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 __(J*w*) = 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

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 A_{4}
(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 A_{4}
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 A_{4}
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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