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

TL;DR

This paper proposes a novel approach to space-time quantization through random discretization, aiming to unify quantum mechanics and relativity by considering fundamental elements with finite sizes and probabilistic properties.

Contribution

It introduces the concept of random space-time discretization as a physical reality, linking quantum particles and space-time quanta, and defining fundamental length via average discretization size.

Findings

Space-time discretization can be modeled as a probability measure space.

Fundamental length is defined as the average size of discretization elements.

Quantum particles are identified with space-time quanta in this framework.

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.