"General theory of a particle mechanics" arising from a fractal surface

TL;DR

This paper develops a unified theoretical framework linking quantum, classical, and relativistic mechanics through hypercomplex algebra stability, introducing a fractal surface model of space and visualizable geometric representations of fundamental functions.

Contribution

It proposes a novel unified theory of mechanics based on hypercomplex algebra stability and introduces a fractal surface concept underlying physical space.

Findings

Unified mathematical foundation for different mechanics types

Introduction of a fractal surface model of space

Geometric visualization of key physical functions

Abstract

The logical line is traced of formulation of theory of mechanics founded on the basic correlations 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 a notion of basic fractal surface underlying the physical three-dimensional space is introduces, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.