The Periodicity of Atomic Matter

There are 81 naturally occuring non-radioactive elements with 264 stable isotopes. Each of the 264 nuchdes is characterized by a mass number, A, an atomic number, Z, and a neutron munber, N = A— Z, that respectively specify the number of nucleons (protons -I- neutrons), the number of extranuclear electrons and the number of neutrons per atom. Because Z and N are both integers the composition of the stable atomic nuclei is conveniently specified as the rational fraction, Z/N which, with one exception, is less than one and always larger than the irrational fraction, r = 0.61803. the golden ratio. 

This observation is readily explained by the way in which atomic energy levels respond to apphed pressure. The Z/N ratio of unity is inferred to 

The shift of electronic energy levels under pressure predicts a redshift in all spectra eminating from regions of high space-time curvature. This includes all galaxies and quasars and their immediate environments. Consistent interpretation of observed redshifts on these grounds would drastically modify the picture currently based on cosmological Doppler shifts. 

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The main building blocks of the proposed new model are the relationship between geometry, numbers and space the theory of relativity and the periodicity of atomic matter. Taken together, these considerations indicate a cosmic symmetry that defines a harmonious holistic system that embraces all objects from the subatomic to extragalactic scales. The common geometrical factor is the ubiquitous golden parameter, r = 0.61803... 

As discrete numbers of nucleons are involved in the constitution of nuclides the periodicity of atomic matter is readily simulated in terms of the elementary number theory of rational fractions, Farey sequences and Ford circles. 

The first indication that the periodicity of atomic matter depends on the proton neutron ratio was discovered by William Harkins, a decade before the discovery of the neutron. He found that the ratio A — Z)/A never exceeds 0.62 for any stable nuclide. More precisely, it can be shown that the neutron... 

Analysis of the periodicity of atomic matter therefore guides us to a projective model of a closed imiverse in the double cover of four-dimensional projective space-time. Transport across the interface, or along the involution, results in the inversion of CPT symmetry. 

The range of events between the formation of atoms and their eventual disappearance through black holes follow a self-similar pattern that conforms to the curvature of space-time. The periodicity of atomic matter depends on the same number theory that shapes the mutual arrangement of planets, moons, rings, comets and asteroids in a solar system. By a mechanism, to be explored, solar systems are distributed along galactic spiral arms in a pattern like that which prevails in solar systems and atoms. 

It all hangs together. To account for such consilience, Plichta [6] conjectured that numbers have real existence in the same sense as space and time. A more conservative interpretation would link numbers, through the golden ratio, to the curvature of space-time. A common inference is that the appearance of numbers as a manifestation of the periodicity of atomic matter is due to a spherical wave structure of the atom. A decisive argument is that the fiiU symmetry, implied by the golden ratio, incorporates both matter and antimatter as a closed periodic function with involution, as in Fig. 9, in line with projective space-time structure. 

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 four different periodic tables account for the observed elemental diversity and provide compelling evidence that the properties of atomic matter are intimately related to the local properties of space-time, conditioned by the golden parameter r = l/. The appearance of r in the geometrical description of the very small (atomic nuclei) and the very large (spiral galaxies) emphasizes its universal importance and implies the symmetry relationship of self-similarity between all states of matter. This property is vividly illustrated by the formulation of r as a continued fraction ... 

The involution that occurs in projective geometry defines conjugate regions with time inversion and conjugate forms of matter. The function that describes the observed periodicity of atomic matter is of the same projective form and varies with local space-time curvature. This variation shows that spectroscopic analysis of light waves, stretched between sites of different curvature, must be frequency shifted, as observed. 

The subsequent discovery (Boeyens, 2003) of the grand periodicity of atomic matter put these speculations into sufficient perspective to allow definite conclusions about the projective topology of space-time and the universe. In the final analysis, all conclusions reached in this work can be reduced to the gauge principle, as summarized in Appendix B. Some readers may like to set the scene by reading this appendix before the main text. 

Surfaces are found to exliibit properties that are different from those of the bulk material. In the bulk, each atom is bonded to other atoms m all tliree dimensions. In fact, it is this infinite periodicity in tliree dimensions that gives rise to the power of condensed matter physics. At a surface, however, the tliree-dimensional periodicity is broken. This causes the surface atoms to respond to this change in their local enviromnent by adjusting tiieir geometric and electronic structures. The physics and chemistry of clean surfaces is discussed in section Al.7.2. 

Mendeleev s reluctance toward reduction was not widely shared. One of the codiscoverers of the periodic system, the German Lothar Meyer, accepted the possibility of primary matter and supported Prouf s hypothesis. He was also happy to draw curves through numerical data, including his famous plot of atomic volumes that showed such remarkable periodicity that it helped in the acceptance of the periodic system. Nonetheless, prior to Thomson s discovery of the electron, no accepted model of atomic substructure existed to explain the periodic system, and the matter was still very much in dispute. 

Why Do We Need to Know This Material Atoms are the fundamental building blocks of matter. They are the currency of chemistry in the sense that almost all the explanations of chemical phenomena are expressed in terms of atoms. This chapter explores the periodic variation of atomic properties and shows how quantum mechanics is used to account for the structures and therefore the properties of atoms. 

In 1920 Bohr turned his attention to the problem of atomic structure. Matters had become somewhat more complicated than they were in Mendeleev s day. By 1920, 14 elements had been discovered that did not seem to follow Mendeleev s periodic law. Called the rare earths, they had similar properties and followed one another in the table of elements they were elements 58 through 71. When Mendeleev formulated his law only two had been discovered, so they didn t seem to present any great problem. But now they presented an anomaly that no one had been able to clear up. A workable theory of atomic structure would have to explain not only why periodicities were seen in the larger part of the table of the elements but also why they disappeared when one came to the rare earths. 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the stmcmre (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms or molecules) within the unit cell. In the case of XRD, the scattering matter is the electron density within the unit cell. Each diffraction maximum is characterized by a unique set of integers h, k and I (Miller indices) and is defined by a scattering vector H in three-dimensional... 

J. Barrett, Atomic Structure and Periodicity, Royal Society of Chemistry, Cambridge, 2001. This book is meant to act as preliminary reading for the present text, but covers the subject matter in a largely non-mathematical way. The theoretical basis of the Periodic Table is dealt with in considerable detail and is followed by discussions of the periodicities of the main physical and chemical properties of the elements. 

Leopold May goes back even further in time to outline a variety of atomistic ideas from aronnd the world. His chapter Atomism before Dalton concentrates on conceptions of matter that are more philosophical or religiotts than scientific, ranging from ancient Hindu, to classical Greek, to alchemical notions, before touching on a few concepts from the period of early modem science. May is Professor of Chemistry, Emeritus, at the Catholic University of America in Washington, DC. 

Almost all chemical properties can be explained in terms of the properties of atoms, so this material is central to developing an understanding of chemistry. The topics we cover here account for the structure of the periodic table, the great organizing principle of chemistry, and provide a basis for understanding how elements combine to form compounds. The material is also important because it introduces the theory of matter known as quantum mechanics, which is essential for understanding how electrons behave. 

The principle that governs the periodic properties of atomic matter is the composition of atoms, made up of integral numbers of discrete sub-atomic units - protons, neutrons and electrons. Each nuclide is an atom with a unique ratio of protonsmeutrons, which defines a rational fraction. The numerical function that arranges rational fractions in enumerable order is known as a Farey sequence. A simple unimodular Farey sequence is obtained by arranging the fractions (n/n+1) as a function of n. The set of /c-modular sequences ... 

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