© Oleg O. Fejgin

Contact to the author: tor@3s.kharkov.ua

It is known, that historically precise mathematical formulation of a quantum theory has developed integration of two various interpretation approaches. First - based on a principle of conformity of Bohr, Fourier - representations of an orbit of an electron and a mathematical formalism of a matrix mechanics; second - from a wave mechanics and differential Schrödinger equations. The first attempts of wave-corpuscle duality interpretation were reduced to concept of statistical waves of the probability, developed in representation about localization of the abstract mathematical quantity in multivariate configurationally space. Now, basic quantum-theoretical examinations focused in the field of Abelian theories quantization, chrono-dynamics topologies of structural spaces and local continuums structurization in cosmological aspect of their evolution [1].

In the present operation examination of methodological bases of build-up of principles, quantum-theoretical chrono-discretization on datum a wave mechanics reinterpretation is prolonged. The quantum-wave relation for microscopic objects can be presented; it is similar to principles entered in [4], as

h_e h_t = l m dl/dt, (1)

where h_e and h_t - builders of quantum of activity in energy and temporal representation; m - mass of a microscopic object; l =nl_h length of associated waves; dl/dt=kl_h/h_h - the instantaneous velocity, here n, k – chrono-quantum numbers, and l_h =ch_t - corresponds to fundamental quantum length. In view of the given labels it is gained

h_t = l_h (knm/h_e)^0,5. ( 2 )

From the formula (2), it is visible, that quantum objects chrono-discretization it is bound to their energy and mass. Transferring to the analysis of consequences of application of principle chrono-quantum digitizations, we shall consider classical spatial localization of dot objects reinterpretation. Dynamics of such objects is characterized with the following trivial analogs of differential relations:

V = kl_h/h_t, w = kl_h/h_t, p = m kl_h/h_t, F =Δm kl_h/h_t². (3)

From the equations (3), the formal follows of reinterpretation a classical principle of causality:

F =Δp/h_t = Δm kl_h/h_t², Δl/h_t = p/m = kl_h/h_t. (4)

The given formulas define change of an impulse and coordinates of the material point to within quantities l_h and h_t at determination of a primary field of forces. In a wave mechanics, localization is determined by a wave function [2]:

ψ = ψ (l, t). (5)

Each such psi-function contains an undular package of monochromatic waves which impulses are made in an interval:

Δp = h_eh_t |Δl | l ^-2. ( 6 )

The classical wave theory compares (6) inversely proportional dependence of an interval for equality Δl localizations of undular process from parameters of interfering waves Δl and Δp. From told follows, that spatial localization of quantum objects may occur to within l_h, energy up to h_e, and time up to h_t, parameters of localization of velocity and an impulse are accordingly defined. The limiting transition to quasi-classical localization of a microscopic object is probable at observance of the following requirements: the peak spatial reduction of a undular package and slowly varying coordinate function of a lapse rate of a potential energy in an external field. At temporal-energy reinterpretation relations of indeterminacy, it gives the following boundary measure for process of localization:

Δl Δp = h_eh_t, ΔEΔt = h_eh_t. (7)

Trivial transformations, partitioning of temporal, and energy components allow receiving:

Δl Δp/Δt = h_e, ΔE = h_e, Δt = h_t. (8)

Having predetermined boundary measure of existential localization, it is possible to compare chrono-energy digitizations of a variation of a psi-function to the relevant values dynamic variable. Then probable model representations of solutions of a Schrödinger equation will be reinterpretation, as the time localizations on the allocated time shells [4]. Analogous temporal determinations are similar to original diffraction process on knots of the virtual lattice in space absolute attributes of events. Here we for the first time collide about enough composite questions, the bound with concept of a relativity temporal dynamics in the environmental physical world [3]. Proceed from extensiveness and depth of the mentioned concepts the author hopes to return to them in the special publication.

REFERENCES

1. Fermi E. Molecules, Crystals and Quantum Statistics. – N.Y., 1966.
2. Slater J.C. Concepts and Development of Quantum Physics. – N.Y.: DP, 1969.
3. Fejgin O.O. DISCRETE - TEMPORAL MODEL OF UNIVERSE
4. Fejgin O.O. Discrete Principles of Quantum Chronodynamic

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