The intrinsic method
The document can be discovered on vixra.
The intrinsic method is a mathematical tool bringing a part of the answer to the so-called (E) question. It only works in any three-dimensional space and, if considered separately from the extrinsic method, it is an incomplete procedure.
Consider a deformed cross product in E(3, K) where, usually, K represents either R or C. Consider the image of that product in the dual space E*(3, K). The question is: “How can I divide it and get a pair ([P], z) in M(3, K) x E(3, K) such that |ÙA(a, b) > = [P].|b > + |z >?”
- Since this method (i) does not give indications on the residual part of the decomposition (see the semantic) and (ii) is yielding a main part [P] differing from the trivial decomposition, it must be confronted with the results of the extrinsic method.
Despite of its incompleteness, this method can be applied in diverse domains. It gives some interesting information on well-known situations:
- A link between the picture of classical 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 vacuum”.
- A hint on the masses inside lattices: “Electrons in a lattice” (also called Bloch’ electrons).
- A direct coincidence between the determinant of the main part [P] 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: “The Tully-Fisher law as quantum gravitational effect?” (Document 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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Last edited: 11/02/2021