It is natural to count, that any new theory including chronoquantum mechanics, represents in the basis only the relative true, but it, certainly, does not give the foundation for the prior non-recognition of new ideas brought by it and concepts. Chrono-physical concepts of this or that shape, undoubtedly, will undergo the further development, but most likely, their evolution will go aside the further withdrawal from classical representations of a quantum mechanics. In accordance with structurization of physical reality to become clearly, that the development of new chronoquantum's representations will be accompanied by origin of a lot of metaphysical problems of the bound with the analysis the nature of an enclosing material world. Similar problems directly or indirectly concern connection between tools of observation of appearances and parameters of microscopic objects, and fundamental concepts of probability of the fresh wording principle of causality.

In the present conferring the further development of the conceptual plan of model operations of processes temporally localizations of microscopic objects in boundaries of the chosen existential continuums is considered. Further properties of wave functions, as solutions for analogs of Schrödinger equations are comprehensively analyzed. Based on the obtained outcomes comparisons and deductions about applicability of a principle of superposition of chronoquantum's states are made at temporally localizations of microscopic objects on strict sequence chosen continuums. Thus dualism of a phenomenological covariance of model build-ups discrete temporalogy by engaging of some reference procedures from mathematical methods of physics. The given methods, first, include the homogeneous linearization at theoretical exposition of dynamics of localization of the material microscopic objects. It is shown, that model interpolation of special sections of a quantum mechanics and a field theory can be reached by contextual installation of the linear quantum functionals, the bound with properties of metric space, and a perfect vacuum.

Radiating from far-reaching analogies, in a basis àòåìïîðàëüíîé concepts of development of world around the extending model concept uniform is possible to put fields from which it is possible to deduce deductively properties of space - time in a continual approximation. The given concept of discrete temporalogy concerns to discharge is inductive synthesized conceptual platforms, being inherently, one of subitems quantum chronodynamic, including the relativistic theory of discrete chrono-field [7, 9, 11]. One of principal singularities of the new theory is representations about structure uniform chrono-field, the continuous in an interior frame of reference and discrete - continual for exterior observer.

The similar problematic enters in relativistic quantum chronophysics /RQCP/. Continuity RQCP will consist in the complete correspondence of its paradigm to main principles of a reference quantum mechanics, including adequate interpretation the basic conceptual devices of field theories of a perfect vacuum and fundamental particles. On epistemological essence, RQCP supplements variability of the modern unifying physical theories of space and time. In ontological plan, RQCP structurization's accepts of causal relationships, spreading them on all without elimination the material appearances of an enclosing real.

For quantum mechanical processes by boundary magnitudes Planck parameters, and as the following point of a temporal dial, obviously serve, it is necessary to count a lifetime of the easiest virtual particles. Given temporal distance determines kinetics of localization of microscopic objects on chosen temporal envelopes of an existential continuum /CTEEC/ [7 - 9]. Their existence can be connected, both with cosmological aspects, and with a problematic of the virtual structures in a perfect vacuum [1, 4].

The quantum mechanical exposition of behaviour of microparticles is grounded on several fundamental deductions among which the major are principles of a wave-corpuscle dualism and indeterminacy:

Δp Δx ~ ΔE Δt ~ h (e) h (t); (1)

Where p - impulse; x - coordinate; E - an energy; t - time; h(e) - chronoquantum; h(t) - energyquantum. According to (1) velocity, as well as impulse of a particle cannot have a defined value simultaneously with its coordinates. However, the product of a velocity and time gives mechanics transition of a microscopic object, as magnitude obviously smaller the Planck length compared to a fundamental metric size of a mesh of space [5]. Therefore lack at a particle of a velocity simultaneously with coordinates means, that if the position of a particle is localized in the present instant through chronoquantum its coordinates will already not have any defined value. In a frame of reference of the given localization there is only some probability of a determination of a particle in this or that point of space, hence, the concept of a trajectory loses the sense. Purely on other the situation will look on the part of the extraneous "timeless" observer, for it passage of a microscopic object to new parameters will mean its localization in next CTEEC. The quantum mechanical undular psi-function, which quadrate of the module gives a probability distribution of a determination of microparticles in space, too interpretation in chronophysics, as assigning probability of localization of a microscopic object on chosen CTEEC. Accordingly, probability amplitudes CTEEC - in an operational aspect [6] will look like localizations

{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)>, <T(b)|T(a)> = S <T(b)|T(b-a)><T(b-a)|T(a)>, <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)>; (2)

where T(a), T(a, b), T(b), T (i), T (j) - the CTEEC of terminating, transitional and intermediate states, accordingly; i = a, b-a, b, …, (b> a) - sequence of the CTEEC; d (j, i) - a Kronecker's delta. Probability amplitudes of localization's processes in a complex conjugate to amplitudes of inverse passages and from the point of view of the nonrelativistic quantum mechanical analysis represent outcome of an approximation for infinitesimal intervals of time.

In a classical quantum theory, the undular psi-function defines a state of a system on all a time interval of its existence. From here it is usually concluded, that the derivative on time from an undular psi-function should be determined by a value of function:

dψ /dt = <L>ψ = (2π i / h) dS /dt = (2π i / h) <H>ψ, ψ = const exp[ i S / h(e) h(t)], <L(d)>ψ = Δψ / h(t) =

= [2π i / h(t) h(e)] ΔS / h(t) = [2π i / h(t) h(e)] <H(d)>ψ. (3)

where <L>, <H> and S - quantum mechanical analogs of operators of Lagrange, Hamilton and a mechanical operation. Operationally - differential equalities (3) make one of the basic groups of the equations of chronoquantum's mechanics. At the complete identification of an aspect of a quantum mechanical Hamiltonian it is possible to count, that the equations (3) determines undular psi-functions of the given physical microsystem.

Discrete - temporal aspect of the relevant quantum mechanical Lagrangians can be installed to similarly common quantum mechanical principle of operational representation of physical quantities, at passage to semiclassical exposition of some wave function In turn it can be is interpreted as comparison to any microplants of a chronodynamic operator, a defining requirement of its localization on chosen CTEEC. Relations (2) and (3) also contain discrete-temporal a pre-image of the basic analytical shapes of a quantum mechanics - Schrödinger equations in various representations.

To one of temporal's researches directions is chronophysics a perfect vacuum, the filled the subpartial virtual particles. Aspects of detailed elaboration of solutions in the given problematic are bound to an extension of a definition chronoquantum's Hamiltonian of the free particles as

<H(d)> = const [h(t) h(e)]^2 <L(d)>. (4)

It is obvious, that the generalized aspect of the chronoquantum's mechanical equations of an aspect (3) with Lagrangians (4) similarly classical fashion of a Schrödinger equations for the free particle with the solutions linking wave-corpuscle performances through chronoquantum's parameters. In classical representations of a quantum mechanics, the wave function should be the unique, the continuous, and terminating in all metric space.

The Schrödinger equations for the free particle have the relevant terminating solutions including an ionization continuum of energies. The bound particles obey terminating solutions at a discrete energy distribution. At multiparticle ensemble of interdependent microparticles, the complete gang of coordinates in multivariate configurational space determines the wave function. Passing to chronoquantum's mechanics, it is possible to note, that the ionization continuum of microparticles corresponds them to localization in boundaries particular CTEEC at determination of their world lines. It follows, as from common principles õðîíîäèíàìè÷åñêîé digitization of physical event's space and from interpretation their quantum mechanical analogs:

|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(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)>,

T(b) = S <T(i)|U(b – a)|T(j)> T(a) = S {d(i, j) – const H[T(a)] (b – a)} T(a); (5)

here C(i), D(i) - populations of base quantum mechanical embodyings in õðîíîêâàíòîâîì representation for localizations on next CTEEC; Ò(À) and Ò(Â) - the chosen frame of references. The equations (5) illustrate a principle of chrono-relativism, consisting in various levels of identification of a microscopic object depending on a temporal aspect of references. Formulas (2) - (5) can be interpreted also in language of psi-functions through concept of probability amplitude of localization of some CTEEC. Accordingly, localization in next CTEEC will be featured the following linear combination of psi-functions:

ψ = const(1) ψ(1) + const(2) ψ(2), |ψ|^2 = |const(1)|^2 |ψ(1)|^2 + |const(2)|^2 |ψ(2)|^2 +

+ {const(1)* const(2) ψ(1)* ψ(2)* + const(1) const(2)* ψ(1) ψ(2)*}. (6)

Formulas (6) determine a principle of chronoquantum's states superposition, adequate to model representations about properties of chrono-functions "to sew together" next CTEEC in uniform chronodynamic's structure. Nevertheless, it is possible to assume, that there is a group of temporal's models where the given amplitude can vary depending on a position of plant on direct of substantial time. Thus, the amplitude of each complete localization will be proportional to amplitudes of localizations on the next envelopes, increased on a series of the weight coefficients similar to quantum numbers.

In the most common sense of the equation (6) define regularities of quantum's chronodynamic. Radiating from earlier obtained temporal reinterpretation [2, 3] the basic equations of a quantum mechanics for transtemporal matrixes, it is possible to enter correctly enough concepts about the one-dimensional linearization of strictly sequential population developing CTEEC:

<T(b)|T(b-a)|T(a)> = <T(n+1)|T(n)|T(n-1)> => |T(b-a)> = S |T(n)><T(n)|T(b-a)> = S |T(n)> C(n). (7)

It is known, that properties of the wave functions, satisfying to solutions of a Schrödinger equations, have common character, including uniqueness, a continuity and a finiteness. For chronophysics, it means an identification of a frame of reference with some chosen CTEEC. Then the Schrödinger equations for the free particle will have terminating in all space CTEEC of a solution at any positive and zero value of an energy, making the continuous energy distribution.

In case of the bound particle, the quantum theory predicts presence of a discrete spectrum, at a wave function of points of multivariate configurational space. Here the direct analogy between processes on strict sequence CTEEC is observed.

Conceptually - logic connections between next CTEEC are grounded on analog of a principle of superposition of psi-functions. Owing to an operation of the given principle a Hamiltonian of the linear wave equation of the made system at inverse of a frame. The operating invariance of a specular reflection in quantum physics reduces in a spatial parity conservation law of a quantum state. The spatial parity conservation law determines inversion of psi-functions with deviation them on even and odd. A spatial parity conservation law it is partial regulates probability of a generation - dissipation of the made systems with maintenance of a moment.

Together with a principle of an indistinguishability of microscopic objects, quantum conservation laws govern appearances of trans-localization, appearing for the detached onlooker as temporal change of actual events. Relocating of adequate microscopic objects in boundaries of the arbitrary dual system corresponds to the following equality of analytical shapes:

ψ[j (1), j (2)] = exp(i a) ψ[j (2), j (1)] = exp(2 i a) ψ[j (1), j (2)] = ± ψ[j (2), j (1)],

ψ[j (1), j (2)] ~ ψ{n[j (1)]} ψ{k[j (2)]} ± ψ{n[j (2)]} ψ{n[j (1)]}. (8)

where j (1), j (2) - populations of coordinates and spins of microparticles. The relation (8) shows that the system of two identical particles can be featured the symmetric transformation by psi-functions. In quantum terms, the symmetry of psi-functions is defined to a spin of particles. To the particles possessing a half-integer spin, antisymmetric psi-functions are compared, and with particles to an integer spin - the symmetric.

The surveyed group of chronoquantum's principles of continuum's digitization should be spread and to a perfect vacuum, for example in representation of Dirac. Under the theory of Dirac of property of physical space were defined by vacuum as a world material background. In the modern quantum mechanics, all fundamental particles are considered as quantums of the relevant field structures that for a physical system of vacuum is interpreted, as a population of fields without actual particles. It is known, that under laws of a quantum mechanics for any field oscillations are characteristic.

In case of a perfect vacuum, it will be so-called "zero" oscillations accompanying with a birth and vanishing of virtual particles, relevant to the nature of each concrete field. Realization of the universal law of conservation of energy demands for the given virtual particles of observance of fundamental property of specifically short lifetime. According to principles of chronophysics, it can mean presence the temporal-virtual localization, parting next CTEEC.

Macroscopic display of the virtual properties of a perfect vacuum by probably only mediate fashion in effects of Lamb detrusion of levels of lines of atoms, attractions of plates in vacuum, the abnormal moment of magnet of electrons and interaction of quantums. Quantum chronophysics it is possible to count other important corollaries of appearances tunneling and superconductivity.

The obtained outcomes (3 - 8) for linearization of microobject's localization in view of influence of virtual particles of a perfect vacuum will gain a final aspect:

<T(b)|X|T(b-a)|Y|T(a)> = <T(n+1)|T(n+1/2)|T(n)|T(n-1/2)|T(n-1)>; (9)

where X and Y - factors of the virtual localization; T(n+1/2) and T(n-1/2) - relevant the virtual CTEEC. Thus, the virtual properties of a perfect vacuum can be featured in terms localizations, switching it in the common plan of digitization. The physics of virtual particles supposes their origin not only in vacuum. It is considered, that they constantly arise and disappear near to fundamental particles and at their interaction. Thus, the virtual partial electrocharges act the virtual positrons and electrons, polarizing enclosing vacuum. Because of polarization of vacuum around of charged particles, there is the bound with them the structural pulsatory charged envelope reducing their effective charges that is exhibited in macroscopic effects of interpartial interaction.

From point of view RQCP, it can be interpreted, as the virtual localization of quantum microscopic objects in borderline fields or in other methodological approach, as a delocalization on the virtual CTEEC. Their participation in processes of localization can be presented as a modification of a spectrum of eigentones chrono-fields. Here actual enough and debatable problem identification of the virtual processes on terrain clearance makes axes of temporal events. Radiating from principle terrain clearance virtual particles, it is possible to assume, that their occurrence is bound to interaction of next envelopes CTEEC.

Further, it has been shown [6], which the probability amplitude of the basic passage from one CTEEC in another is equal to the total of products of amplitudes of the intermediate and terminating localizations direct and conjugates representation:

{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)>,

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

<T(b)|T(a ® 1, b ® ¥ )|T(a)> = <T(b)|T(S)|T(a)> = S <T(i)|T(S)|T(j)>|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)>; (10)

where T(a), T(a. b), T(b), T(i), T(j) - the CTEEC of terminating, transitional and intermediate states, accordingly; i = a, b-a, b, …, (b> a) - sequence CTEEC. Probability amplitudes of localization's processes in a complex conjugate to amplitudes of inverse passages and from the point of view of the nonrelativistic quantum mechanical analysis represent outcome of an approximation for infinitesimal intervals of time.

From relations (10) 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),

|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)],

<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)>,

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

<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)

Here C(i), D(i) - populations of base quantum mechanical embodyings in chronoquantum's representation for localizations on next CTEEC.

Identification of the complete population strictly sequential localizations on CTEEC means terrain clearance determination of world lines of the material plants. It follows from common principles to digitization of physical events and can be interpretation, as chrono-relativism consisting in various levels of identification of a microscopic object depending on a temporal aspect of reference frame. Thus, the amplitude of localization can vary depending on a position of plant on direct of time and will be proportional to probabilities of next envelopes, increased on a series of weight coefficients:

T(b) = S <T(i)|U(b–a)|T(j)> T(a); U[T(b), T(a)] = d(i, j) – const H[T(a)] (b–a),

T(b) = S {d(i, j) – const H[T(a)] (b–a)} T(a), const [T(i) – T(i+1)] / h(t) = S H[T(a)] T(i) <T(b)|T(b-a)|T(a)> = <T(n+1)|T(n)|T(n-1)> => |T(b-a)> = S |T(n)> <T(n)|T(b-a)> = S |T(n)> C(n); (12)

where U(a, b) = <b|U|a> - a matrix of trans-temporal localizations of the material object. In the most common, sense of expression (11) and (12) define of discrete-temporal interpretation the basic equations of a quantum mechanics for trans-temporal matrixes. Here there is a possibility enough correct introduction of a conceptual means for covariant homogeneous - linearized translations of the material plants of a microcosmos on strict sequence developing CTEEC. Thus, following the entered nonconventional chrono-quantum mechanical nomenclature, we shall consider, that the probability amplitude trans-temporal passage between strictly next localizations of analog of the same material plant on population CTEEC will make

P[U(a, b)] ~ const F* i / h(t); (13)

where F* - the dimensionless energy potential of a quantum microscopic object.

The carried out examination shows, that the scientific - materialistic analysis of the modern state of a problematic of harmony of quantum and cosmological appearances can be successfully supplemented important semantic component RQCP. Basic building blocks RQCP are model plans of self-consistent interaction of quantum microscopic objects in temporal boundaries of chronoquantum's magnitudes and relevant to them principles of a relativistic covariance and conservation laws. Special complexities in RQCP arise at attempts discrete analysis of canonical relations of a relativistic quantum theory of a field, but already prestress outcomes show their possibility of interpretation on a conceptual basis of discrete quantum temporalogy [10, 11].

In an inference it is necessary to note, that examination problems of chronophysics has the important heuristic value and can help with the analysis of shortages of old theories and build-up new, more adequately fundamental physical regularities formative a uniform pattern.

1. Feygin O.O. Discrete - temporal model of Universe // SciTecLibrary (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

8. Feygin O.O. Mechanics of chrono-quantums // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/5978.html

9. Feygin O.O. Quantum temporallogy // Ibid. - http://www.sciteclibrary.ru/eng/catalog/pages/6375.html

10. Feygin O.O. Model linearization of quantum chronodynamic // SciTecLibrary (2004). - http://www.sciteclibrary.ru/rus/catalog/pages/7015.html

11. Feygin O.O. Principles of chronoquantum mechanics // Ibid. – http://www.sciteclibrary.ru/rus/catalog/pages/7016.html

Back