Intrinsic method in a four dimensional space - Immersion


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Author: © by PERIAT, T.

Title: Intrinsic method in a four-dimensional space, ISBN 978-2-36923-099-1, v3, 10 September 2021, FR, 26 pages.

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The first part of this document recalls the physical motivation (see the page: J.C. Maxwell revisited) at the root of the whole theory that I have labeled the Theory of the (E) Question (TEQ), comes back on the first steps of its development, essentially focused on the understanding of what happens in a three-dimensional world.

The second one is starting a global exploration in which I try to articulate the four three-dimensional subspaces that are implicitly contained a any four-dimensional space. That questioning is obviously related to a deeper understanding of an ancient and very challenging problematic: the immersion.

In my document, I only expose the situation as I understand it, putting the diverse stones of the debate on the floor, enumerating the topic of importance (the Euclidean enigma, the curvature tensor, the Petrov’s classification, etc.), but not going further, just insisting on the difficulties, the conceptual and technical ones.

The third one is ignoring all this in centering the discussion on the calculation of the strategic discriminant for specific types of cubes: anti-reduced, antisymmetric and both. The latter case turns out to be bring two specific relations: the first one is a polynomial of degree three and the second one is introducing a kind of four-dimensional spinor.

The fourth part proposes an application concerning the covariant version of the Lorentz law for motions due to electromagnetic fields. It also suggests a scenario explaining the three generations of leptons (caution: it is only a proposition).

© Thierry PERIAT.

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Last edited: 15/09/2021