A missing link: What is behind de Broglie's “periodic phenomenon”?

The present work constitutes an attempt to give the interpretation of de Broglie's internal periodic phenomenon which ascribes the frequencym₀c²/h to each single entity in its eigensystem of coordinates. This phenomenon provides existence in principle of the ideal proper-time scale, making it possible to identify the geometric proper-time interval with a physically existing one, thus ensuring the realization of basic postulates of the relativity theory. According to the latter, neither time nor de Broglie's frequency are invariant with respect to the Lorentz transformation of the coordinate system. A search for the fundamental invariant demands passing over to dimensionless quantities, and we suggest to consider as such the integer numbers. Then it is the entity's periodic phenomenon which, after multiplying by the lasting proper-time, results in the open ordered sequence of natural numbers. The progressing course of numbers is ensured by the time course, whilst their ordering is connected with coherence. Such a sequence of numbers, once appeared in time, has to be conserved in space-time, demanding the periodic phenomenon's phase to be invariant with respect to the Lorentz transformation. This, in its turn, yields de Broglie's waves of matter, which are at the bottom of quantum physics. Thus, the most intrinsic feature of a fundamental entity has to be identified with its internal frequency, in order to ensure the actual existence of the sequence of natural numbers as the basic object of arithmetic.