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Probable interpretation of a quantum theory makes one of its key features and is expressed in inevitability of some indeterminism of the physical phenomena. Obvious exaggeration will not count, that this implies a lot of problems and even obvious contradictions so the basis of quantum mechanical representations is not represented by the complete. The nature of some phenomena of a quantum mechanics not up to the extremity is clear and leans in basic on intuitive physical representations. In the circumstances, it is quite possible, that input of new model concepts from field discrete temporallogy in a new fashion will allow to illuminate some traditional sections of a quantum mechanics and even to give them the modern cosmological interpretation.

Central idea of a wave mechanics is the wave-corpuscle dualism of the material objects. Radiating from this, mathematical methods of the theory of the differential equations with partial differential coefficients it is possible to show, that the wavelength of any particle is equal to the relation of a Dirac constant and its impulse. Accordingly, the shape and parameters of waves of a substance will be featured with solutions of a differential Schrödinger equation with partial differential coefficients for a so-called psi-function. The given solutions are accepted for counting natural, or characteristic, functions. In discrete reinterpretation similar functions are considered in a context of probable processes of localization of microscopic object in the allocated chronoquantum state on some allocated temporally shell of a continuum (TSC) [1-3].

The probability amplitude of TSC - localization in an operational view [6] will look like

{T(b)} = <T(b)|T(a, b)|T(a)> = S <T(b)|T(i)> <T(i)|T(a, b)|T(j)> <T(j)|T(a)>, (1)

where T(a), T(a, b), T(b), T(i), T(j) - the TSC of terminating, transition and intermediate states, accordingly. The given operation has the most various physical consequences, reinterpret determination of the kinetic states of a continuum, as TSC- localization of the cosmological order [1, 4, 5].

In the present operation based on model, interpretation of relations (1) earlier received theoretical results for a mechanics of chronoquantums [7, 8] develop. In the previous examinations [2, 3] identification of the arbitrary states of a psi function was carried out cumulative the TSC - localizations with the various probability amplitudes which are included in (1). Further, it was shown [6], that the probability amplitude of the basic transition from one TSC in another is equal to the total of products of amplitudes of the intermediate and terminating localizations: 

<T(b)|T(a)> = S <T(b)|T(b-a)> <T(b-a)|T(a)>,<T(b)|T(a)> = <T(a)|T(b)>*. (2)

where i = a, b-a, b, …, (b > a) - a sequence the TSC, thus the probability amplitude of transition from one TSC in another in expression (1) in a complex conjugates to amplitude of return transition.

The complete plurality of the intermediate the TSC - localizations makes logically consistent dynamic pattern of the environmental physical world. In an extreme case, the aggregate quantum-theoretical probability of temporally localizations corresponds to concept so-called S - representations: 

<T(b)|T(a® 1, b® ¥ )|T(a)> = <T(b)|T(S)|T(a)> = S <T(i)|T(S)|T(j)>. (3)

Computational methods S - matrixes consist in summation of iterative approaches for the close the TSC with an afterexpansion on all interval of transition. Maximum close are next consecutive the TSC. For them duration of an interval of localization is supposed equal to one chrono-quantum, and itself fundamentally - partial temporally transition will look, as 

|T(a-1)> = T(a-1, a)|T(a), <T(b)|T(a-1)> = <T(b)|T(a-1, a)|T(a)>, <T(i)|T(a-1)> = <T(i)|T(a-1, a)|T(a)>. (4)

From the point of view of the nonrelativistic analysis of a quantum mechanics of the equation (4) represent result of approach for an infinitesimal interval of time. From last relation (4) the opportunity of decomposition on the intermediate the TSC - localizations relevant to classical basic states follows: 

<T(i)|T(a-1)> = S <T(i)|T(a-1, a)|T(j)> <T(j)|T(a)>, T*(i, a-1) = S T*(i, j). (5)

In expression (5) it is taken into account, that the probability of stochastic localization of a microscopic object on some allocated the TSC will be accordingly equal [6, 7]:

|T(i)|^2 = const / {exp[ i E t / h(t) h(e)]} = IT[E(0), t(0)]|^2 / {exp[ i t / h(t)]}^[E / h(e)], (6)

where E, t - energy and time of existential localization; h(e), h(t) - energy and chrono-quantum builders.

Expressions (6) in a new fashion allow reinterpreting a quiescence of a microscopic object with energy E(0). In this case, the quantum-mechanical probability amplitude of the complete spatial identification will be invariance at phase inverse. The paradoxicality of a situation for probability of similar existential localization speaks the limiting value of coordinate-pulsing product dp dx, included in a reference quantum-mechanical relation of indeterminacy:

dp dx ~ h; [m k l(h) / h(t)] [n l(h)] ~ h(t) h(e); [E h(t)^2 / l(h)^2] [k l(h) / h(t)] [n l(h)] ~ [r k n h(t) h(e)] ~ h(t) h(e); (7)

here m - a nonrelativistic rest-mass; k, n, r - numerical constant of proportionalities between fundamental parameters the TSC and flowing macro-parameters; l(h) – distances of metric phase passages, commensurable with Planck long [5]. The detailed analysis of formulas (7) reveals the defined differences of chronodynamic reinterpretation from the standard theory, consisting in temporally localizations of any material plant on defined TSC. For microplants, the situation when separate components have full various energies and varying amplitudes of probability is characteristic. The standard theory predicts here occurrence of interference effects with resulting variable probability for some gang of stationary conditions. On the other hand, chronodynamic assumes localization on the TSC without dependence from mass and a spatial expansion of physical plant.

Let us add the reinterpreted fashion of the basic quantum state from (4), process of the complete localization on some allocated T(i, j):

<T(b)|T(a)> = S <T(b)|T(i)> <T(i)|T(a)>; <T(j)|T(i)> = d(j,i); <T(b)|T(j)> = S <T(b)|T(i)> <T(i)|T(j)>; (8)

there d(j, i) – Kronecker’s figure. One of requirements of localization on T(i, j) from (5), consists in independence of background of mechanical development of a microscopic object. Identification of the complete plurality of base localizations on strictly consecutive the TSC, means terrain clearance determination of a world line of the given microscopic object [1, 4, 7]. Thus, the subset of basic states in chrono-quantum representation has necessary completeness and consistency. It follows from principles of chrono-dynamic formation of plurality of physical events at activation of metric transition tentative the TSC.

Classical quantum-theoretical representations are closely bound to concept of a triplet of the basic states. In a linearized subspace of events the TSC, it may be reinterpreted, as localization with the basic weight coefficients for some allocated quantum-mechanical vectors of states:

|T(b)> = S |T(i)> C(i); C(i) = <T(i)|T(b)>; |T(a)> = S |T(i)>D(i); D(i) = <T(i)|T(a)>; <T(a)|T(b)> = S D(i)* C(i); (9)

here C(i), D(i) - populations of base quantum mechanical realizations in representation for localizations on next the TSC. It is necessary to note, that the set of equations (9) illustrates a principle of chrono-dynamics relativism, consisting in various levels of identification of microplants depending on an aspect of temporally system. For an interior frame of reference the outcome of passage between the next conditions will be described by amplitude of probability of localizations as

<T(b)|T(A)|T(a)> = S <T(b)|T(i)> <T(i)|T(A)|T(j)> <T(j)|T(a)>, (10)

where Ò(A) - allocated frame of reference. At transformation of a frame of reference in Ò(A) the relation (10) transfers in

<T(b)|T(A)T(B)|T(a)> = S <T(b)|T(i)> <T(i)|T(A)|T(j)> <T(j)|T(B)|T(z)> <T(z)|T(a)>, (11)

where quantities A and B are similar on sense to reference quantum-mechanical functionals. Formulas (10) and (11) it is possible to interpret the TSC through concept of probability amplitude of localization of some. The given amplitude may vary depending on a standing of object on direct natural time. Thus, the amplitude of each complete localization will be proportional to amplitudes of localizations on the next shells, increased on a series of weight coefficients:

T(b) = S <T(i)|U(b – a)|T(j)> T(a), (12)

where U(a, b) = <b|U|a> - a matrix a trance-temporally localization of the material object. In the most blanket sense, the key equation (12) defines chrono-dynamics of a quantum mechanics. Radiating from earlier received discrete reinterpretations [2, 3] the basic equations of a quantum mechanics for a trance-temporally matrix it is possible to write down:

U[T(b), T(a)] = d(i, j) – const H[T(a)] (b – a), (13)

where H[T(a)] - chrono-mechanical Hamiltonian; (b - a) - an interval of localization. Accordingly, the formula (12) will become:

T(b) = S {d(i, j) – const H[T(a)] (b – a)} T(a), const =6, 28 (-1)^0,5 / h(t) h(e). (14)

With the help of several trivial transformations the equation (14) is transformed in

const [T(i) – T(i+1)] / h(t) = S H[T(a)] T(i). (15)

The relation (15) contains changes of a level of localization of a psi function on various the TSC through matrix H[T(i)]. Thus, expression (15) is discrete-temporally a prototype of the quantum-mechanical law for dynamics of the world.

The carried out examination shows, that for chrono-quantum-dynamics descriptions of the Universe correctly enough it is possible to enter concepts about presence of strictly consecutive plurality developing the TSC. Thus, existing set of all without exception of discrete representations the TSC will form consecutive points on an axis of time. Thus, blanket chrono-quantum-dynamics the description of an environmental nature on the offered model representations will include also relational time of change of the conditional radius of TSC on which any material object is located at a motion on the world line. According to a principle of indeterminacy an interval of localization on the arbitrary, the TSC will correspond to duration of chrono-quantum, as well as an interval parting next TSC. Boundaries of logic reinterpretation of a fundamental principle of causality and determinism of the environmental physical world allow expanding the theoretical description of similar discretely-temporally mechanical models. More precisely the structure of the above-stated discrete model could be described in various frames of reference. So in space of attributes of events where move the TSC, the model is substantive-static, and in natural boundaries of the arbitrary the TSC - chrono-dynamic. The offered concept of space-time may unit fragmentary models, valid for a particular level of the organization of a substance, consolidating laws of development micro-and mega structures in world around. The separate question makes a view of fundamental correlations between consecutive of TSC. Here it is necessary to carry out additional examinations, but already in zero approach, it is possible to tell, that as a basis for cross-identical correction of psi-functions of any material objects the original field of probable localization on various the TSC serves. The following deduction concerns metric structure the TSC. The basic restriction on velocity of a motion of physical objects streams from reasons of presence of fundamental length of cosmological phase transitions, and stability of sub nuclear micro particles appears directly the bound with their level of localization of energy. We shall note that the question on bounded ness of velocity of distribution of field formations is closely bound to wave-corpuscle dualism of the material objects. Finally, the concept of discrete space-time as four-dimensional variety may appear rather fruitful idea for theoretical and mathematical physics.

1. Feygin O.O. Discrete-Temporal Model of Universe. // SciTecLibrary.com.2003.- http://www.sciteclibrary.ru/eng/catalog/pages/5159.html

2. Feygin O.O. Discrete principles of quantum chronodynamic. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5200.html

3. Feygin O.O. Quantum-theoretical chrono-discretization. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5201.html

4. Feygin O.O. Cosmological principles of quantum chronophysics. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5296.html

5. Feygin O.O. Chronodynamic reinterpretation of Planck’s lengths. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5348.html

6. Feygin O.O. Temporal quantum functionals. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5658.html

7. Feygin O.O. Concepts of quantums chronophysics. // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5813.html

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