Procedure of distances decompactification in the relational approach

Within the framework of the relational approach to the space-time and physical interactions, the main task is to derive classical space-time concepts from the more fundamental laws of the microworld. Particularly, these concepts include dimensions number, signature and length (classical distance). The latter can be obtained by solving the problem of decompactification for a given system of particles. This paper provides a mathematical formulation of this problem within the systems of relations theory. It is shown that the relations used in the formulation of this problem describe the elementary processes of emission and absorption of electromagnetic radiation. The solution of such a problem for a real physical system is associated with the need to take into account a large number of phase contributions of emitted but unabsorbed radiation. So, there is considered the problem of classical distances decompactification for a system of a finite number of emitters and absorbers with a limited spectrum of the hydrogen atom. The technique of the numerical solution is discussed and its results are presented under the given constraints.