“General Theory of Particle Mechanics” arising from a fractal surface

We trace the logical line of formulating a theory of mechanics founded on the basic relations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical conse...

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Bibliographic Details
Published inGravitation & cosmology Vol. 21; no. 1; pp. 19 - 27
Main Author Yefremov, A. P.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2015
Subjects
Astronomy
Astrophysics and Astroparticles
Classical and Quantum Gravitation
Observations and Techniques
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Fractal Density
Pauli Equation
Physical Unit
Logical Line
Dual Number
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Summary:We trace the logical line of formulating a theory of mechanics founded on the basic relations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical consequences of a single condition of stability of exceptional algebras of real, complex and quaternion numbers under transformations of primitive constituents of their units and elements. In the course of the study, the notion of a basic fractal surface underlying the physical three-dimensional space is introduced, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.
ISSN:0202-2893
1995-0721
DOI:10.1134/S0202289315010144