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It is demonstrated that all stable (non-radioactive) isotopes are formally interrelated as the products of systematically adding alpha particles to four elementary units. The region of stability against radioactive decay is shown to obey a general trend based on number theory and contains the periodic law of the elements as a special case. This gen...
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... more convenient mapping of the isotope distribution is obtained by plotting proton:neutron ratio as a function of atomic number, as in Fig. 2. This diagram shows development of both even series, characterized by mass numbers of 4n and 4n+2, respectively. The two different patterns used to represent each of the two series serve to distinguish between forward and reverse progressions as discussed. Like the 4n series, the second series also consists of 81 stable isotopes. Open ...
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... the three isotopes of Si, the second ends with the third of the five isotopes of Ti and the third ends with the fourth of the five isotopes of Zn. The isotope at the end of each period is invariably an apparently arbitrary one within the range for that element. A more precise definition of each period is obtained by using the coordinate axes of Fig. 2. Instead of linear arrays, the sets of 24 isotopes in each period now occur in well-defined blocks, shown in Fig. 7. The positions of straight lines that separate the isotopes belonging to contiguous blocks, are fixed within very narrow limits. The procedure is illustrated by drawing a set of slanted lines to separate the hypothetical ...
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... connecting line between p/n = 1 at Z = 0 and p/n = 0.618 at Z = 102 (AC) defines, to fair approximation, the discontinuous stability curve empirically inferred before (Fig. 2). If points on this line represent the maximum p/n ratio allowed for stable even mass-number isotopes, the minimum number of neutrons that stabilize an isotope of given atomic number p, is given by: The two simple formulae, Eqs (3) and (4) may be used to calculate the range of stability for isotopes of each element in the triangle of ...
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Citations
... Not only the topology of space-time, but also the physical content of the universe, resembles the natural number system in remarkable detail [2]. This explains the unreasonable effectiveness of mathematics as a scientific tool and the success of number theory to predict natural phenomena as a manifestation of cosmic symmetry [2,3]. The physical world, as an image of the natural numbers, can never be known in more detail than the number system. ...
... Despite a number of uncertain half-lives, a reasonable estimate of 264 divides the stable (non-radioactive) nuclides into 11 periods of 24. Plotting the ratio of protons:neutrons (Z/N ) for all isotopes as a function of atomic number, the hem lines that separate the periods of 24, intersect a reference line, at Z = τ , in Z-coordinates which correspond to well-known ordinal numbers that define the periodic table of the elements [2,3]. Remarkably, the same hem lines intersect a reference line at Z/N = 0.58 in atomic numbers that correspond to the closure of the calculated wave-mechanical energy levels for hydrogen. ...
Bohmian mechanics developed from the hydrodynamic interpretation of quantum events. By this interpretation all dynamic variables retain their classical meaning in quantum systems. It is of special significance in chemistry as a discipline which is traditionally based on the point electrons of quantum field theory. It could be more informative to assume a non-dispersive electronic spinor, or wave packet, with divergent and convergent spherical wave components, and with many properties resembling those of a point particle. Complex chemical matter is endowed with three attributes: cohesion, conformation and affinity, which can be reduced to the three fundamental electronic properties of charge, angular momentum and quantum potential, known from the wave structure. The chemical effects of these respective scalar, vector and temporal principles, all manifest as extremum phenomena. The optimal distribution of electronic charge in space appears as Pauli's exclusion principle. Minimization of orbital angular momentumbecomes the generator of molecular conformation. Equilization of electronegativity, the quantumpotential of the valence state, dictates chemical affinity. The chemical environment is said to generate three emergent properties: the exclusion principle, molecular structure and the second law of thermodynamics. These concepts cannot be predicted from first fundamental principles. Only by recognition of the emergent properties of chemistry is it possible to simulate chemical behaviour. The exclusion principle controls all forms of chemical cohesion, atomic structure and periodicity; molecular structure underpins vector properties such as conformational rigidity, optical activity, photochemistry and other stereochemical phenomena; while transport properties and chemical reactivity depend on the second law. Simulation of these chemical concepts by constructionist procedures, starting from basic physics, is impossible. The ultimate reason is that complex chemical properties are not represented by quantum-mechanical operators in the same sense as energy and momentum. The Bohmian interpretation, which enables the introduction of simplifying emergent parameters, in analogy with classical procedures, allows the calculation of molecular properties by generalized Heitler-London methods, point-charge simulation and molecular mechanics.
... He also derived theoretical models for the analysis of molecular geometry, such as the puckering of 5, 6 and n-member rings [2][3][4] (his three papers on the analysis of ring puckering in these compounds alone have been cited over 400 times). Jan has, in his own distinctive and novel way, made a wealth of contributions to the understanding of fundamental concepts in chemistry and science in general, which include studies on the valence-bond and electron-pair bonds [5][6][7][8][9][10][11], single-crystal neutron diffraction studies [8], molecular modelling and the modelling of multiple metal-metal bonds [12][13][14][15][16][17][18][19][20], the nature of the electron and electron spin [23,24,29], ionic radii [22], electronegativity [27,37], angular momentum [35], periodicity [32,37] and the link between number patterns and na ture [33]. Jan Boeyens only realized later in his career that several common themes permeate his research, and in recent years he has succeeded in weaving these threads together in the books and chapters in books to integrate his ideas on the nature of matter and molecules, the origins and theoretical description of matter, the nature of space, cosmology and general relativity [38][39][40][41]. ...
Jan C.A. Boeyens – A Holistic Scientist
Jan Christoffel Antonie Boeyens was born 75 years ago on October 2, 1934 in a farming community in the small rural town of Wesselsbron in the Free State Province of South Africa. Growing up in such a region, it was natural to develop a love of Nature in all her manifestations, and especially a love of the open veldt, and Jan was no exception in this regard. He loved to walk alone in the veldt, contemplating and observing. In rural communities every boy then had to learn some of the practical manual skills required to make life comfortable. He loved to work with his hands building things and doing woodwork of outstanding quality. He lived with his wife Martha on a farm on the banks of the Crocodile River outside Pretoria. He named his home “Blandings” after the fictional location in the stories of British writer P.G. Wodehouse. This was an ideal location for him, where the open veldt allowed him to take long walks, giving him an opportunity to contemplate, to think and to dream up new, unexpected, simple and elegant solutions for old scientific problems, with the emphasis on the concepts “simple” and “direct”, always emerging as ingenious models escribing aspects of Nature.
... 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. ...
The composition of the most remote objects brought into view by the Hubble telescope can no longer be reconciled with the nucleogenesis of standard cosmology and the alternative explanation, in terms of the ?-Cold-Dark-Matter model, has no recognizable chemical basis. A more rational scheme, based on the chemistry and periodicity of atomic matter, opens up an exciting new interpretation of the cosmos in terms of projective geometry and general relativity. The target readership includes scientists, as well as non-scientists - everybody with a scientific or philosophical interest in cosmology and, especially those cosmologists and mathematicians with the ability to recast the crude ideas presented here into appropriate mathematical models. © Springer Science+Business Media, LLC 2010. All rights reserved.
... pri školjkah ali rogovih živali. Tokunaga (2003, 164) je pri analizi prostorske organiziranosti porečij ugotovil, da imajo posamezni deli porečja, projicirani na dvodimenzionalno ravnino, podobne lastnosti kot enodimenzionalni tako imenovani kvazikristali (Al 65 Cu 20 Fe 15 ), ki pri rasti sledijo Fibonaccijevemu zaporedju (Boeyens 2003). Zakonitostim teorije kaosa sledita tudi razvoj in prostorska razporeditev prsti (Phillips 1995a, 57;Dunlap 1997, 121;Baas 2002, 313 Fibonaccijevo zaporedje 0,0-2,9 0,0-1,9 0,0-1,9 0,0-1,9 0,0-1,9 3,0-5,9 ...
... The intriguing consequence is that the number a then corresponds to the total number of different isotopes of the unique elements which, like the elements, are expected to obey a periodic law [8]. ...
... A simple demonstration of the general periodic law is achieved [8] on plotting atomic numbers (Z) of all stable (non-radioactive) nuclides against the proton :neutron ratio Z=ðA À ZÞ as shown in Fig. 3. The points cluster in a well defined region identified by an irregular profile that alters direction at positions labelled by their atomic numbers. ...
... In addition, these numbers are distributed symmetrically about 51. The four periodic laws defined in Fig. 5 are related in the sense that each of them fits the compact periodic table (Fig. 4) such that all energy shells close in either period 2 or 8 [8]. From the spacing of points at the ratio 1.04, it is inferred that two extra groups of 24 nuclides become stable against b-type decay. ...
Fibonacci phyllotaxis is one of many examples that demonstrate the relationship of biological growth patterns with the golden mean and self-similar symmetry, also observed in scale–rotational crystal growth. An equivalent relationship of natural-number patterns with the structure and periodicity of atomic matter is demonstrated. A generalized, closed periodic law that reveals the hidden symmetry in the periodicity of atomic matter is derived and related to the variability of electronic configuration of atoms, as a function of thermodynamic conditions, to nuclear synthesis and to the DNA code. Implications on space-time structure are discussed.
Classical science reached maturity in the discovery of the electromagnetic field and the periodic variation of the chemical properties of atoms, for which no theoretical explanations existed. The theory of relativity and quantum theory, in the form of wave mechanics, developed in response. The details are briefly discussed and critically examined. By design, the theory of relativity provided a common basis for mechanical and electromagnetic motion, which could be refined into a model for gravitational interaction. The search for an equivalent space-time origin of the electromagnetic field resulted in the recognition of gauge fields, one of which gave birth to wave mechanics. As a theory that underpins atomic periodicity and chemistry it has only been partially successful and, reduced to a scheme of quantum chemistry, based on real linear functions, has failed completely.
The concept of matter waves as a product of four-dimensionally curved space-time is examined. A vital step in the analysis is taking cognisance of the controversial concept of an all-pervading aether. The discrepancy between relativity and quantum theory is traced to the three-dimensional linear equations of wave mechanics, in contrast to Minkowski space-time. The notion of space-like interaction is re-examined and shown to arise from a superficial interpretation of space-time curvature. The more appropriate projective topology is shown to be suitable, in principle, to define four-dimensional matter waves. The transformation from the more general underlying space-time to the familiar three-dimensional affine space is shown to be mediated by the golden ratio, which is further characterized in terms of Fibonacci numbers, Farey sequences and other concepts of number theory. It is demonstrated conclusively that the observed periodic table of the elements and the wave-mechanical approximation are correctly simulated by number theory, with a clear distinction of the respective four- and three-dimensional bases of the two models.
The origins and development of the electronegativity concept as an empirical construct are briefly examined, emphasizing the confusion that exists over the appropriate units in which to express this quantity. It is shown how to relate the most reliable of the empirical scales to the theoretical definition of electronegativity in terms of the quantum potential and ionization radius of the atomic valence state. The theory reflects not only the periodicity of the empirical scales, but also accounts for the related thermochemical data and serves as a basis for the calculation of interatomic interaction within molecules. The intuitive theory that relates electronegativity to the average of ionization energy and electron affinity is elucidated for the first time and used to estimate the electron affinities of those elements for which no experimental measurement is possible.
The quantum and relativity theories of physics are considered to underpin all of science in an absolute sense. This monograph argues against this proposition primarily on the basis of the two theories' incompatibility and of some untenable philosophical implications of the quantum model. Elementary matter is assumed in both theories to occur as zero-dimensional point particles. In relativity theory this requires the space-like region of the underlying Minkowski space-time to be rejected as unphysical, despite its precise mathematical characterization. In quantum theory it leads to an incomprehensible interpretation of the wave nature of matter in terms of a probability function and the equally obscure concept of wave-particle duality. The most worrisome aspect about quantum mechanics as a theory of chemistry is its total inability, despite unsubstantiated claims to the contrary, to account for the fundamental concepts of electron spin, molecular structure, and the periodic table of the elements. A remedy of all these defects by reformulation of both theories as nonlinear wave models in four-dimensional space-time is described. © Springer Science+Business Media Dordrecht 2013. All rights are reserved.
