Revealing the Uncertainty and Absolute Certainty Principles in the Kinetics of Objects Formation

The paper presents some examples revealing the uncertainty and absolute certainty principles in kinetics of objects formation that are different in their physical nature and in space scales: sub-stances of microcosm, nanoparticles and mesostructures, astrophysical and cosmological objects. Under the proposed kinetic approach, the uncertainty principle covers a wider spectrum of processes of approaching to equilibrium and object formation, than the absolute certainty principle. It refers, in particular, to nano-range-of-problems and mesoscopics as well as to cosmology. Both principles predict formation of objects that are not well-known or, at least, well-described so far. Among these are neutron-rich super-heavy and giant nuclei, biologic and organic-silicon mesoobjects, cosmological objects with the sizes considerably exceeding the size of a light sphere.


Introduction
The papers [1]- [6] consider principle issues of dynamics of quantum systems and description of object properties different in physical nature and in spatial scale: from substances of microcosm to cosmological structures. A special case here is the recent study into nanoclusters, nanostructures and nanomaterials. ϕ of density distribution in space of these object sizes a (t is the current time). In addition, a general issue about fields of application of concepts of quantum system dynamics under the uncertainty principle [2] [3] [4] and absolute certainty principle [5] has been put forward and partially studied. In the light of a universal relationship 1 4π a k ∆ ⋅ ∆ ≥ (resulting from Fourier theorem) for dispersions of a coordinate a and a wave number k, valid for a wave of any physical nature, in case of asymptotic coherent state of a quantum system, when dispersion product has the minimum value, and dispersions of values are replaced by values themselves, the uncertainty and absolute certainty principles are connected by a one-to-one correspondence [9]. It is shown that a type of the growth law for such objects depends on the fact, what exactly principle is assumed as a basis for consideration. This paper gives summary, discussion and progress of the results from [7] [8] [9], in light of notions [1]- [6], using examples for formation of microcosm objects (elementary particles and atomic nuclei), nanoparticles and mesoobjects (diamonds, protein substances), astrophysical objects (neutron stars, white dwarfs, globular clusters of red giants) and the observable cosmological structures (superclusters of galaxies).

Results and Their Discussion
Derived in Refs. [7] [8] [9] phenomenological laws of a sizes growth of volume packed objects with the t time and expressions for their characteristic sizes in formats of the uncertainty and absolute certainty relationship within the space of sizes are given in Table 1.
Here p p m a t ∆ = ∆ ∆ is uncertainty of momentum p, m is object mass, ΔE is width of energy level E of the excited state of quantum mechanical system determined by nature of objects and a mode of process,  is the reduced Planck constant, 0 0 , a m is size and mass of an embryo, t i is characteristic time scale of an elementary (single) act of objects interaction, α is geometrical factor (for a cube 1 = α , for a sphere π 6 α = ), K c is phenomenological action constant in cosmic scales, ρ is density of observed substance in the Universe, ρ c is substance critical density at which the Universe becomes closed, c is light velocity. Physical meaning of the relationship between uncertainties "coordinate-momentum" is in the fact that during a period of time i t t ∆ ≡ of elementary (single) act of objects interaction, the exact size of each object cannot be determined until this interaction is finished. It is associated with the fact that up to the end of the single act, it is impossible to determine the correlation between the object and each interacting surface element. In the format of absolute certainty, the relationship "coordinate-momentum" implies that at each time, the object under consideration is strictly localized within the space of sizes. Table 2 provides examples of how the above principles manifest themselves when describing formation of objects in the processes of approaching to equilibrium [7] [8] [9]. The given results are in agreement with the generally known  Thereby, the developed asymptotic method for investigating the kinetics of formation of objects with quantum properties, corresponding to the principle of intellectual asceticism [3] and statement [4] about adequacy of phenomenological description of physical phenomena or physical objects, has a sufficient level of generality to be used in problems of high energy density physics and in physical chemistry of high intensity processes. Below are the examples of how uncertainty principle and absolute certainty principle are applied in problems of objects formation in microcosm, nano-and mesocosm, and cosmos.

Microcosm
Based on the law of growth for objects in the format of the uncertainty principle . In [7] the following equation for fundamental mass is given: It follows from here that value approximately corresponds to the mass value of a dark matter particle determined in [11] according to the data of astrophysical observations and equal to 192 GeV. It should be noted that expression (1) is definitely connected with determination of Compton wave-length of a material particle mc =   , and the above value of a fundamental length is adequate to the current concepts. However, the above value of fundamental mass has been obtained beyond general approaches and standard models [2].

Nanometric and Mesoscopic Objects
In the field of nanosized scale and mesoscopics the uncertainty principle covers the whole spectrum of object formation processes described in refs. [6], [12] [13] [14]. Two types of objects are considered: 1) clusters with the lattice formed of atoms of a single type, oscillating as harmonic oscillators with the typical frequencies ~10 12 -10 14 s −1 ("atomic" nanocrystals); 2) clusters formed by macromolecules revealing both oscillating nature of inner motions with the given frequencies, and rotational isomerism with the frequencies ~10 10 -10 11 s −1 ("molecular" nanocrystals). The question arises of whether there is any influence of collective quantum structure properties on the processes of their formation and growth and on the values of their typical sizes. As the objects of the first type, it is reasonable to consider crystals with covalent carbon bonds C-C i.e., nanodiamonds characterized by expressed phonon effects associated with exchange interaction of atoms. As the objects of the second type, it is reasonable to consider protein nanoparticles consisting of amino acid molecules, since the latter are In general, the mechanism of formation of macroscopic diamond particles from nanodiamonds described in works [7] [9] covers all available data about sizes relating to both artificial diamonds obtained in static and dynamic synthesis, and natural diamonds.
One of topical trends of nanoscience and nanotechnology consists in the creation and the study of biological materials, in particular, the study of physical mechanisms of protein biosynthesis [6] [12]. .42 nm a = [12] are regarded as embryo, from above mentioned formula we gain that the greatest size of objects is equal to max 0.6 m un a ≈ µ [9]. The calculated results [9] testify to the fact that at the "instant" excitation of In case of continuous protein nanofibres (linear nanostructure), one can use the method from [7] and obtain the following expressions for determining typical values of the thickness d and the length l of the objects: With the typical parameter Thereby, the results from the relationship "coordinate-momentum" in the space of object sizes are indicative of the fact that in the system of amino acid molecules, accidental formation of quasi-crystalline nanoparticles and mesoobjects corresponding in their sizes to essential proteins and cells is possible. These "incorrect" (mutational) objects can grow on these or those crystallization centers without formation of polypeptide bonds, i.e., without formation of "correct" biological code. At the same time formation and growth of such nanoparticles and mesoobjects is possible on fragments of damaged proteins and cells as on the centers of crystallization. All this is in compliance with the generally known concepts concerning mutations of biological structures at a molecular level.
As for the all-known ideas concerning possible origin of life on the Earth as a result of amino acids brought onto the Earth from space, in [9], in the format of the uncertainty principle, it is shown that the objects with sizes from 30 -45 nm (ribosomes, inside which protein synthesis occurs) to 0.4 μm (nanosized protozoan) can be generated from amino acid fragments formed under impacts of meteorites against the earth surface.

Astrophysics and Cosmology
With reference to the processes of cosmic scale, it should be noted that the uncertainty principle [8] predetermines currently observed Universe accelerated 10 m , determined in [18] based on relationship between physical constants.
The existence of multiple interacting universes does not contradict the statement about existence of a set of images of a "unique specimen" [18].
One can try to evaluate the range of "rigid" sizes of astrophysical and cosmological objects based on the principle of absolute certainty. In case of supernova explosion, one should substitute Planck constant in the proper formula of Table   1 by the determined in [7] The minimum value of the carried away energy at supernova explosion is equal to 41 min 10 J E = [19]. As a seed mass, we will formally accept Chandra- is the mass of Sun [20]. Hence, we obtain that The set spatial range 6

Issues for Further Studies
In terms of evolution of the results, one can try to consider the possibility of formation of objects that have not been yet discovered or are not widely known and

Super-Heavy and Giant Nuclei
In microcosm in the format of the uncertainty principle, such an object can be a final nuclide with a mass number near to 470 end A ≅ [7]. In [9], in a format of the absolute certainty, there is a prediction of existence of giant nuclei with the This reaction assumes formation of "neutron" nuclei in material domains rich in muon antineutrino. The latter are particles "gluing" giant nuclei from inside similarly to what pions do in usual nuclei [21]. Apparently, such hypothetical nuclei can be near to neutron star surfaces (in a crust or liquid domain), where heavy nuclei are located [20] [21].
The abovementioned similarity of muon antineutrino and pions implementing the strong interaction between nucleons in nuclei [21], allows us to put a question whether muon antineutrino are carriers of some type of interaction between nucleons inside giant nuclei similar to strong interaction. Table 3

Nanoproblems and Mesoscopics
In nano-range-of-problems and in mesoscopics the following important issues can be determined: 1) capability check for formation of protein nanoparticles in conditions of relatively low temperatures (e.g. in deep waters); 2) search for new unknown or little-known biological nanoparticles and mesoobjects. Below are some qualitative considerations referring to the given issues.
1) Formulae [7] for calculation of average size nanoparticles in Debye approximation are overwritten in the following way: Small flux of embryos: Large flux of embryos: [12] [14].
2) In the format of absolute certainty with the average density of amino acids   [12]. Such analogy expands a range of questions related to the study of life as a nanoscale phenomenon [14].
Based on the data on atomic radii and the lengths of interatomic bonds [25], it is possible to evaluate an embryo size of a rubber polymer as 0 0.4 nm a ≅ . Resulting from the mentioned value of average density of organic-silicon components, we will determine the mass of the least sphere-shaped embryo as This size in a scale of magnitude corresponds to the sizes of biological mesoobjects [12] and protozoa (archaea) [26]. The calculated sizes can be signifi-

Maximum Cosmological Objects
With reference to unobservable cosmological objects, cosmic sphere [8] with

Conclusions
The method for studying kinetics of formation of objects with quantum properties regarding for uncertainty and absolute certainty principles has been developed. This method is based on the concept of distribution density wave in the space of these object sizes. It is shown that a type of the growth law for objects depends on the fact, what exactly principle is assumed as a basis for consideration.
Substances of microcosm, nanoparticles and mesostuctures, astrophysical and cosmological objects have been considered. The obtained results are in agreement with the generally known conceptions.
Under the proposed kinetic approach, the uncertainty principle covers a wider spectrum of object formation processes than the absolute certainty principle. It Both principles predict formation of objects that so far are not widely known or, at least, well described in scientific literature. Among these are neutron-rich super-heavy and giant nuclei, biologic and organic-silicon mesoobjects, cosmological objects with the sizes considerably exceeding the size of a light sphere.