Cosmic self-similarity

In chemical systems intramolecular interactions depend on the exclusion principle that limits interatomic electron density according to the golden ratio (Boeyens, 2008). 

Intergalactic structures are not known in sufficient detail for comparison with molecular structure but there are indications that galactic clustering involves plasma helds in the form of hlaments and ropes. 

The current understanding of interaction between stellar objects is clouded by biased estimates of the cosmic distance scale and may improve after reassessment of cosmological redshifts. 

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The proposed (Manuel et al., 2006) nuclear cycle that powers the cosmos has many elements in common with some of our arguments. Not unlike the periodic model of stable nuclides and the notion of cosmic self-similarity these authors suggest that stars are subject to the same types of interaction that occur in radioactive nuclides, which depend on the relative amounts of nucleons defined by the numbers A, Z and N. Because of chemical layering an accumulation of neutrons that resembles a neutron star develops at the core of an ordinary star. This core is left behind as the remains of a supernova. 

Empirical evidence at variance with standard cosmology is, likewise, totally ignored. Even the most fundamental of empirical observations, known as universal CPT (charge conjugation-parity-time inversion) symmetry, which dictates equal amounts of matter and antimatter in the cosmos, is dismissed out-of-hand. Less well known, but of equal importance, cosmic self-similarity, is not considered at all. 

Optimization by a golden spiral predicts the correct distribution of matter in the solar system [31], with the inference that the spiral structure reflects space-time topology. Fractal models of the universe, which imply cosmic self-similarity, would then indicate the same optimization for extranuclear electron density. The resulting wave structure inevitably carries an imprint of the golden ratio. 

We now consider the possibility of characterizing the electronic structure of atoms as it relates to cosmic self-similarity and the periodicity of atomic matter. 

The distinctive property of logarithmic spirals is the constant dilatation for equal rotations. A dilative rotation of 2n transforms any point on the spiral into a homothetic point, which is similarly placed and directed. The spiral, said to be homothetic to itself, therefore has the property of self-similarity at all scales. We note that the origin (r, 0 = 0) transforms into the homothetic points e" " after n rotations. We propose that this property, described by the three fundamental constants e, n, and r, is related to the general curvature of space-time, which is responsible for the observed cosmic self-similarity e for growth, n for rotation, and X for dilatation. 

The demonstration [1] that both Lorentz transformation and quantum spin are the direct result of quaternion rotation implies that aU relativistic and quantum structures must have the same symmetry. This is the basis of cosmic self-similarity. The observation that the golden mean features in many known self-similarities confirms that r represents a fundamental characteristic of space-time curvature. The existence of antimatter and the implied CPT symmetry of space-time favors... 

Cosmic self-similarity has been documented and discussed many times with reference to atomic nuclei, atomic structure, the periodicity of matter, covalence, molecular conformation [26], biological structures, planetary and solar systems [27], spiral galaxies and galactic clusters [28]. The prominent role of the golden ratio in all cases can only mean that it must be a topological feature of space-time structure. 

We contend that the shape of large molecules in empty space is affected by the topology of the four-dimensional space-time manifold. Guided by the principle of cosmic self-similarity, it is reasonable to assume that, like many spiral galaxies, extended molecules tend to curve like the surface of a golden spiral. It lies in an... 

If cosmology is to be consistent with all of science it requires serious revision in order to come into line with chemical evidence pertaining to the periodicity of matter, the cosmic abundance of nuclides and the self-similar symmetry between objects large and small. All of these aspects, either refute, or remain neutral to the provisions of the big-bang model. A valid model, in line with... 

As recently shown (Boeyens, 2009) the Bode -Titius law, which hints at some harmonious regular organization of planetary motion in the solar system, is dictated by a more general self-similar symmetry that applies from subatomic systems to galactic spirals. The common parameter is the golden ratio, r = 0.61803. Any such cosmic symmetry should be dictated by a successful cosmological model. 

From any point of view, be it magic, religion or science, there is consensus about the splendid nature of the cosmic whole. One man s divine plan is another s magical harmony or consilience among the laws of Nature. Unity of knowledge about the natural world is not in dispute. The most striking manifestation of this unity occurs as self-similarity across all levels of observation, from the infinitesimally small to the astronomically large. 

The recognition of self-similarity simplifies the description of the physical world, all in response of the vacuum to the curvature of space-time, but complicates the perception of three-dimensional beings of their four-dimensional environment, which they are physically unable to visualize. The perceived infinity of space is the illusion created in simply-connected tangent space by the multiply-connected cosmic reality. The large-scale structure of the imiverse is destined to remain unknown for a long time. 

Synthesis of these notions leads to an alternative cosmology that has little in common with the standard model. It may not have the same dogmatic appeal as the big bang, but it unifies a growing body of discordant empirical evidence, based on all the matter and energy in the universe, the Copernican principle and sound mathematics, without singularities. It has the potential directly to address the basic notions of chirality, astronomical anomalies, holistic self-similarity and other cosmological puzzles, such as Zwicky s paradox, in addition to traditional celestial mechanics. In effect, it calls for the re-examination and re-interpretation of the cosmic whole. 

From this observation we infer self-similarity on a cosmic scale, from atoms to galaxies, which implies the same numerical basis for the atomic models of Nagaoka and Bohr, assumed to be self-similar with the rings of Saturn and the planets, respectively. In principle, the periodic accumulation of extranuclear electron density on an atom could also be optimized by specifying an appropriate convergence angle. 

It is also known as self-similarity, a concept which is intimately related to the golden ratio, and known to operate on a cosmic scale. Our observations may therefore be rationalized by considering elementary matter as the product of large-scale space-time curvature, as described by the golden ratio. We reach the provocative conclusion that a construct, which is entirely governed by the properties of the golden ratio and number theory, predicts the electronic configuration of all atoms, without reference to any chemical know-how, as a basis of a chemical theory. 

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