Alexander P. Yefremov is a Russian physicist, vice rector at Peoples' Friendship University of Russia and director of its Institute of Gravitation and Cosmology. He has worked at the Peoples' Friendship University of Russia (PFUR) since 1977, among others as its vice rector and head of its physics division. Yefremov is known for his work in theoretical physics, among others, for his fundamental work on the role of quaternion geometry space in quantum mechanics and field theory.

Heuristic Schrodinger equation of quantum mechanics QM perfectly describes the micro-world phenomena, but remains an axiomatic hypothesis having no logical explanations and properly formulated correspondence principle with classical mechanics. However, resent investigations demonstrate immanent presence of this basic QM law in pure mathematics of hyper complex quaternion – Q numbers. We outline the logics and stages of this discovery.

A deeper analysis of the Q-algebra whose “imaginary” units behave as a vectors initiating a 3D Cartesian frame involving the spectral theorem of the theory of matrices reveals existence of a pre-geometric fractal surface, a “square-root slice” of a 3D space. Simple distortions oscilla-tion and stretching of the surface violate the Q-algebra multiplication; a condition providing the algebra’s “eternal” stability takes the shape of a continuity-type math unit-less equation com-prising an arbitrary vector. We chose this vector as the oscillation gradient; these pure math ac-tions have amazing results.

The stability condition fractalizes, and when written in the physical micro-world units, it be-comes precisely the Schrodinger equation of QM. The particle’s wave function then is image of oscillating 2D area of the pre-geometric space predicted by Wheeler. Respective 3D physical object is a massive point rotating about an axis. In the “lab” conditions, the fractal equation converts precisely into the Hamilton-Jacobi equation of classical mechanics, the oscillation phase acquiring sense of the action function. Finally, constancy of particle’s rotational velocity leads to the Einstein’s relativistic mechanics.

Thus, the math of Q-numbers unites quantum, classical, and relativistic mechanics in one theory