3D-brane universe model

Ruslan A. Sharipov.   1 ... 11 12 13 ... ru The energy conservation law is one of the fundamental laws that permeates all sections of physics. In classical field physics it has two forms: integral form and differential form. In integral form, it is written as follows: The first integral in the formula expresses the total energy contained in the volume Ω. The second integral in the formula is the energy flow through the boundary of the volume Ω. Verbally the energy conservation law is expressed as follows: the change in the amount of total energy in the volume Ω occurs only due to the energy flowing through the boundary of this volume. H in the formula of the energy conservation law denotes the total energy density of all fields, including the gravitational field. J in this formula denotes the vector of the total energy flux density of all fields, including the gravitational field. The components of this vector are numbered with the superscript i . These same quantiti...

 Ruslan Sharipov.   1 ... 10 11 12 ... ru The Lagrangian L is included in the action integral, which we considered in the previous post " The Lagrangian approach to deriving the equations of gravity in the new theory ". The Lagrangian L itself is expressed in the form of a three-dimensional integral of the Lagrangian density. As we see from these formulas, the Lagrangian density is the sum of two terms — the Lagrangian density of the gravitational field and the Lagrangian density of matter. The Lagrangian density of matter describes the dynamics of matter. It depends on a specific type of matter that can be cosmic dust, gas, liquid, solid, or even dark matter. We will leave the choice of Lagrangian density of matter for later. Now let's consider the choice of the Lagrangian density for the gravitational field. The dynamic variables of the gravitational field in the new theory are a three-dimensional metric and a scalar function denoted by the letter g with...

Ruslan Sharipov 1 ... 9 10 11 ... ru The Lagrangian approach to deriving various equations is associated with the name of Joseph Louis Lagrange. Detailed information about him can be found in Wikipedia . In mechanics and in physics his name is associated with the so-called "least action principle". According to this principle, the evolution of a physical system occurs in such a way that some integral over time turns out to take the smallest possible value. This integral is called the action integral. It is usually denoted by the letter S. The function L in the integral S is called the Lagrange function or the Lagrangian. In field theories it is itself an integral over spatial variables. In the spatial integral L we see a function denoted by the same letter, but in a calligraphic style. This is the Lagrangian density. It is represented as the sum of two terms: the Lagrangian density of the gravitational field and the Lagrangian density of matter. We will d...

Ruslan A. Sharipov. 1 ... 8 9 10 ... ru We shall discuss the equations of the gravitational field in the new theory of gravity, which is called «3D-brane universe model». I am the author of this theory. Therefore, you will receive first-hand information without any distortion. The gravity equations in the new theory are subdivided into two groups. The equations of the first group have the form They depend on two indices i and j . When these indices are rearranged, the equations do not change. Therefore, different equations are obtained only for the following values of the indices: (i=1,j=1), (i=1,j=2), (i=1,j=3), (i=2,j=2), (i=2,j=3), (i=3,j=3). This means that the total number of different equations in the first group is 6. The second group of gravity equations in the new theory contains only one equation. As a result, the total number of the gravity equations in the new theory is 7. For comparison, the number of different gravity equations in Einstein’s ...

Ruslan A. Sharipov. 1 ... 7 8 9 ... ru ttt Einstein's equation was written by him in 1915. A historical essay about it can be found in Wikipedia . It captivated and captivates many people with its simplicity and elegance. In Wikipedia you will find this equation written with the plus sign in front of the constant Λ. I wrote it with the minus sign. This is my mistake. It was admitted long time ago in 1997, when I was writing my textbook “ Classical electrodynamics and  theory of relativity .” The Internet in Russia and in the city of Ufa was much less accessible that time than it is now. Also there was no Wikipedia; it appeared only in 2001. It was necessary to go to libraries and rummage through catalogs in search of even older textbooks. But I was lazy. In order not to contradict my textbook, I now write Einstein’s equation with the minus sign in front of Λ. This is not a big problem. It is enough to take the constant Λ itself with the opposite sign. Despite its vi...

Ruslan A. Sharipov. 1 ... 6 7 8 ... ru The “3D-brane universe model” is the name of a new non-Einsteinian theory of gravity. This theory is based on criticism and denial of the space-time as a material entity. However, it does not deny all the achievements of Einstein's theory and strives to digest and incorporate everything that is possible from Einstein's theory. In this article we analyze the elements of continuity between the two theories. In Einstein's theory gravity is described by a four-dimensional metric. It can be understood as a 4x4 matrix, which is shown in the figure to the left of the arrow. The components of this matrix depend on coordinates and time. Space-time in the new theory is subdivided into a foliation of 3D-branes. Each of these branes corresponds to one of the moments in the evolution of the real three-dimensional universe. The foliation of 3D-branes determines the choice of special coordinates, which are called comoving coordinates, an...