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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.

The papers [

This paper gives summary, discussion and progress of the results from [

Derived in Refs. [

Here Δ p ~ p = m Δ a / Δ 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, h is the reduced Planck constant, a 0 , m 0 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 α = 1 , for a sphere α = π / 6 ), 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 Δ t ≡ t i 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.

Objects | Uncertainty principle (un) | Absolute certainty principle (ac) |
---|---|---|

Microcosm and mesostructures | Relationship: Δ a ⋅ Δ p ≈ ℏ / 2 Growth laws: 〈 a 〉 3 / 2 d 〈 a 〉 ≈ ( ℏ a 0 3 / 2 2 m 0 t i ) 1 / 2 d t , 〈 a 〉 3 / 2 d 〈 a 〉 ≈ ( a 0 3 Δ E 2 m 0 ) 1 / 2 d t Maximum size a max u n ≈ 2 m 0 a 0 3 9 ℏ Δ t min | Relationships: a p = ℏ / 2 , E t = ℏ Growth law a 4 d a = ( ℏ / 2 α ρ ) d t Maximum size a max a c ≈ ( ℏ t i max 6 m 0 ) 1 / 2 ≅ ℏ ( 6 m 0 E min ) 1 / 2 |

Objects of astrophysics and cosmology | Relationships and growth law | Δ a | ⋅ | Δ p | ≅ K c / 2 . | Δ E | ⋅ | Δ t | ≅ K c 〈 a 〉 2 d 〈 a 〉 = ( 1 / 2 ) ( ρ c / ρ ) 1 / 2 a 0 2 c d t | Relationships and growth law a p ≅ K c / 2 , E t ≅ K c 〈 a 〉 2 d 〈 a 〉 = ( 1 / 2 ) ( ρ c / ρ ) a 0 2 c d t |

Objects | Uncertainty principle | Absolute certainty principle |
---|---|---|

Microcosm | Formation of hadron jets from quarks | Formation of carbon nuclei in quark environment → carbon cycle in stars |

r-processes; deeply inelastic relativistic processes in nuclei Stable nuclei | s-processes | |

Formation of super-heavy nuclei up to mass number A e n d ≅ 470 | Formation of giant nuclei with a max a c ≈ 1.6 × 10 − 12 m | |

Mesostructures | Typical sizes of all known artificial and natural diamonds: from 0.7 nm to 20 sm | Typical size of a carbonado-type diamond (≈0.1 mm) |

Characteristic sizes of protein nanoparticles, ribosomes and mesoobjects (archaea, cells): from ≈ 1 nm to ≈ 7 μm | Characteristic size of insulin (≈ 2 nm) | |

Stars | Typical times of formation and a size of neutron stars: 0.17 - 17 s, 16 km | Typical times of formation and a size of neutron stars: 0.17 - 17 s, 16 km |

Globular clusters of red giants | Average size is 200 ps (parsec) | |

Superclusters of galaxies | Average size is 84 Mps (megaparsec) | Average size is 36 Mps |

conceptions. One can see that under the proposed kinetic approach the uncertainty principle covers a wider spectrum of processes for objects formation as compared to the absolute certainty principle. At the same time, both principles mutually complement each other.

Thereby, the developed asymptotic method for investigating the kinetics of formation of objects with quantum properties, corresponding to the principle of intellectual asceticism [

Based on the law of growth for objects in the format of the uncertainty principle [

m f u n d = ℏ c a f u n d . (1)

It follows from here that m f u n d c 2 = ℏ c / a f u n d = 196 GeV [

In the field of nanosized scale and mesoscopics the uncertainty principle covers the whole spectrum of object formation processes described in refs. [^{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 characterized by strong bonds of C-C, C-N and C-O type that provide high-frequency oscillating constituent of internal motion, and by rotational isomerism and low-frequency component of spin-lattice relaxation creating conformational motion with the typical times τ = 10 − 10 - 10 − 7 s .

In general, the mechanism of formation of macroscopic diamond particles from nanodiamonds described in works [

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 [

At the same time, in [

In case of continuous protein nanofibres (linear nanostructure), one can use the method from [

d = a 0 ( 2 m 0 a 0 2 ℏ t i ) 1 / 4 , (2)

〈 l 〉 = ( ℏ m 0 t ) 1 / 2 . (3)

With the typical parameter t i ≡ t R = 2 π ℏ b / k B 2 θ R T [_{B} is Boltzmann constant, b is a number of crystal-forming bonds, θ R is the typical rotational bond temperature (≈2.6 K), T is ambient temperature), we derive from the formula (2) that for the embryos like glycine (the least amino acid with m 0 = 1.25 × 10 − 25 kg , a 0 = 0.42 nm [

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 [

With reference to the processes of cosmic scale, it should be noted that the uncertainty principle [

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

a max a c = ℏ ( 6 m 0 E min ) 1 / 2 → a max a s t r = K G ( 6 m 0 E min ) 1 / 2 .

The minimum value of the carried away energy at supernova explosion is equal to E min = 10 41 J [

a max c = M c G 6 c 2 ≅ 6.7 × 10 26 m

The set spatial range 1.36 × 10 6 - 6.7 × 10 26 m includes the sizes of objects from dwarf stars to the observed space domain (light radius is approximately equal to 1.323 × 10 26 m ). In particular, it refers to a size of supercluster of galaxies evaluated in [

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 therefore, are not described in scientific literature in details.

In microcosm in the format of the uncertainty principle, such an object can be a final nuclide with a mass number near to A e n d ≅ 470 [^{−}^{15} m of strong interaction between nucleons in usual nuclei. Due to Coulomb repulsion of protons, nuclear forces cannot hold compactly such a huge system consisting of protons and neutrons bound by just strong interaction. It should be noted that the calculated nucleus size corresponds in an order of magnitude to the Compton wavelength of muon neutrino/antineutrino with the rest mass m ν μ = 0.19 MeV [

ν ¯ μ + p → n + μ + .

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 [

The abovementioned similarity of muon antineutrino and pions implementing the strong interaction between nucleons in nuclei [

Nuclei | Usual [ | Giant [ |
---|---|---|

Type of interaction | Strong | Assumed |

Carriers | Pions | Muon antineutrino |

Rest mass m r , MeV | 139.57 | 0.19 |

Compton wavelength ƛ = ℏ / m r c , m | 1.46 × 10 − 15 | 1.05 × 10 − 12 |

Nucleus radius R, m | ~ 10 − 14 | ≈ 0.8 × 10 − 12 |

Yukawa ratio, m^{−1} U n u c l ~ exp ( − R / ƛ ) / R | ~ 10 12 | ≈ 3 × 10 11 |

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 [

Small flux of embryos: 〈 a 〉 ≈ ( 75 k θ D 8 π ρ ) 1 / 5 t 2 / 5 , (4)

Large flux of embryos: 〈 a 〉 ≈ ( 27 k θ D a 0 2 ⋅ 6 1 / 3 π 5 / 3 ρ ) 1 / 6 t 1 / 3 . (5)

It has been accepted that Debye parameter θ D approximately corresponds to the averaged characteristic oscillation temperature of bond expansion (C-C, C-O, C-N) of 1500 K [^{−10} s [^{−7} s [

2) In the format of absolute certainty with the average density of amino acids ρ = 1.3 × 10 3 kg ⋅ m − 3 [

Organic-silicon mesoobjects [

Based on the data on atomic radii and the lengths of interatomic bonds [

a max u n ≈ 2 m 0 a 0 3 9 ℏ Δ t min ≅ 60 nm ,

where Δ t min = 1 / ω e c = 7 × 10 − 14 s ( ω e ≅ 10 5 m − 1 [

a max u n ≈ 2 m 0 a t r a n s 3 9 ℏ Δ t min ≅ 4 μ m .

This size in a scale of magnitude corresponds to the sizes of biological mesoobjects [

With reference to unobservable cosmological objects, cosmic sphere [

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 especially refers to nano-range-of-problems, mesoscopics, and to cosmology.

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.

The author is grateful to the professor Jean-Paul Auffray for the attention and valuable comments to works [

Lin, E.E. (2018) Revealing the Uncertainty and Absolute Certainty Principles in the Kinetics of Objects Formation. World Journal of Mechanics, 8, 82-93. https://doi.org/10.4236/wjm.2018.84007