domains. It gives some interesting information on well-known situations:

  • A link between the picture of strings in elongation and the equation of state for the empty regions of our universe: “Vacuum and strings”.
  • The existence of a volumetric density of force in vacuum: “Maxwell’s equations for electromagnetic fields in vacuum.
  • A hint on the masses inside lattices: “Electrons in a lattice (also called Bloch’s electrons)”.
  • A direct coincidence between the determinant of the main part and the square of the momentum in Minkowski geometry: “The Klein-Gordon equation”.
  • The possibility to build the first stones of a quantum theory with the main part of some non-trivial decomposition; with application in cosmology: “The Tully-Fisher law as quantum gravitational effect?” (on Zenodo.org).

None of these investigations are definitive since they all are developed in a limited three-dimensional environment and because they should all be confronted with the extrinsic method. It is highly recommended to countercheck them yourself. Discussions are welcome; just contact me via the electronic form.

© Thierry PERIAT.

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