Space-time discretization: the way to the fundamental element without a determined form

Abstract

The concept of the random discretization of the space-time is suggested. It is the way to consistent compatible synthesis of quantum and relativistic principles and principle of geometrization. The basic idea of this concept is physical reality of the finite sizes fundamental element of the quantized space-time. The flat space-time with random discretization is described as the probability measure space with the set of all possible discretizations of the flat continual space-time as the set of points. The probability measure can depend on the geometric parameters of discretizations (a number of regions of a discretization, their volumes, areas etc.). In this concept the fundamental length can be defined as the average value of the linear size of a fundamental element. In this concept the "particle" quantum and the space-time quantum are identical.