### Statistical Ensemble Technique (SET)

The statisitcal ensemble technique uses the following simple idea. A set (statistical ensemble) of many identical stochastic systems is a deterministic system. This system has all attributes of a dynamic system: dynamic equations, expressions for the current, for the energy-momentum tensor and for other conservative quantities, although each stochastic dynamic system, constituting the statistical ensemble, has none of these attributes.

Besides, if one of dynamic variables of the statistical ensemble can be considered as a probability density, the statistical ensemble can be used as a tool for a calculation of average values of physical quantities.

Thus, the statisitcal ensemble has two independent properties.
1. The statistical ensemble is a dynamic system.
2. The statistical ensemble is a tool for a calculation of average values.

In application to the theory of quantum phenomena the first property appears to be most important. A usage of the dynamic properties of the statistical ensemble is referred to as the statistical ensemble technique (SET). In application to the theory of quantum phenomena the second property of the statistical ensemble associates with the quantum axiomatics (a specific quantum way of a calculation of average values).

Applying SET to a relativistic quantum particle, one shows that the quantum effects can be explained on the base of only dynamics (the first property), 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.

Application of SET can be manifested in the following example. In the relativistic case, when there is no dynamic variable which can be interpreted as a probability density, the statistical description is carried out on the base of two different sides of the statistical ensemble.

On the one side the dynamic system E (statistical ensemble) is a set of identical independent (and hence, non-interacting) stochastic systems Sst. There are no dynamic equations for Sst.

On the other side the same dynamic system E is a set (not a statistical ensemble) of identical interacting classical systems Scl. There exist dynamic equations for Scl.

Comparing the two sides of the same dynamic system E, one concludes that the interacting classical dynamic systems Scl of E describe the mean motion of the stochastic systems Sst. In other words, a statistical description of stochastic systems is carried out on the base of dynamic properties of the statistical ensemble (considered as a dynamic system). The second property of the statistical ensemble is used rather slightly, or is not used at all. The force field, responsible for quantum effects, carries out a dynamical consideration of statistical effects, connected with the stochastic systems description.