Yu.V.Nachalov

The Basics of Torsion Mechanics.

1. The general principle of inertia as a generalization of Newton's mechanics.

As is well known, Newton's law of inertia can be written in analytical form as follows:

d (mv) = 0 ; v = const
dt

(m - mass, v - velocity vector) Thus Newton's mechanics considers inertial movement as non-accelerated rectilinear motion. But as is well known from Euler's works, there exists an analogue of Newton's first law for rotational motion:

d (Jw) = 0 ; w = const
dt

(J - the moment of inertia, w - angular velocity vector.) These equations demonstrate that if external moments are absent, then the angular impulse Jw of the rotating solid body is constant. That means that the angular velocity of the rotating solid body will also be a constant. Thus these equations show that there exists not only rectilinear inertial motion, but also rotational inertial motion. This fact does not contradict Newton's mechanics, since Newton's mechanics simply does not take this fact into consideration. The rotational (torsion) principle of inertia can be formulated as follows: If external moments are absent, then the angular velocity of the rotating body remains constant. The combination of the principle of rectilinear inertia (in the sense of Galileo-Newton) with the principle of torsion inertia allows the formulation of the general principle of inertia: If no forces are acting, and no angular moments are acting, then the motion of the solid body is inertial. This general principle of inertia was first formulated by G.I.Shipov [1].

The general principle of inertia is the generalization of Galilei-Newton's principle of inertia, and it shows that there exists not only non-accelerated inertial motion (as in Newton's mechanics) but also accelerated inertial motion (since rotation is a motion with acceleration). Thus the general principle of inertia shows that Newton's mechanics is incorrect for any systems having rotation.

2. Torsion Interactions.

According to Newton's second law: F = ma, there is a row of generalized Newton's equations in the modern theory of fields. In these generalized equations, F is considered to be a force acting upon a charge having mass m. As a result of the geometrization of physical interactions (for instance in Einstein's gravitational theory) Newton's equations were replaced by the geodetic equations. It should be emphasized that in both cases (in Newton's and in Einstein's mechanics) the accelerations (it doesn't matter: 3- or 4-dimentional) in the equations are polar vectors. Polar vectors are formed as the second derivatives of translational coordinates x, y, z, ct. Let's formulate the following definition: If an interaction results in polar accelerations, then this interaction is a polar interaction. Thus the modern theory of fields operates with polar interactions. But as is well known, there exist interactions which result in axial accelerations. For example, angular acceleration is an axial vector. In classical mechanics, such interactions can be described by Euler's equations for rotational motion: M = Jw. (J - the moment of inertia, w - angular acceleration, M - external momemt)

We can formulate the following definition: If an interaction results in axial accelerations, then this interaction is an axial (torsion) interaction. It should be emphasized that there exist no fundamental generalizations for the equation M = Jw in the modern theory of fields. Thus the modern theory of fields operates only with polar interactions, and torsional interactions are not taken into consideration.

3. Torsion mechanics as a generalization of Einstein's mechanics.

As is well known, Einstein's general relativity theory operates with 4 translational coordinates x, y, z, ct. Einstein's GR does not take into consideration the fact that the accelerated system can possess an angular momentum. Thus Einstein's mechanics does not take into consideration the existence of torsion interactions or the torsion principle of inertia.

In 1986 M.Carmeli attempted to create a special principle of rotational relativity [2] as an addition to Einstein's special principle of translational relativity. But Carmeli's approach didn't take into consideration some problems of inertia forces, and M.Carmeli could not finish the program of rotational relativity. The program of rotational relativity has been completely realized in the framework of the so-called theory of the physical vacuum by G.I.Shipov [3]. Shipov rigorously showed that Einstein's translational relativity should be complemented with a rotational (torsion) relativity. The combination of translational and torsional relativities allows the development of a new mechanics which is termed the mechanics of an orientable material point (the mechanics of a material point with spin or torsion mechanics) [1]. The mechanics of a material point with spin describes the motion of an accelerated system by 10 equations, but not by 4 equations as in Einstein's mechanics, and this mechanics is a generalization of Einstein's mechanics. It has been shown that the complete description of the motion of an accelerated system with spin cannot be made in the framework of Riemannian geometry used in GR. The space of torsion mechanics has the structure of the geometry A4 (the geometry of absolute parallelism). The geometry of absolute parallelism was first examined in the works of R.Weitzenbock [4,5]. It is interesting to note the fact that, in the framework of A4 geometry, A.Einstein has authored the greatest number of works (13) devoted to the unified field theory in comparison with the other geometries.

In [6,7] it was shown that the torsion of A4 geometry causes torsion fields which define the density of all matter, and which are responsible for the existence of inertial forces. In this sense, the torsion field can be considered as Einstein's unified field. In [8] it was shown that the mass of any physical object can be altered as the result of alterations to the torsion fields of this object. A mechanical system which can realize linear movement without using frictional or reactive forces has been proposed, and movement equations have been written and solved. It has been shown that an isolated mechanical system can realize movement using the specially organized rotation of elements within the system. It should be noted that the first working devices using this principle were already demonstrated in the 1960s by V.N.Tolchin, the Head Designer at the Perm machinery factory, who was the first inventor to realize that it is possible to control inertia forces [9].

An understanding of the methods of torsion field generation allows a rigorous theoretical interpretation [3,8,22] to be given to all phenomena demonstrated by gyroscopes and gyroscopic systems [10-14], and to the phenomena observed in various experiments with spin-polarized particles (e.g. [15-21]).

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