Infinite Hierarchical Nesting of Matter
The proposed theory Infinite Hierarchical Nesting of Matter is a cosmological framework that suggests that matter can be divided or reduced infinitely, as opposed to atomism. As such it lies in stark contrast to the standard model making it an alternative philosophical, physical and cosmological theory. This concept is based on inductive logic and reaches conclusions about the structure of the observed universe. Metaphysical schools studying this theory focus on the fundamental organizing principles of nature. Initial versions of this theory were known as the Discrete Fractal Paradigm, and subsequently the Discrete Self-Similar Cosmological Paradigm .
The famous Russian poet Valery Bryusov.  said:
"Perhaps, these electrons
Are the Worlds, where five continents,
Arts, knowledge, wars, thrones
And memory of forty centuries!"
Quod est inferius est sicut quod est superius
Da Vinci designed the pyramid schema of mechanics, according to which: All natural forces – which he called the "four forces" – movement, mass, force and collision – are based on the system of the pyramids and follow naturally from one another. This principle of the pyramid in which energy gathers and is then lost in a geometrical proportion, has been made a basis of mechanics. "The uniform theory of field" of Albert Einstein was based on an establishment of conformity between principles of realization for all physical phenomena in the Universe – from space-time up to atom.
This axiom regarding the similarity of all real communication between science, philosophy, and religion lies unchanged.
Within the limits of classical cosmology, this paper tried to resolve the modeling of the hierarchical structure of the Universe developed by Carl Ludwig Charlier on the basis of idea of Johann Heinrich Lambert.  then attempted to solve the underlying paradox. In 1908 Charlier publisheded a theory of the structure of the Universe. According to which, the Universe represents an infinite set of systems escalating in order of complexity then entering each other. In this theory, individual stars form a galaxy of the first order, a set of galaxies of first-order forms a galaxy of second-order, and so on to infinity. On the basis of such a representation about a structure of the Universe Charlier came to a conclusion. That in an infinite Universe the photometric paradox is eliminated. If distances between peer systems are sufficiently large compared with their sizes it leads to continuous reduction of average density of substance during the process of transition to systems of a higher order. For the elimination of paradox it is required, that the mass density fall more quickly, than in inverse proportion to a square of distance from the observer. Such dependence of mass density in the Metagalaxy is not yet observed, therefore the modern explanation of Olbers paradox is based on other principles (for example, red shift, general relativity and so on). However the idea about a complex structure of the Universe and an enclosure of systems on different levels remains and develops. Albert Einstein and F. Selety discussed the hierarchical model of Charlier in 1922 - 1924 years. 
According to the fractal cosmology, the distribution of matter in cosmological systems occurs according to a certain law, depending on the size of systems, taking into account the principle of similarity occurring structures. Benoît Mandelbrot – in order to solve the mathematical theorem: infinite hierarchical (recursive) self-similar sets, for the description of the given systems creates a new term – fractal. The cosmological and philosophical views of Mandelbrot in historical aspect are well described in his unpublished paper " Two heirs to the Great Chain of Being "  and in the book written together with Yurij Baryshev and Pekka Teerikorpi .  Baryshev applies the fractal cosmological model with the fractal dimension D = 2 in order to interpret the redshift of galaxies as a result of gravity. This model with the help of dark matter can explain the observed large-scale distribution of matter and associate it with the background radiation. 
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.  The hypothesis of large numbers was also considered by Hermann Weyl,  Arthur Stanley Eddington,  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.  The idea of nesting of matter was also considered by M.A. Markov  and D.D. Ivanenko (maximon - hadron - Metagalaxy). 
In the late 1970's and 1980's the idea had become so increasingly widespread that the infinite nesting of matter became suitable not only to explain certain phenomena and the guidance links between micro and macrocosm, but that it could become a new scientific paradigm.   
Another name for this paradigm — Discrete Self-Similar Cosmological Paradigm.  It implies similarity between infinite numbers of discrete matter levels, and this cosmological paradigm assumes a unified description not only of large cosmological systems (stars, galaxies, metagalaxies, etc.), but also of the smallest objects – molecules, atoms, elementary particles, etc. Due to this widespread support, in Russia, the theory of infinite nesting of matter is considered a full fledged theory in systems science and systems theory, which are intended to describe cosmic systems, their origin and evolution.
This cosmological paradigm completely abolished the formal restrictions of atomism in the theoretical and experimental study of the levels of matter such as elementary particles. Infinite hierarchical nesting of matter claims the unacceptability of the general theory of relativity to describe the entire Universe, and precludes the Big Bang as a likely scenario of the Universe's development. The theory is acquiring great importance in the study of universal mechanisms of formation of objects, the emergence of fields and forces, their origin and interaction at different levels, and of matter in an infinite universe. An important result was the justification of a fifth, scale dimension of space-time.
Compilation and systematization of facts substantially accelerated in the beginning of 21st century, thanks to artificial satellites, modern means of observation – infrared telescopes and computer analysis of accumulated material, and deepening knowledge in the field of elementary particles.
Robert L. Oldershaw , the independent researcher of college Amherst (Massachusetts, USA) in a number of works since 1978 developed models of cosmological self-similarity (The Self-Similar Cosmological Model). He has allocated three basic levels of matter – nuclear, star and galactic levels. According to his work, 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.   Oldershaw remarks, that the overwhelming quantity of matter in space contains in the lightest elements – hydrogen and helium, and at the level of stars – in dwarf stars with masses ranging between 0.1 – 0.8 solar masses. In addition examples of similarity exist in:
Definition of coefficients of similarity in mass, in size and in time of processes between nuclear and star systems. Oldershaw carries out comparisons of the Solar system and Rydberg’s atom with numbers of orbits n = 168. Concluding that compared to hydrogen there correspond stars with mass of the order of 0.15 solar mass. Additionally he claims 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 it begins to be possible to do exact 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 treated as charged and rotating black holes, whose radius in the first approximation can be estimated from the Schwarzschild equation:
where is the constant of gravitation, acting on the given level of matter, and for the atomic level, for the level of stars, for the level of galaxies.
Assuming that strong gravitational constant m3•s–2•kg–1, Oldershaw calculates a matching radius of an electron being 4∙10-19 m, and the radius of the proton 0.81∙10-15 m. Stars and galaxies are assumed also to be 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. Galaxies then correspond to the proton and the more massive atomic nuclei. To estimate the size of globular clusters and galaxies it then becomes necessary to multiply the radius of the electron and radii of atomic nuclei by the value of Λ2. As can be seen from this comparison, there is no complete parallel, since black holes are only suspected in some globular clusters and galaxies, but do not obscure these objects completely. Therefore, Oldershaw introduces for the electron, a concept of a halo consisting of tiny particles that form the matter of the electron. This halo surrounds the center of an electron, just as external stars in globular clusters surround the nucleus of the cluster. According to Oldershaw, dark matter should consist of black holes.
Sergey I. Sukhonos  in a number of works  has shown existence of the separate material formations located on an axis by 13 discrete groups through equal intervals in a logarithmic scale. The greatest discovered size belongs to the Metagalaxy, the least – to a hypothetical particle called a maximon, some twenty orders smaller then nucleon. Metagalaxies, nucleons, and maximons belong to the basic levels of matter. Between them, are all known objects whose properties periodically repeat with the attitude of the sizes near 1022. Sukhonos highlights the fractal phenomena in nature, and also proves 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 utilizes ideas about a fourth, scalar dimension and corresponding interaction, and also wave representations. He uses the term "wave of sustainability". Which refers to a scalar axis 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  from Korea criticizes the theory of the Big Bang in connection with logical contradiction – on greater scales nearby space objects never will make more than one orbit near each other because of the constant expansion of the Universe, despite of gravitational communication between them. Proceeding from idea of recursive cosmology, by comparison of the sizes between kernels of galaxies and nuclear kernels, galaxies and atoms, congestions of galaxies and molecules possessing a factor of similarity in size about 1030 can be defined. The same value is deduced for factors of similarity in time, connecting duration of the similar processes in nuclear and galactic systems. 
Sergey G. Fedosin , the physicist and the philosopher from Perm, Russia, mathematically has successfully calculated the basic features of the theory, having passed from qualitative conclusions to quantitative results in his monograph on the theory of similarity. 
Eighteen levels of matter from preons up to metagalaxies were divided into basic and intermediate stages in masses and dimensions, and between them can be derived relations of similarity. The main scales in this range of levels of matter are the level of elementary particles and the level of stars. At these levels there are many of the most stable and long-lived carriers; such as 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 states of such matter are 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 can be assumed that the same quantum particles are 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, and speed S, through the 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 consists of a star of minimum mass and a planet as the analogue of the electron. Degenerate compact stars like white dwarfs and neutron stars possess their own coefficients of similarity, based on the ratio comparing 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 a factor of similarity of P = 1.4 •1019. Full energy of a neutron star without taking into account the 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 the 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. By calculation it then 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 systems possessing the mass and number of planets similar to atoms of oxygen, compares to the mass of the Sun and that mass exceeds the lightest stars in the same way as the mass of atom of oxygen exceeds mass of atom of hydrogen. The Milky Way galaxy, together with galaxies such as the Large Magellanic Cloud and Small Magellanic Cloud form a congestion of galaxies similar on a mass scale to a molecule of water H2O. Our Galaxy is considerably more massive then the Magellanic Clouds and parallels the role of an atom of oxygen (or may be fluorine). Around of the given congestion of three large galaxies are orbiting about 14 dwarf galaxies which can be named galactic analogues of the 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. 
Just as on the axis of mass (and on the axis of the sizes), all natural bodies settle down into discrete groups. The attitude of mass between any of the next groups can be seen as the same number. Hence, mass increase of objects occurs on a geometrical progression, the same is true concerning the sizes of objects. It allows the observer to compare attitudes of similarity between various levels of matter and by that in advance to predict still more about investigated badly objects. As a consequence, SPФ symmetry similarity is generated between the basic levels of matter. An analogue of similar symmetry is CPT symmetry used in 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.   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 – nuons. At the level of stars analogues of the nuons are white dwarfs, whose number exceeds the number of neutron stars. Fedosin shows that the overall mass of the nuons 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 nuons, but not the result of the dark energy activity. 
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, and explained the origin of mass and inertia.   In a similar way he derived the formula for the Coulomb force between the electric charges, the energy density and the penetrability of the charged particles of the vacuum field in the matter. 
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. 
Strong gravitational constant which is equal to m3•s–2•kg–1, can be calculated through the coefficients of similarity between atomic and stellar systems. The idea of infinite nesting of matter was the basis for the construction of substantial electron model and explaining 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. Therefore quantum properties of elementary particles and their resulting symmetry during interactions in the fundamental fields can be derived. In particular, in the substantial neutron model and substantial proton model it is 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 zero electromagnetic energy becomes comparable to the energy density of strong gravitation.  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 study of the origin of fundamental gravitational and electromagnetic interactions in articles   leads to the following picture of disposition of the basic levels of matter: the level of graons – the level of praons – the level of nucleons – the level of stars – the level of supermetagalaxies. The distribution of material objects in the Universe is described with the help of scale dimension, which extends over all levels of matter. Due to the similarity of matter levels, each basic level of matter consists of the objects of the underlying basic level of matter. Hence it follows that protons, neutrons, electrons, and all elementary particles consist of neutral and positively charged praons and negatively charged praelectrons. In turn, the main components of praons must be graons, in which smaller particles can also be found. This is how the principle of nesting of matter is realized and the substance is found that the material objects at all levels of matter are built of. This substance is a multicomponent structure consisting of the objects of basic levels of matter, which appear to be the most dense and stable due to the balance of the corresponding fundamental forces. The carriers of the substance are graons, praons, nucleons, neutron stars and other similar objects with the highest energy density.
The detailed philosophical analysis of the theory of infinite nesting of matter was carried out by Sergey Fedosin in 2003.  At each level of matter, characteristic basic carriers and boundary points of measurement are allocated. Transitions from one level of matter to another are carried out under the law of transition of quantity and in quality when the quantity of carriers in object exceeds the admissible borders of the measurements typical for the given object. Examples of fractal structures at various spatial levels of matter are the result. Owing to hierarchical structure of the Universe consisting of objects similar each other, repeatability of elements of the natural phenomena, the unity and integrity of the Universe is supported, in addition 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 from one level: the smallest prions and ending with the whales are present in all other living structures 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 manifests as the distribution of organisms of different species scale or levels according to mass and size. Leading to an infinite nesting of levels living matter in each individual living organism.  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. 
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.  He concluded: nonrandom accumulations of matter-energy in physical space-time self-organizes into interacting, interrelated subsystems or components. In such complex structures, he identified eight "nested" hierarchical levels, including cells, organs, organisms, groups, organizations, communities, societies, and supranational systems. Nesting is defined that an organ is composed of many cells, and the 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 can determine 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.
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. 
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.  Authors had made attempts to reveal a uniform principle of micro and macrocosms. For achievement of this purpose, methods of transformation between similarity and dimensions of physical quantities are used. The gravitational field equations are Faraday - Maxwell fields.
Denial of the Big Bang and interpretation of red shift in spectra of far galaxies as Doppler effect, allows this model to develop a 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.
Unified structure of Universe. About similarity micro-and a macrocosm.
A system of the Universe was published in the book "Rise of the Worlds" (2003).  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.
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 www.scalativity.com .
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.    
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.
Raelian cosmology is based on similar cosmological sights at the structure of the Universe.