© Oleg O. Feygin

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

The basis of the modern hypothetical models featuring dynamics of development of existential continuums, as a rule, consists of quantum-theoretical ideas. Particular interest of interpretation of the basic concepts of a quantum mechanics here may represent, by eduction of chrono-energy making of classical Plank’s quantum. The given operation may have various physical consequences, translating determination of the kinetic states of a continuum in representations about stochastic localizations, including the cosmological order. Fundamental temporal digitization of energy and a substance gives in occurrence of a gang of the representations serving as a basis for build-up of original quantum chrono-dynamics, kinetics, and cosmology. Together it gives all in occurrence of synthetic subitems blanket discrete physical temporallogy as a chrono-quantum mechanics.

The present operation is devoted to model interpretation of reference quantum representations on a basis before the received theoretical results for a mechanics of chrono-quantums [1-7]. In the previous examinations [2, 3] description of the arbitrary state of a psi function was compared cumulative chrono-quantum localization on temporal shells of a continuum /TSC/ - T(i) to various probability amplitudes. It was shown, that the probability amplitude of transition T(i) of one TSC in another makes the total of products of amplitudes of transition of the intermediate the TSC on amplitudes of transition of them in terminating the TSC. The given total is entered by all terms concerning everyone the TSC and having the following operational representation:

, (1)

Where i = a, b-a, b, …, (b > a) - a sequence of 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:

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

The quantum-theoretical probability of chrono-energy localization of a microscopic object on some allocated the TSC will be accordingly equal [6, 7]

|T(i)|^2 = const 1/{exp[i E t/h(t) h(e)]} = IT [E(0), t(0)]|^2 1/{exp[i t/h(t)]}^[E/h(e)], (3)

Where E, t - energy and time of existential localization; h(e), h(t) - energy- and chrono-quantum builders. Expressions (2) and (3) in a new fashion allow to interpret 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 completely invariant at phase inverse. The paradoxicality of a situation for probability of similar existential localization speaks the limiting value of 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); (4)

here m - the nonrelativistic rest mass; k, n, r - numerical coefficients of proportionality between fundamental parameters of TSC; l(h) – Plank’s equal-distances [5]. The detailed analysis of formulas (4) reveals particular differences of chrono-dynamic interpretation from the reference theory, consisting in chrono-quantum localizations of any material object on the certain TSC. For difficultly microscopic objects, the situation when separate builders have the complete various energies and varied probability amplitudes is characteristic. The reference theory predicts here occurrence of the interference effects with resulting variable probability for some gang of stationary states. On the other hand, chrono-quantum dynamics guesses localization on the TSC without dependence from spatial extent of physical objects.

Let us add the interpreted fashion of the basic quantum state from (4), process of the complete localization on some allocated TSC 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) >; (5)

Here d(j, i) – Kronecker’s figures. 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 metric transitions in 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 interpreted, 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); (6)

Here C(i), D(i) - pluralities of base quantum-mechanical embodyings in chrono-quantum representation for localizations on next the TSC. It is necessary to note, that the system of the equations (6) illustrates a principle of chrono-dynamic relativism, consisting in various levels of identification of microobject on a kind temporal systems of readout. For internal system of readout, the result of transition between the next conditions will be described by amplitude of probability of temporal localizations as

<T(b)|T(A)|T(a)> = S <T(b)|T(i)><T(i)|T(A)|T(j)><T(j)|T(a)>, (7)

Where Т(A) - the allocated frame of reference. At transformation of a frame of reference in Т(A) the relation (7) 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)>, (8)

where quantities A and B are similar to quantum-mechanical functionals. The carried out examination shows, that the arbitrary states of a microsystem may be submitted as a peak-a-boo linear combination of chrono-quantum localizations on a sequence the TSC. Thus, there is a particular quantity of discrete representations a TSC, which is included in the blanket quantum mechanical description of a nature on the modern physical analogs. Briefly, their essence it is possible to formulate the TSC on which any material object is located as presence of plurality. The interval of localization on the arbitrary the TSC corresponds to duration of chrono-quantum, as well as an interval parting next TSC. Similar model representations allow expanding boundaries of logic interpretation of a fundamental principle of causality and determinism of the environmental physical world.

1. Feygin O.O. Discrete-Temporal Model of Universe. // Ibid. - 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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