RESEARCH INTERESTS

Introduction and the Concept

Louis de Broglie used to say that the fundamentals of physics should be reconsidered from time to time. Paul A. M. Dirac in one of his last works (1984) noted: Physics should be based on strict mathematics because the fundamental ideas of the existing theory are wrong; a new mathematical basis is needed. And since the mid-1980s, in line with those pronouncements, I began to focus my main interests on the study of fundamental physics in pure geometrical terms. I try to show how the physical notions, rules and laws would appear from a mathematical space.

I carry out my research on the construction of quantum mechanics in real space, on the fusion of submicroscopic quantum mechanics with quantum gravity, and on the microstructure of the universe. I have examined how the main notions of fundamental physics (particle, mass, velocity, de Broglie wavelength, Planck's constant, Compton wavelength, etc.) can be deduced from the discrete geometry of space and the submicroscopic mechanics developed on the scale about 10^-30 m (according to the modern knowledge at this size all types of interactions come together). Specifically, in collaboration with Professor Michel Bounias we worked together on the project "On the theory of space". Leading French mathematician Michel Bounias, a man of big heart, passed away on 23 March 2003. Let he be remebered forever. Here is my article written in his memory (pdf file)

We started from topology, set theory and fractal geometry. In our opinion such notion as space-time is only "ad hoc" hypothesis, which is in severe conflict with such fundamental notion as a mathematical space. Time has been considered as something that independent from space but it should appear in space if one endows space by special properties and rules. A mathematical space that Professor Bounias and I have been constructed, is endowed with all the properties needed for fundamental physics. This is an antipode to the notion of space-time that cannot be called microscopic.