Vladislav. V. Kamakin, EngD. Moscow, Russia. 

vladvladkamakin@yandex.ru                                                                                          Published 05.11.2021 on «Tsenamica» website

Abstract: the presence of cenoses in the micro- and macrocosm demonstrates the operation of the laws of the science of «cenology» in a wide (up to 35 orders of magnitude!) dimensional range.         

 Key words: cenosis, cenology.

The object of the science of cenology is a cenosis — a complex system consisting of elements with a rank hyperbolic distribution W(r), obtained as a result of the ranking procedure, where the W value of the feature elements of one species is put in line with the number r (rank) of the species in ascending order. Depending on the nature of the elements, there are two types of cenoses: biogenic and abiogenic. The elements of biogenic cenoses are structural forms resulting from the activities of living matter and mind. In particular, technogenic cenoses consisting of elements of this or that instrumental base [1], as a result of intelligent activity, can be attributed to the biogenic type. On the contrary, abiogenic cenoses are formed mainly from elements of cosmic matter. Thus, astronomical observations have shown that many cosmic objects (solar system, galaxies, galaxy clusters, etc.) are abiogenous cenoses (cosmocenoses/astrocenoses). In particular, there is a hyperbolic rank distribution of our Galaxy’s stars by surface temperature and the same distribution by masses of neighboring galaxies from our environment [2] (Fig.1 a, b). On this basis it was concluded that our Galaxy is an astrocenosis within an even larger cosmocenosis of ~ 3∙10²² m in size — the Local Galactic Group.    

a)b)

                                                                                                Fig.1.

(a) GRR of stars in the Galaxy by surface temperature W, 10³K, r is the rank of the star subclass; (b) Rank distribution of masses of the nearest galaxies in solar masses (Ms ∙ 10⁹).

Meanwhile, at the opposite end of the dimensional scale the presence of abiogenous cenoses is also possible. Let us show this on the example of a cloud of virtual photons around a solitary charge in the physical vacuum.

                                            Fig.2 Image of a cloud of virtual photons around an electric charge.

Quantum mechanics explains the force of Coulomb interaction between electric charges by momentum transfer as a result of exchange of virtual photons surrounding a particle (Fig. 2). Let us determine the dependence of the number N_∆p(r) of virtual photons with momentum Δp on the distance r to the charged particle. A virtual particle is a quantum fluctuation, which is characterized by some properties of real particles. Its existence is determined by the Heisenberg uncertainty principle, which admits the violation of the energy conservation law for extremely small intervals of time [3]. At zero energy of a virtual photon, the latter carries an impulse Δp ≠ 0 and a force F proportional to the number N of photons participating in the exchange: 

                                                       F ~ NΔp                                                     (1)

 At the same time, it has been experimentally established that the Coulomb interaction force between two charges of value q at distance r with regard to (1) is equal to: F = — Kq²/r²~ NΔp , where K = 9∙10⁹ [in∙m∙k-1]-electrostatic constant. At the same time, based on the uncertainty relation: Δx Δp ~ ℏ, where ℏ = ℎ/2 is the so-called Planck constant with a line.  Then for Δ𝑥 ~ r we have:                                                                                                                                                                                                                                                                            F = — Kq²/r² ~ NΔp ~ ℏNr                                      (2) 

Let us estimate the value of N in a particular situation [4]. If the distance between the charges r is, say, a centimeter (10-² m), then the De Broglie wavelength of a virtual photon is also about 1 centimeter, and the momentum of such photon is Δp ~ℏ/r ~ 10-³²kg∙m∙s-¹. A potential difference V of 1 volt induces charges Q ~ Vr/K ~ 10-¹¹ coulomb. Then the force F= KQ²/r² is about 10-¹º N. Dividing the force F by the photon momentum, we obtain the number N = F / Δp ~ 10²² virtual photons surrounding the charge.  Taking into account (2), the force F of interaction of two unit charges e at distance r is equal:

                                                 F = Ke²/r² =   hN/ r 

 Then the  dependence of the number N_Δp of virtual photons with momentum Δp , on the distance r : 

                                                     N_Δp(r)= Ke²/ℏr, 

There is a hyperbolic dependence of the number N_Δ𝑝 on the distance r to the charge:

                                          N_Δ𝑝 (r) =  A/r , где A= Ke²/ℏ .                                   (3) 

Taking into account oscillation (constant emission-absorption of virtual particles), one can expect the presence around an electric charge in vacuum of a dynamic cenosis of virtual photons, in which the number N_Δ𝑝 of particles having momentum Δp decreases with distance r from the charge according to the hyperbolic law (3) peculiar to cenosis. As it is known [5], the scales on which quantum processes involving a particle are essential are determined by its Compton wavelength. Let us use this value to estimate the characteristic dimensions of the «virtual» cenosis. For the electron the reduced Compton wavelength is most often used  λ_o^e: 

                                            λ_o^e  =  h/2πmc = 3,86 ∙ 10^-13 m,                                             

where:  c = 299792458 m/s is the speed of light, h = 6.626 ∙ 10 -34 J/s is Planck’s constant,         m = 9.10938210-31 kg is the mass of the electron.

Fig. 3 shows schematically a cenosis localized within the Compton wavelength of the electron, consisting of virtual photons, for which the number N_∆p(r) with momentum ∆p has a hyperbolic dependence on the distance r to the charged particle.

                                                                                                 Fig. 3.

These examples show that such objects of cenology as, for example, abiogenic cenoses, with sizes ranging from ~4∙10^-13 m for virtual cenoses in the microcosm to ~3∙10²² m for astro- and cosmocenoses, cover a range of at least 35(!) orders, which definitely places cenology among important disciplines in the field of knowledge.                                                         

                                                                                                Cited:

1. Kudrin B.I. My Seven Differences from Zipf // General and Applied Pricing. — 2007. — № 4. — С. 25-33.
2. Gurina R.V. Cosmic systems as astrocenosis/ Pricelogical modeling: theoretical foundations and practical results. Proceedings of XV Conference on Philosophy of Engineering and Techniques and Seminar on Pricelogy. Vol. 47. «Pricing Studies.» — Moscow: Technetics, 2011. — С. 178-
3. Myakishev G.Y. Virtual particles / Physics of the microworld / Edited by D.V. Shirokov. — M. Sovetskaya Encyclopedia. 1980. — 528с.
4. livejournal.com. From:(Anonymous),December 14th,2014.
5. V. I. Grigoriev, «Compton wavelength,» BSE.