Foundations

Basic stones

Three fundamental hypotheses are characterizing the GTR-p theory:

  • The discussion is developed in a four-dimensional real vector space E(4, R) referred to a canonical basis.
  • The time is a vector (the arrow of time).
  • Basis vectors can vary and their successive partial derivations up to the p-th order are again in E(4, R).

With these simple assumptions, two crucial results can be obtained when p = 2:

  • There is a mathematical object of which the components are mimicking those of the Riemann-Christoffel curvature tensor; I provisory label it with the composed word “pseudo-tensor”.
  • The whole coherence is obtained under one important condition: the partial derivates of the four basis vectors form a Clifford algebra; this mathematical fact suggests the existence of electromagnetic fields with a geometrical origin.

Document available on zenodo.org (extern link).

These preliminaries have caught my attention because they seemingly furnish two essential ingredients allowing the construction of a unified theory containing gravitation and electromagnetic fields in a four-dimensional space.

In what follows, I am checking the plausibility of these premises.

© Thierry PERIAT.

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Last edited: 31/07/2021