Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter

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This page is an essay by Sergey Fedosin, a Russian physicist and academic, and represents his original research and personal opinions. It should not be taken as representing standard scientific understanding, but is presented here for discussion and review.

Theory of infinite hierarchical nesting of matter (or theory infinite self-similar nesting of matter) — as opposed to atomism, alternative philosophical, physical and cosmological theory. This theory is based on inductive logic conclusions about the structure of the observed infinite universe. Metaphysical school, studying this theory, focuses on the fundamental organizational principles of nature and initially called the concept Discrete Fractal Paradigm, and then Discrete Self-Similar Cosmological Paradigm .
Hoag's object as analogue of the hydrogen atom in macrocosm

Basic elements of the theory[edit]

The Discrete Self-Similar Cosmological Paradigm focuses on nature’s fundamental organizational principles and symmetries. It emphasizes nature’s hierarchical organization of systems from the smallest observable subatomic particles to the largest observable superclusters of galaxies. The new paradigm also highlights the fact that nature’s global hierarchy is highly stratified into discrete Scales, of which we can currently observe the Atomic, Stellar and Galactic Scales. A third important principle of the paradigm is that the cosmological Scales are rigorously self-similar, such that for each class of objects or phenomena on a given Scale there is analogous class of objects or phenomenon every other cosmological Scale. The self-similar analogues from different Scales have rigorously analogous morphologies, kinematics and dynamics. [1] From the physical point of view the similarity relations lead to similarity of matter levels and SPФ symmetry, which asserts the invariance of physical laws operating on different levels of matter.

  • In the given theory there are no elementary particles of matter (see preon, parton, electron, quark, Action/Reaction_Theory); the matter is infinitely divisible, as opposed to the theory of atomism, which assumes the existence of minimal units of the matter.
  • The Universe consists of an infinite number of enclosed levels of matter with characteristics similar to each other. This leads to the similarity of cosmic systems, including the similarity of shapes, sizes, masses, rates of processes and equations of motion.
  • Each level of the matter includes carriers with the certain spectrum of the sizes and masses. The matter is organized itself in stable conditions under the influence of fundamental forces and interactions of objects of different systems.
  • Allocation of cosmic objects on the levels of matter that are the stepping stones of the infinite hierarchy of cosmic systems, is based on geometric progression.
  • The course of time in terms of rate of occurrence of similar events is much faster at a microlevel and more slowly at a macrolevel.
  • Each sort of "elementary" particles (electrons, nucleons, etc.) does not consist from strictly identical on mass and the size of particles.
  • The Universe is eternal, thus carriers of the matter constantly are born and then are transformed to carriers of the same and-or other levels. That the theory falls outside the limits not only atomism, but also the Big Bang which limiting history of the Universe by the moment of its creation.
  • Space-time determined by the structure of the matter. Time in the given theory – independent coordinate from space, also is derivative of speed of movement and development of the matter. In science widely used four-dimensional space-time, consisting of three spatial dimensions and time. In theory of infinite nesting of matter is proved the existence of the fifth, scale dimension.
  • Action of forces of gravitation and electromagnetism can be explained by modified Le Sage's theory of gravitation. Objects of different levels of matter generate radiation in the form of streams of particles and field quanta, resulting in aggregate to the formation of the fundamental forces acting on objects from other levels of matter. It is also possible that the gravitational field is ordered in a special way the electromagnetic field of a underlying level of matter. [2]
  • There is a difference between the concepts of "quantity of matter" and gravitational mass, implying that under certain conditions, different amount of substance may have the same gravitational properties. This follows from the dependence of the gravitational forces on the velocity of the bodies and the dependence of gravitational mass on the mass density, also bodies contribute to the mass from its gravitational and electromagnetic fields.
  • Mass as a measure of inertia on the level of elementary particles is determined by strong gravitation, and at the macro level – the usual gravitation.
  • Distribution of systems with living beings among cosmic systems has the same laws, which are inherent to systems with non-living matter.

The historical information[edit]

That matter is divisible to infinity, claimed still Aristotle, Descartes, and also Gottfried Leibniz [3] in his monadology. Isaac Newton wrote: "Nature is very similar to itself and is very simple, performing all the great movements of celestial bodies with the help of attraction, gravity ... and every small particle motion of these bodies – with the help of other attractive and repulsive forces binding particles." [4] In each particle, no matter how small it is, "there are the cities occupied by people, cultivated fields, and the sun, the moon and other stars like ours" – claimed the Greek philosopher Anaxagoras in his work on gomeomeriya in V century BC. The supporter of the given theory was also known Russian poet Valery Bryusov. [5]

"Perhaps, these electrons
Are the Worlds, where five continents,
Arts, knowledge, wars, thrones
And memory of forty centuries!
Still, perhaps, each atom –
the Universe, where hundred of planets;
There – everything, that is here, in volume compressed,
But also what here is not present."

Quod est inferius est sicut quod est superius[edit]

That is above, similarly to that is below. This principle uttered more two thousand years ago, has been accepted for an axiom by followers of hermetic religious philosophy. This current of times of late antiquity from which in Middle Ages the alchemical science and which was the forerunner of three movements which have partially lived up to now was born: movements of illuminatus, frank-macons, and movements rosenkreuzers. Many most outstanding scientists of Middle Ages and New time have been connected with any of these movements, mainly because these organizations stored at themselves the information inaccessible to other. Hermetists approved analogy between microcosm and macrocosm: in religious sense, this analogy was understood as conformity of the God and the person created on an image and similarity divine. However in a science the statement about general analogy can be understood much more widely.

Modern science increasingly confirms the true and fundamental tenets set forth in the ancient philosophical texts. In particular, the theory about similarity of the processes occurring on macro-and microlevels, is coordinated with Hermes's statement. Study of extraordinary people thinking leads to the same conclusions. Such great researchers as Leonardo da Vinci, possessed ability simultaneously to perceive the whole and its parts; the principle of its researches consist in the analysis – division of the phenomena into probably small components – and their synthesis in new configurations. Da Vinci designed the pyramid scheme of mechanics according to which all natural forces – which he called the "four forces" – movement, mass, force and the collision – are located on the system of the pyramid and occur from one another. This principle of the pyramid in which energy gathers and lost in a geometrical proportion, has made a basis of mechanics. "The uniform theory of field" of Albert Einstein has been directed on an establishment of conformity between principles of realization of all physical phenomena in the Universe – from space up to atom.

On the other hand, metaphoricalness – the feature inherent, in particular, in the statement of Hermes about general analogy, is the general feature of thinking of pathbreakers and authors of ancient texts. “I wish to know ideas of the God, all rest – is details”, Einstein wrote. The metaphor is an analogy. The central positions on which the science is based, at all aspiration to accuracy and unambiguity, also appear metaphoric.

On the basis of the axiom about similarity of all real communication between science, philosophy and religion is established.

Kant and Lambert[edit]

In a basis of cosmological representations of Immanuel Kant there was a recognition of existence of uncountable set of star systems which can be united in systems of higher order. At the same time each star with the planets and their satellites forms system of the subordinated order. The Universe, hence, not only is spatially infinite, but also structurally diverse, as its structure includes space systems of different orders and the sizes. Putting forward this position, Kant came nearer to idea about structural infinity of the Universe which has received fuller development in cosmological doctrine of the contemporary of Kant, German scientist Johann Heinrich Lambert in 1761. Baruch Spinoza was an adherent of the Infinite hierarchical model of the Universe.

Fournier D'Albe[edit]

Irish scientist Edmund Edward Fournier D'Albe has made the assumption, that the scale of ranks reaches also into matters, by reduction. [6] At Fournier D'Albe a denominator of a progression, i. е. the attitude of the linear sizes of a star and atom or the sizes of a star of supraworld and stars of "our" world, being atom of supraworld, is expressed by number 1022. Such parity of spatial sizes Fournier D'Albe distributed for the time too. One second in our world in opinion Fournier D'Albe – is hundred billions years in a life of infraworld, and second in supraworld is equal hundreds billions our years. Konstantin Tsiolkovsky was familiar with works of Fournier D'Albe.

Infinite Universes and photometric paradox of Olbers[edit]

Within the limits of classical cosmology this paradox tried to resolve in model of the hierarchical structure of the Universe developed by Carl Ludwig Charlier on the basis of idea of Johann Heinrich Lambert. [7] In 1908 Charlier has published the theory of a structure of the Universe according to which the Universe represents infinite set of systems of the escalating order of complexity entering each other. In this theory, individual stars form a galaxy of the first order, a set of galaxies of first-order forms galaxy of second-order and so on to infinity. On the basis of such representation about a structure of Universe Charlier has come to conclusion, that in the infinite Universe the photometric paradox is eliminated, if distances between a peer systems are sufficiently large compared with their sizes. It leads to continuous reduction of average density of space substance in process of transition to systems of higher order. For elimination of paradox it is required, that the mass density fell more quickly, than in inverse proportion to a square of distance from the observer. Such dependence of mass density in the Metagalaxy is not observed, therefore the modern explanation of Olbers paradox is based on other principles (for example, red shift is considered, theory of general relativity is used). However the idea about a complex structure of the Universe and an enclosure of systems of the different level remains and develops. Albert Einstein and F. Selety discussed the hierarchical model of Charlier in 1922 - 1924 years. [8]

Fractal cosmology[edit]

According to the fractal cosmology, the distribution of matter in cosmological systems occurs on a certain law, depending on the size of systems, taking into account the principle of similarity occurring structures. Benoît Mandelbrot – the founder of the mathematical theory infinite hierarchical (recursive) self-similar sets, for the description of the given systems enters the new term – fractal.[9] Cosmological and philosophical sights of Mandelbrot in historical prospect are well displayed in his not published note " Two heirs to the Great Chain of Being " [10] and in the book written together with Yurij Baryshev and Pekka Teerikorpi . [11] Baryshev applies fractal cosmological model with the fractal dimension D = 2 for the interpretation of the redshift of galaxies as a result of gravity. The model with the help of dark matter can explain the observed large-scale distribution of matter and associate it with the background radiation. [12]

Achieved results[edit]

In 1937, Paul Dirac suggested that the parameters of large cosmological systems can be connected with the parameters of elementary particles with the help of some large coefficients. [13] The hypothesis of large numbers considered also Hermann Weyl, [14] Arthur Stanley Eddington, [15] Oskar Klein, Pascual Jordan and others.

Gérard de Vaucouleurs in 1970 used the hierarchical model to describe changes in the density of galactic systems, depending on their characteristic size. [16] The idea of nesting of matter was also considered by M.A. Markov [17] and D.D. Ivanenko (maximon - hadron - Metagalaxy). [18]

In 1978 Abdus Salam suggested that the hadrons can be regarded as microuniverses in de Sitter space, with the acting there strong gravitation. [19]

Hierarchical model of the world is supported by large group of scientists: from Italy, among which Erasmo Recami, P. Caldirola, P. Castorina; Brazilian scientists W.A. Rodrigues, J.M. Martınez, V. Tonin–Zanchin, Slovak scientist M. Pavsic; A. Neil from U.K./Denmark; Indian scientists P. Ammiraju, K.P. Sinha, C. Sivaram, and others. They view the elementary particles inside as microuniverses, [20] and outside as objects such as black holes. [21] [22] In this regard, the hypothesis of large numbers again considered. [23] In addition to the application of general relativity ideas to describe the objects of the microworld, there was another trend - the use of quantum approach for predicting the most probable orbits of planetary systems of stars. Overview of some results contained in Quantization of parameters of cosmic systems.

In the late 1970's and 1980's the idea has become increasingly spread that the infinite nesting of matter is suitable not only to explain certain phenomena and the guidance links between micro and macrocosm, but that it could become a new scientific paradigm. [24] [25] [26]

One of the names of this paradigm — Discrete Self-Similar Cosmological Paradigm. [27] It implies similarity of infinite number of discrete matter levels, and the cosmological paradigm assumes a unified description not only large cosmological systems (stars, galaxies, metagalaxies, etc.), but also the smallest objects – molecules, atoms, elementary particles and all the components that make up their stuff. From this point of view, the theory of infinite nesting of matter is a theory in the systems science and systems theory, intended to describe the cosmic systems, their origin and evolution.

In this cosmological paradigm completely abolished the formal restriction of atomism on the theoretical and experimental study of the levels of matter, of which consist of elementary particles. Infinite hierarchical nesting of matter indicates the unacceptability of the general theory of relativity to describe the whole Universe, and excludes the Big Bang as the scenario of the Universe development. In addition, it is acquiring great importance to study universal mechanisms of formation of objects, the emergence of fields and forces, their origin and interaction at different levels of matter infinite universe. An important result was the justification of the fifth, scale dimension of space-time.

Compilation and systematization of facts substantially accelerated in the beginning of XXI century, thanks to artificial satellites, modern means of observation – an infrared telescope and computer analysis of the accumulated material, and deepen knowledge in the field of elementary particles. The focus of the authors specified further has been directed to the design theory of infinite nesting of matter as an independent and necessary for further progress in science research.

Robert L. Oldershaw[edit]

Robert L. Oldershaw [7], the independent researcher of college Amherst (Massachusetts, USA) in a number of works since 1978 developed model cosmological self-similarity (The Self-Similar Cosmological Model). He has allocated three basic levels of matter – nuclear, star and galactic levels. The matter is concentrated to the given levels basically in the form of nucleons and stars, and stars also in the majority are a part of galaxies. [28] [29] Oldershaw marks, that the overwhelming quantity of matter in space contains in the easiest elements – in hydrogen and in helium, and at the level of stars – in stars-dwarfs with mass 0.1 – 0.8 solar mass. Besides are available much another examples of similarity:

  • Rotation of carriers near each other under action of the force, decreasing in inverse proportion to a square of distance.
  • Often observable jets and emissions of a matter of the identical form in star and galactic systems.
  • The attitude of the sizes of the greatest atoms to the size of a nucleon of the same order, as the attitude of the size of greater star systems to the size of a neutron star.
  • Dependences between spin and mass, between the magnetic moment and spin have the identical form at nuclear and star systems.
  • Rydberg’s atoms show dependence between radiuses and the periods of fluctuations electrons, very similar to Kepler's law for planets.

Definition of coefficients of similarity in mass, in size and in time of processes between nuclear and star systems Oldershaw carries out through comparison of Solar system and Rydberg’s atom with number of orbit n = 168. Thus to hydrogen there correspond stars with mass of the order of 0.15 solar mass. The coefficients of similarity in size and time are considered equal to each other and have the value of Λ = 5.2∙10 17 , and the coefficient of similarity in mass has the form ΛD = 1.7∙1056, where the exponent D = 3.174 . As a result of such comparison begins possible to do exact enough predictions of mass and the sizes of stars, galaxies, the size of proton, the periods of rotation of galaxies, etc. Oldershaw believes that elementary particles should be as charged and rotating black holes, whose radius is in the first approximation can be estimated from the Schwarzschild equation:

~ R=\frac {2G_{\psi} M}{c^2} ,

where ~G_{\psi} is the constant of gravitation, acting on the given level of matter, and ~\psi= -1 for the atomic level, ~\psi=0 for the level of stars, ~\psi= +1 for the level of galaxies.

Assuming that strong gravitational constant ~G_{-1}=2{.}18 \cdot 10^{28} m3•s–2•kg–1, Oldershaw finds a matching radius of the electron 4∙10-19 m, and the radius of the proton 0.81∙10-15 m. At the level of stars and galaxies are assumed also objects like electrons and protons. In particular, at the level of stars, black holes are attributed to the electric charge with value of up to 1.5∙1018 C. At the level of galaxies globular clusters of stars correspond to an electron and galaxies − to the proton and the more massive atomic nuclei. To estimate the size of globular clusters and galaxies it is necessary to multiply the radius of the electron and radii of atomic nuclei on the value of Λ2. As can be seen from this comparison, there is no complete similarity, since black holes are only suspected in some globular clusters and galaxies, but do not cover these objects completely. Therefore, Oldershaw introduces for the electron the concept of a halo consisting of tiny particles that form the matter of the electron. This halo surrounds the nucleus of an electron as well as external stars in globular clusters surrounding the nucleus of the cluster. According to Oldershaw, dark matter should consist of black holes.

Sergey I. Sukhonos[edit]

"The wave of sustainability." On the scale axis of the universe all the main sites and their "core" are periodically. At the bottom is given the periodicity of location on the same axis scale "zones of influence" four basic forces of nature.

Sergey I. Sukhonos [8] in a number of works [30] has shown existence of the separate material formations located on an axis of the sizes by 13 discrete groups through equal intervals in logarithmic scale. The greatest considered size belongs to the Metagalaxy, the least – to a hypothetical particle maximon, on twenty orders smaller then nucleon. Metagalaxy, nucleons and maximon belong to the basic levels of matter, between them there are all known objects which properties periodically repeat with the attitude of the sizes nearby 1020. Sukhonos pays attention to the fractal phenomena in the nature, and also displays bimodality when objects show supplementary properties: spiral and elliptic galaxies; subdwarfs as primary stars of the Galaxy with deficiency of heavy elements, and usual stars of the main sequence; planets external and internal; processes of synthesis and division, monocentric and polycentric structures at different levels of matter. For an explanation of specified laws Sukhonos involves idea about the fourth, scale dimension and corresponding interaction, and also wave representations. With the "wave of sustainability" scale axis is divided into three major intervals − microinterval, macrointerval and megainterval (the word micro here means small, rather than a millionth of the size).

Yun Pyo Jung[edit]

Yun Pyo Jung [9] from Korea criticizes the theory of the Big Bang in connection with the logic contradiction – on greater scales the nearby space objects never will make more than one turn near each other because of constant expansion of the Universe, despite of gravitational communication between them. Proceeding from idea recursive cosmology, by comparison of the sizes of kernels of galaxies and nuclear kernels, galaxies and atoms, congestions of galaxies and molecules the factor of similarity in the size about 1030 is defined. The same value is deduced for factor of similarity on time, connecting duration of the same processes in nuclear and galactic systems. [31]

Sergey G. Fedosin[edit]

Sergey Grigor'evich Fedosin

Sergey G. Fedosin [10], the physicist and the philosopher from Perm, Russia, mathematically has proved the basic features of the theory, having passed from qualitative conclusions to quantitative results in his monograph on the theory of similarity. [32]

Eighteen levels of matter from preons up to metagalaxies were divided into basic and intermediate in their masses and dimensions, and between them are derived relation of similarity. The main levels in this range of levels of matter are level of elementary particles and the level of stars. At these levels there are the most stable and long-living carriers, that are nucleons and the neutron stars containing a maximum quantity of composite particles and having a maximum density of matter and energy. The matter of these carriers is degenerate, so their constituent particles are in quantum states with nearly the same energy, and therefore the state of such matter described by the laws of quantum mechanics. In this case a neutron star contains about Φ = 1.62•10 57 nucleons, and by induction it is assumed that the same quantum particles contained in the nucleon. As a consequence of the similarity of the atomic level and the level of stars quantization of parameters of cosmic systems is found.

Determination of coefficients of similarity in mass Φ, in size P, in speed S, in duration of similar processes Π is made by means of the hydrogen system. At the level of atoms the hydrogen system is a hydrogen atom, and at the level of main-sequence stars − the corresponding planetary system consisting of a star of minimum mass and a planet as the analogue of the electron. For degenerate compact stars like white dwarfs and neutron stars are entered their own coefficients of similarity, based on the ratio to the parameters of the proton. For magnetars as analogues of the proton the electric charge with value of 5.5∙1018 C and the magnetic moment of 1.6∙1030 J / T are predicted.

The ratio of radius of a neutron star to radius of a proton gives factor of similarity on size P = 1.4 •1019. Full energy of a neutron star without taking into account energy of rest is defined by expression Es = MsC2, where C= 6.8•107 m/s – characteristic speed of particles of the neutron star, Ms – mass of the star. Similarly for a nucleon full energy En = Mnc2, where c = 2.9979•108m/s – speed of light and characteristic speed of particles in the matter of nucleon, Mn – mass of a nucleon. The ratio of speed C to speed of light c gives factor of similarity on speed S = 0.23. The factor of similarity on time is Π = P /S = 6.1•1019. From here follows, that processes at the level of nucleon matter proceed in Π time more quickly, than at the level of neutron stars.

The theory of similarity predicts, that among stars the lightest are stars with mass of 0.056 solar mass. Such stars are now discovered and are called brown dwarfs or L-dwarfs. Solar system on the mass and number of planets similarly to atom of oxygen as the mass of the Sun exceeds mass of the most easy stars in the same way as the mass of atom of oxygen exceeds mass of atom of hydrogen. Our Galaxy Milky Way together with galaxies Large Magellanic Cloud and Small Magellanic Cloud form the congestion of galaxies similar on mass to a molecule of water H2O. Our Galaxy is considerably massive then Magellanic Clouds and plays the role of atom of oxygen (or may be fluorine). Around of the given congestion of three large galaxies are rotated about 14 dwarfish galaxies which can be named galactic analogues of electron. The values of typical parameters of dwarf galaxies were confirmed, with the mass of 4.4 ∙ 106 solar masses and the radius of up to 371 pc.[33] [34]

As on the axis of mass (and on the axis of the sizes) all natural bodies settle down discrete groups the attitude of mass between any next groups is the same number. Hence, growth of mass of objects occurs on a geometrical progression, the same is fair concerning the sizes of objects. It allows to compare with attitudes of similarity between various levels of matter and by that in advance to predict still more about investigated badly objects. As consequence, SPФ symmetry of similarity is entered between the basic levels of matter. Some analogue of similar symmetry is CPT symmetry known in the quantum field theory.

In addition, Fedosin found a connection between mass and energy of the space objects, corresponding to Einstein's formula (mass–energy equivalence), identified stellar constants, such as stellar Planck constant, stellar Dirac constant and stellar Boltzmann constant, calculated the angular momentum and the radius of the proton as well. [35] [36] A comparison of the prevalence of stars of different masses with the prevalence of atomic nuclei proved discreteness of stellar parameters and one-one correspondence between the chemical elements and the stars.

The explanation of the red shift in spectra of remote galaxies and cosmic microwave background radiation from the concept of an expanding Universe seems inadequate, and invites other explanations. It leads to the idea of cosmic red shift and microwave background radiation as a consequence of interaction between photons and previously unknown particles. At the level of stars analogues of the new particles are white dwarfs, whose number exceeds the number of neutron stars. Fedosin shows that the overall mass of the new particles in the Universe of the same order as the mass of all the known nucleons. Thus the problem of invisible dark matter may be solved. The question must be raised about the need for the existence of dark energy. In particular, the effect of attenuation of radiation from the distant supernovas is considered to be the consequence of scattering of photons on the new particles, but not the result of the dark energy activity. [37]

Fedosin using Le Sage's theory of gravitation based on the notion of gravitons derived the formula for Newton's gravity, found the energy density and the penetrating power of gravitons in the matter. [38]

In order to describe the nuclear forces in the gravitational model of strong interaction he introduces the concept of the gravitational torsion field and uses strong gravitation, as constituent parts of strong interaction between elementary particles. [39]

Strong gravitational constant which is equal to ~\Gamma=1.514 \cdot 10^{29} m3•s–2•kg–1, can be calculated through the coefficients of similarity between the atomic and stellar systems. The idea of infinite nesting of matter was the basis for the construction of substantial electron model and explaining of electronic spin. Model of quark quasiparticles shows that quarks can be represented as a combination of the two phases of hadronic matter and therefore, they are quasiparticles. In this case, the composition of hadrons can be reduced to quarks only for the formal description of properties of hadrons, but the actual reason for the idea of quarks is discrete and quantum properties of elementary particles and the resulting symmetry of their interactions in the fundamental fields. In particular, in substantial neutron model and substantial proton model are found that the mass of the nucleons is in a narrow range of masses as a consequence of the equation of state of hadronic matter and its evolution in the field of strong gravitation.

The electric charge of the proton appears in the reactions of the weak interaction in neutron matter during beta decay and reaches a maximum when the density of the zero electromagnetic energy becomes comparable to the energy density of strong gravitation. [2] Analysis of electric and magnetic polarizabilities of nucleons shows that they can be understood without invoking the idea of quarks.

In the concept of general field it is shown that the gravitational and electromagnetic fields, the acceleration field, the pressure field, the dissipation field, the fields of strong and weak interactions, and other force fields can be combined into one. The general field is universal in the sense that it operates at all levels of matter and allows us to describe the equation of motion of any object with the help of one tensor equation.

The detailed philosophical analysis of the theory of infinite nesting of matter was carried out by Sergey Fedosin in 2003. [40] At each level of matter characteristic basic carriers and boundary points of the measure are allocated. Transitions from one level of matter to another are carried out under the law of transition of quantity in quality when the quantity of carriers in object exceeds the admissible borders of the measure typical for given object. Examples of fractal structures at various spatial levels of matter are resulted. Owing to hierarchical structure of the Universe consisting of objects similar each other and particles of fields, repeatability of elements of the natural phenomena, unity and integrity of the Universe is carried out, symmetry of similarity is shown. The theory of infinite nesting of matter is justified by the law of similarity of carriers of different scale levels.

In addition to infinite nesting of physical material objects of different levels, an infinite nesting of life is found – inside the autonomous living organisms of one level from the smallest prions and ending with the whales are present other living structure of lower levels of scale. In this case there is an interpenetration of the living and nonliving matter, and a clear correlation between the size and mass of living carriers and the corresponding values of physical objects at different levels of matter. Thus, nesting of living matter in natural systems is manifested as the distribution of organisms of different species of scale levels according to mass and size as well as the infinite nesting of levels living matter in each individual living organism. [41] As an illustration, it is known, that in the human body there is so much bacteria that their total mass may be up to two kilograms. [11]

The infinite nesting of living beings is in agreement with the living systems theory of James Grier Miller, which considered many living systems, in order of increasing size, and identifies his subsystems in each. [42] He concluded: nonrandom accumulations of matter-energy in physical space-time organized into interacting, interrelated subsystems or components. In such complex structures, he identified eight "nested" hierarchical levels, including cell, organ, organism, group, organization, community, society, and supranational system. Nesting is defined as that organ is composed of many cells, and body - of many organs, etc. In addition to such qualitative conclusions, in the theory of infinite nesting with the help of similarity of matter levels are determined some quantitative regularities. For example, there are coefficients of similarity in mass, to assess the critical number of living beings, delimiting between themselves different levels of the organization alive.

Tegmark M.[edit]

Max Tegmark classifies different types of simultaneously existing universes, depending on their possible properties. Under this universes he understands objects with dimensions close to the size of our Metagalaxy. It is assumed that such neighboring universes are autonomous and independent from each other, and they may have even other physical laws, or other elementary particles and physical constants. [43]

Leonard N. Plyashkevich, Mira L. Plyashkevich[edit]

Leonard N. Plyashkevich and Mira L. Plyashkevich in their work considered the basic postulates of a variant of cosmology, as an alternative hypothesis of the Big Bang. [44] Authors had been made attempt to reveal a uniform principle of micro and macrocosms. For achievement of this purpose methods of transformation of similarity and dimensions of physical quantities are used. The gravitational field is considered by way of Faraday - Maxwell field. Refusal of the hypothesis of the Big Bang and interpretation of red shift in spectra of far galaxies as Doppler effect, allows to develop hierarchical model of the Universe. The problem of coexistence of usual matter and antimatter is mentioned. The purpose of the work – to show, not plunging into chasms of metric theories, the right to existence and development of hierarchical model.

Boris M. Sirotenko (Boris Antsis)[edit]

Unified structure of Universe.[45] About similarity micro-and a macrocosm.[46]

Salzman L.I.[edit]

A system of the Universe was published in the book "Rise of the Worlds" (2003). [47] The system covers Genesis of inert and living matter. The Universe is represented as a dynamic hierarchy of particular worlds. Subsidiaries of inert matter arise from elementary particles of the parent structure by their gravitational condensation in accordance with the theory of Jeans. It is proved that the condensation is involved only about half of the particles. Others particles with large escape velocity, remain dispersed in space and serve as material for a variety of potential fields. It is shown that the matte of all particular worlds, from the microworld, acquires the properties of superfluidity, superconductivity, etc. It seems macrocosm is the latest in the existing hierarchy. Large-scale constants connecting dimensions and mass of particles, and energy density and the relaxation time of particular worlds are calculated. It is found that, despite the infinite number of particular worlds, all the basic parameters of the Universe are finite. The theoretical possibility of the existence of life in each particular world is discussed and reviewed, what nature took to create highly intelligent beings.

Leonard Malinowski[edit]

The term Scalativity was penned by Leonard Malinowski to differentiate his efforts from, while paying respect to, Laurent Nottale and his work, Scale Relativity or Scalativity. The Scalativity means that absolute uniform scale cannot be detected. Human observers exist at the human scale whereby all measured properties of the Universe can be compared relative to an observer’s approximate mass, size, and awareness of time passage. It seems the human scale is arbitrary.

In Scalativity the currently observable Universe and all its contents such as particles (proton, neutron, electron, photon, neutrino), cosmic objects (galaxies, stars, planets and so on ) and electric field lines, are all presented as completely fractal. A truly Fractal Universe must incorporate infinity completely into Physics as well as Scale Relativity, with the understanding that there must exist self-similarity between scales. It is supposed that the neutron is composed of 1.2 x 1057 subquantum scale (sqs) Hydrogen atoms; an electron is composed of 1.2 x 1052 sqs-Iron atoms with an excess of 2.1 x 1040 sqs-electrons and a photon is composed of 4.5 x 1080 sqs-photons.

It is supposed that the vast majority of stars are cosmic scale nuclei in the process of cosmic scale (cs) beta decay. The sum of electromagnetic and neutrino radiation emitted by a star over its life time is one cs-antineutrino. Our Solar System is may be a cs-neutron in the process of cs-beta decay. The iron/nickel cores of the planets are expected to form one cs-electron of mass 1.084 x 1027 kg. The Sun will be left with 2.1 x 1040 positive ions on its surface. The 2.1 x 1040 ionized electrons will adhere to the cs-electron. The mass of mostly stable cosmic scale nuclei should range from 1 solar mass to 238 solar masses.

According to Malinowski, the Big Bang Universe is fractally self-similar to a cosmic scale 500 Megaton Uranium 235 fission explosion. Spiral galaxies are self-similar to nuclear explosion particles forming and Elliptical galaxies are self-similar to drops of water in the nuclear cloud capturing many cs-neutrons.

With just two postulates, that the pre-solar system mass is the mass of a cosmic scale neutron and that a cosmic scale neutron is composed of 100% Hydrogen atoms, Scalativity can calculate the fractal chemical compositions and binding energies of all nuclei. It is fascinating that to obtain the mass of the very stable nuclei Iron 56 by this method, one must fuse all the quantum scale Hydrogen and quantum scale Helium available in 56 separate protons and neutrons completely to 100% qs-Iron 56. There are many other quantum scale - cosmic scale self-similarities identified at

José Díez Faixat[edit]

In several of his works José Díez Faixat reveals the existence of a very precise spiral rhythm in the emergence of the evolutionary leaps that mark the history of the universe. [48] [49] [50] [51]

Fitting his ‘periodic table’ of rhythms to the date of the appearance of matter –the Big Bang– and of organic life, he find that every single instant of the emergence of successive taxonomic degrees of human phylogeny is marked out with absolute precision: Kingdom: animal, Phylum: chordata, Class: mammal, Order: primate, Superfamily: hominoid, Family: hominid and Genus: homo. The same then occurs with all the stages of maturation of our primitive ancestors: H. habilis, H. erectus, archaic H. sapiens, H. sapiens and H. sapiens sapiens. Once more, the precision of the hypothesis is repeated in the successive transformations that humanity has experienced in its more recent history: the Neolithic, Antiquity, the Middle Ages, the Modern Age and the emergent Postmodern Age. The ‘periodic table’ of rhythms may also provide the key to glimpse the successive phases yet to be deployed in the years to come in an ever-accelerating process that will eventually lead to a moment of infinite creativity –Omega– within a couple of centuries.

The same hypothesis that has behaved with utter precision when applied to the process of global evolution, also does so when cross-checked against the process of development of the individual human being. Within the same time frame, with the same pattern of folding and unfolding, and passing through the same stages, the ‘periodic table’ of rhythms periodically marks out –step by step– the successive phases embryologists, developmental psychologists and spiritual teachers talk of, thus confirming the old idea of phylogenetic-ontogenetic parallelism and pointing, very specifically, to an astonishing fractal and holographic universe.

Cosmology of Raël[edit]

Raëlian cosmology

Raelian cosmology is based on similar cosmological sights at the structure of the Universe.

Theory in pop culture[edit]

  • YouTube|cNV9FEKi9FQ|Intro to cartoon serial Simpsons – The Ziff Who Came to Dinner. The episode the first time is shown 14.03.2004 (to the 125 anniversary from the date of Albert Einstein's birth).
  • The ending of film of Steven Spielberg " War of the worlds " (War of the worlds, 2005) –
  • Song Moby – We are all made of stars, 2002
  • The Dark Tower – a series of novels of Stephen King
  • Final in film " People in black " (1997) / Men In Black – one of the best screen versions of given article.

See also[edit]


  1. The principles of fractal paradigm are presented according to the article «THE HIDDEN MEANING OF PLANCK'S CONSTANT» of Oldershaw R.L. in his letter dated 20.03.2008 and addressed to Fedosin S.G.
  2. 2.0 2.1 Comments to the book: Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. ISBN 978-5-9901951-1-0. (in Russian).
  3. Gottfried Wilhelm von Leibniz, De materia prima, 1670 [1]
  4. Newton I. Optics. 1954, pp. 301.
  5. Valery Bryusov, «The World of electron», 1922, in Russian.
  6. Fournier D’Albe, E. E. Two New Worlds: I The Infra World; II The Supra World, 1907, London: Longmans Green.
  7. Charlier C. V. L., Ark. Mat. Astron. Fys., 1908, Vol. 4, P. 1; Charlier C. V. L. Ark. Mat. Astron. Fys., 1922, Vol. 16, P. 1.
  8. Selety F. Ann. Phys., 1922, Vol. 68, P. 281; Einstein A. Ann. Phys., 1922, Vol. 69, P. 436; Selety F. Ann. Phys., 1923, Vol. 72, P. 58; Selety F. Ann. Phys., 1924, Vol. 73, P. 290.
  9. Mandelbrot B.B. — Fractals — W.H. Freeman, San Francisco (1977), and The Fractal Geometry of Nature, W.H. Freeman, New York (1983).
  10. Benoit Mandelbrot, "Two heirs to the Great Chain of Being", 1982 [2]
  11. Baryshev, Y. and Teerikorpi, P. — The Discovery of Cosmic Fractals — World Scientific Press, London-Singapore, 2002, ISBN 981-02-4872-5.
  12. Baryshev, Y. Field fractal cosmological model as an example of practical cosmology approach. Practical Cosmology, 2008, Vol. 2, P. 60-67.
  13. Dirac P.A.M., Letters to the Editor: The Cosmological Constants, Nature, 1937, Vol. 139, P. 323; Dirac P.A.M., Physical Science and Philosophy, Nature Supplement, 1937, Vol. 139, P. 1001; Dirac P. Cosmological models and the Large Numbers Hypothesis. Proc.R.Soc. A, 1974, Vol. 338, P. 439-446.
  14. G. Gorelik: Hermann Weyl and large numbers in relativistic cosmology. In: Y. Balashov and V. Vizgin (eds) Einstein Studies In Russia (Birkhaeuser, Boston, 2002).
  15. Eddington A. New Pathways in Science. Cambridge University Press, Cambridge,1935, a 233-234.
  16. de Vaucouleurs G. Science, 1970, Vol. 167, P. 1203.
  17. Markov M.A. Zh. Eksp. Teor. Fiz. 1966, Vol. 51, P. 878.
  18. Ivanenko D.D.: in Astrofisica e Cosmologia, Gravitazione, Quanti e Relativit`a – Centenario di Einstein, edited by M.Pantaleo and Finis (Giunti-Barbera; Florence, 1978), p.131.
  19. Salam, A., and Strathdee, J. Confinement Through Tensor Gauge Fields. Physical Review D, 1978, Vol.18, Issue 12, P. 4596-4609.
  20. Recami E. Multi-verses, Micro-universes and Elementary Particles (Hadrons). arXiv:physics/0505149v123, May 2005.
  21. Recami, E. and Castorina, P. On Quark Confinement: Hadrons as «Strong Black- Holes». Letters Nuovo Cimento, 1976, Vol. 15, No 10, P. 347-350.
  22. Sivaram, C. and Sinha, K.P. Strong gravity, black holes, and hadrons. Physical Review D, 1977, Vol. 16, Issue 6, P. 1975-1978.
  23. P. Caldirola, M. Pavsic & E. Recami: “Explaining the Large Numbers by a Hierarchy of ‘Universes’: A Unified Theory of Strong and Gravitational Interactions”, Nuovo Cimento B48 (1978) 205-271.
  24. Chown, Marcus — Fractal Universe — New Scientist — 21 August, 1999.
  25. Gefter, Amanda — Is the Universe a Fractal? — New Scientist — 10 March, 2007: No 2594.
  26. Sergey Khaitun. «Ot ergodicheskoi gipotezy k fraktalnoi kartine mira: rozhdenie i osmyslenie novoi paradigmy», KomKniga, 2007, ISBN 5-484-00565-5 (in Russian).
  27. Robert L. Oldershaw. An Infinite Fractal Cosmos. arXiv:1001.2865v1, 17 Jan 2010.
  28. Robert L. Oldershaw. “Self-Similar Cosmological Model: Introduction and Empirical Tests”. International Journal of Theoretical Physics, Vol. 28, No. 6, 669-694, 1989. [3]
  29. R. L. Oldershaw. Discrete Scale Relativity. Astrophysics and Space Science, Vol. 311, No. 4, pgs. 431-433, October 2007 [4]
  30. S. I. Sukhonos. (Structure of steady levels of the organization of material world), SPb.: Hydrometeoizdat, 1992., and also S. I. Sukhonos. (Scale harmony of the Universe), М.: Sofia, 2000, 312 pp, in Russian. ISBN 5-89117-096-5 .
  31. Yun Pyo Jung. «Infinite Universe In A Mote», Sagyejul Publishing Co., 1994, 290 pp.; «Infinity in a Speck» (Fractal Cosmology)
  32. Fedosin S.G. (1999), written at Perm, pages 544, Fizika i filosofiia podobiia ot preonov do metagalaktik, ISBN 5-8131-0012-1., 
  33. Louis E. Strigari, James S. Bullock, Manoj Kaplinghat, Joshua D. Simon, Marla Geha, Beth Willman, Matthew G. Walker. A common mass scale for satellite galaxies of the Milky Way. – arXiv: Astrophysics (astro-ph), 27 Aug 2008.
  34. D. Adén, M. I. Wilkinson, J. I. Read, S. Feltzing, A. Koch, G. F. Gilmore, E. K. Grebel, I. Lundström. A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs? – arXiv: Galaxy Astrophysics (astro-ph.GA), 7 Oct 2009.
  35. Fedosin S.G. Sovremennye problemy fiziki: v poiskakh novykh printsipov. Moskva: Editorial URSS, 2002, 192 pages. ISBN 5-8360-0435-8.
  36. Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, 2012, Vol. 35, No. 4, P. 349 – 363.
  37. Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Spring 2012, Vol. 23, Special Issues No. 1, P. 3 – 13.
  38. Fedosin S.G. Model of Gravitational Interaction in the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4, No. 1, March 2009, P.1-24.
  39. Sergey Fedosin. The physical theories and infinite hierarchical nesting of matter. Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9.
  40. Fedosin S.G. Osnovy sinkretiki: filosofiia nositeleĭ. – Moskva: Editorial URSS, 2003, 464 pages. ISBN 5-354-00375-X. in Russian.
  41. Fedosin S.G. Nositeli zhizni : proiskhozhdenie i ėvoliutsiia. – S.-Peterburg: Dmitriĭ Bulanin, 2007, 104 pages. ISBN 978-5-86007-556-6.
  42. James Grier Miller, (1978). Living systems.New York: McGraw-Hill. ISBN 0-87081-363-3.
  43. Tegmark M. “Parallel Universes”, Scientific American,2003, Vol. 288(5), P. 41-51.
  44. L. N. Plyashkevich, M.L. Plyashkevich. To the question on similarity of atomic and galactic structures of matter, in Russian.[5]
  45. Boris Antsis. Unified structure of Universe [6]
  46. Sirotenko, B. M. About similarity micro-and macrocosm, Hydrometeoizdat, 1990, 42 pp., in Russian.
  47. L. Salzman. Rise of the Worlds. – St. Petersburg, European House, 2003, 385 p. ISBN 5-8015-0154-1. in Russian.
  48. José Díez Faixat. ¡Bye-Bye, Darwin! The Hidden Rhythm of Evolution. Syntropy 2014 (1): 1-49.
  49. José Díez Faixat. Siendo nada, soy todo (Being nothing, I am everything). DILEMA, S.L. (2008), ISBN-13: 978-8498270969, in Spanish.
  50. José Díez Faixat. Entre la evolución y la eternidad (Between evolution and eternity). Editorial Kairos (1998), ISBN-13: 978-8472453340, in Spanish.
  51. José Díez Faixat. A hypothesis on the rhythm of becoming. World Futures: The Journal of New Paradigm Research, 1993, Volume 36, Issue 1, pages 31-56.

External links[edit]