2018, no. 4

### RELATIONAL STATISTICAL SPACETIME AND JOINT DESCRIPTION OF QUANTUM AND GRAVITATIONAL EFFECTS

#### Aristov V.V.

In the developed variants of the relational statistical concept the spacetime is constructed from atomic until cosmological scales. Discrete constructing of space leads to non-Euclidean geometry om microscales. That results in quantum effects. The other variant of non-Euclidean (Riemann) geometry determined gravity can be specified at macroscopic scales. Combining two geometries in a general mesoscopic case describes both phenomena and the appropriate equation in differences is written. This joint model is valid for all scales. So the joint equation for simulation different effects is presented. This is due constructing relational statistical spacetime. Gravitation and quantum effects are compared for Planck scales, but the present consideration is restricted by atomic lengths. Nevertheless the violation of the classic spacetime is realized for for atomic and Compton scales. Introduction of discrete space and time related to the atomic structure of matter itself implies that the notion of the smooth trajectory at these scales is not valid. The motion equations should be written in small but finite increments. Transition to relationships in terms of space and time measured by macroscopic instruments leads to stochastic factors corresponded to indeterminism of motion. The traditional smooth of spacetime is reproduced at macroscopic (with respect to atomic length) scales. Relational statistical concept provides here the Riemanienen geometry due to nonuniform distribution of masses in comparison with the ideal uniform mass distribution in the model of a rule (rod).

Keywords: spacetime, relational statistical concept, gravitation, quantum effects.

UDC: 53.01, 53.02

PACS: 04.60.-m, 03.65.Ca, 03.65.Fd, 03.65.Ta

DOI: 10.17238/issn2226-8812.2018.4.4-20