(There is a more detailed review in the form of a postscript file)

A possibility of a substantiation of the quatum mechanics is investigated.
It is shown that the quantum stochasticity (a reason of the irreproducibility
of single precise experiments with microparticles) can be explained as
a result of a distortion of the space-time, the quantum constant *h*
being a measure of this distortion. The space-time distortion is such a
deformation of the space-time which converts world lines of real particles
inside the Minkowski space-time into hallow world tubes of a distorted
space-time (DST). World tubes of particles appear
to be stochastic. At a certain kind of distortion a statistical description
of stochastic world tubes is equivalent to the quantum mechanics. It should
note two principal points of such a substantiation:

(i) a discovery of the reason of quantum stochasticity,

(ii) application of a statistical ensemble technique,
describing influence of the stochasticity upon a mean motion of particles.

As a whole the way of the quantum mechanics substantiation reminds that
of the thermodynamics by means of the statistical physics, where one can
see two like principal points.

(1) Discovery of the reason of the thermal stochasticity (heat as a chaotic
molecular motion).

(2) Statistical physics technique, describing an influence of the heat
stochasticity on the Brownian particle motion.

Distortion is a new type of the space-time deformation. Its introduction
and its investigation are possible only in the scope of the metric approach
to geometry (MAG). Usage of this approach leads
to a revision and generalization of the modern geometry and to construction
of T-geometry (geometry of tubes). T- geometry is very general kind of
geometry, including as a partial case Euclidean and Riemannian geometries,
Minkowskian geometry and metric geometry. Two characteristic features of
the T- geometry are:

(1) usage of natural geometric objects (NGO), determined only by metric
properties,

(2) expression of affine geometric properties through metric ones.

Usage of the metric approach to geometry (MAG) and T-geometry admits to answer the following simple and important questions:

In the scope of the contemporary theory there is no constructive answer for these questions, because they relate to axioms of the modern geometry and physics.

A statistical description of stochastic world lines needs a development of a special way of the statistical description appropriate for a description of stochastic lines. The probability theory, as well the conventional statistical physics describe statistics of zero-dimensional objects (points and pointlike particles). They are not adequate for a description one-dimensional objects (world lines). For a description of world lines one uses statistical ensemble technique (SET) which uses a more general concept, than the probability density.

The idea of SET can be illustrated as follows. A destribution of results of many experiments with similar independent stochastic systems are reproducible, although a result of an experiment with a single stochastic system is irreproducible, in general. This fact is interpreted in the sense that a set of similar independent stochastic systems forms a deterministic dynamic system, known as a statistical ensemble of stochastic systems. The statistical ensemble carries out a statistical description of the stochastic system independently of whether or not anyone of dynamic variables of the statistical ensemble can be regarded as a probability density. In other words, a statistical ensemble is considered primarily as a dynamic system and only thereafter as a tool for calculation of mean values.

In application to a quantum system the SET approach means that only dynamic properties of the system are investigated with quantum principles being reserved. Application of the SET to different quantum systems gave unexpected results. Application of SET to non-relativistic electron described by the Pauli equation shows that the electron spin is a collective property, i.e. the spin is a property of the statistical ensemble, but not a property of single electorns constituting this ensemble. (Compare: the temperature is a collective property of molecules in the statistical physics, but at the same time in the axiomatic thermodynamics the temperature is a property of any amount of the matter, including one molecule).

Application of SET to the relativistic electron, described by the Dirac equation, confirms that the electron spin is a collective property. Besides the SET approach shows that the Dirac equation is not relativistic by itself. It becomes relativistic only after a usage and in virtue of the quantum axiomatics.

Applying the SET approach to the dynamic system, described by the Klein-Gordon equation, one obtains that the most of quantum effects can be explained on the base of only dynamics with the QM principles being reserved. This shows that the dynamics (not the quantum axiomatics) is a principal vehicle of quantum effects.

Using SET, one shows that the quantum effects can be explained on the base of only dynamics, i.e. without a reference to the quantum axiomatics. It means that there exists some force field, responsible for quantum effects. This field can produce pairs. It enables to escape from the matter and to exist in the empty space-time. The space-time distortion can be considered as a reason and an origin for this field.

Using SET and investigating interplay between dynamic systems, described by the Klein-Gordon and Dirac equations, one discovers that in (1+1)-dimensional space-time these dynamic systems are distinguished only by definition of the current and the energy-momentum tensor. Non-relativistic character of the Dirac system is displayed in the case of (1+1)-dimensional space-time also.