Размерность пространств реальных сред

Abstract

RU: Установлено, что размерность пространства полностью анизотропной среды равна 24. Геометрическая модель такого пространства представляет собой совокупность восьми трехмерных прямоугольных систем координат, состоящую из четырех базисов положительного и четырех отрицательного направления осей координат, сопряженных между собою общей девиаторной плоскостью и гидростатической осью, лежащей на одной линии, разделенной началом координат на два противоположных направления, причем системы попарно, как одно целое, повернуты вокруг гидростатической оси на углы 90°, 180°, 270° относительно одного базиса, принятого за исходный. Даны примеры использования открытия в механике деформируемых сред.

EN: Problem statement. Significant difficulties appeared while the attempts to use the concept and the model of three-dimensional space for solution of the problems, for example, in mechanics of deformed anisotropic bodies, in physics for development of the theory of elementary particles and single theory of field. It is expected that new ideas will appear in the mentioned sciences with opening real dimensionality of anisotropic environment spaces. Dimensionality of space is the number of independent dimensions characterizing the environment.

Analysis of publications. Nowadays there are two approaches to the explanation of the space. The basis of the first one is on Democrit’s idea used by Newton where vacuum is referred as the special kind of objective reality.

The second approach of understanding the space comes from Aristotle and Leibnitz. They consider geometrical characteristics of the material objects and properties of their environments [3].

A number of scientists stick to the combined version of the views on the space. According to M. I. Duplischev [1, page 28], «SPACE together with MATTER is the primary substance of the NATURE… and everywhere has its material content… is the endless reservoir of discrete matter of any forms and structural creations» [1, page 32]. Pramatter filling the space is ether. Ether particles are absolutely elastic small balls moving chaotically in the vacuum. [1, page 28]

O. Yulanov [6] thinks that the ether of physical vacuum is torsional (twisted, vortical) electromagnetic field, energy carriers that create the particles of the substance.

F. Engels [2] stated that through any point it is possible to draw three mutually perpendicular lines that means 2 vectors of the opposite direction. That is why vacuum is 6-dimensional. Nowadays it is supposed that the space is 3-dimensional.

To discover independent spatial directions in the environment, which resist to deformations of stretching and pressing in different ways, there were taken the following postulates:

1) two opposite vectors of different signs on one line acting by turns are independent and create 2–dimensional space;

2) two perpendicular vectors of the same or different signs acting simultaneously are independent and the space in case of different vector signs is divided by the bisector of the angle between them on two nonuniform spaces;

3) on the plane four perpendicular vectors coming from the same origin of coordinates pairwise positive and negative but not having turns of the signs, acting by turns in pairs, create two 2–dimensional independent spaces divided by the bisector on the positive and negative direction of the vectors;

4) two opposite differently signed 3–dimensional bases combined by the the same origin of coordinates, deviatoric plane and perpendicular hydrostatic axis divided on the negative and positive directions create 6–dimensional basis.

Conclusion. These postulates combined with the turns of 6–dimensional basis around its hydrostatic axis on the angles multiple of 90°, made it possible to come to the conclusion: dimensionality of the space of fully anisotropic environment is 24. Geometric model of such space represents a set of 8 three-dimensional rectangular coordinate systems consisting of 4 bases of positive and 4 bases of negative direction of the axis of coordinates coupled by common deviatoric plane and hydrostatic axes, lying at the same line divided by the starting point of the coordinate in two opposite directions, wherein systems in pairs as a whole are turned around hydrostatic angle of 90°, 180°, 270° relatively to one basis taken as a source.

There were given the examples of using open space in application to development of different-module theory of elasticity and for determination of the criteria of limiting state of anisotropic bodies while its tension.