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Matter-Wave Mechanics
Abstract
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.
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The accepted structure of space and the vacuum derives from the results of relativistic cosmology and quantum field theory. It is demonstrated that an interface between enantiomeric regions of a closed universe, related by an element of PCT symmetry along the interface, represents a construct with all the attributes required of the theoretical vacuum. In-so-far as quantum behaviour is then seen to be induced by the vacuum interface, quantum mechanics emerges as a special case of classical mechanics, rather than the latter being a subset of the former. This removes the quantum-mechanical observational problem, explains the cosmological large-number coincidences, accounts for the anti-matter in the cosmos, and explains the asymmetry of beta-decay. The big bang is not a necessary ingredient of the proposed scheme since it is predicted that time has no beginning.
Philosophers have long speculated that a link exists between natural numbers and the physical world...Pythagoras: "...all is number" John Dalton (1803): "...Atoms combine in simple numerical ratios..." Prout's hypothesis, published anonymously in 1815: "...the elements are different aggregates of the atoms of primordial hydrogen..." Alexandre Émile Beguyer de Chancourtois (1862): "...the properties of the elements are the properties of numbers..." William Harkins (1921): "...the ratio Z/(A - Z) never exceeds the value 0.62 in atomic species..." Within this book, readers with an interest in mathematics, science or natural philosophy will find this expectation addressed.
Chemistry from First Principles is written for any chemist who requires a fundamental understanding of the complexities of chemistry. It provides a clear interpretation of chemical theory from first principles. This book examines the appearance of matter in its most primitive form, from the vacuum and the diversity that results from the fusion of elementary units in the genesis of atomic matter; considers the empirical rules of chemical affinity that regulate the synthesis and properties of molecular matter; analyzes the compatibility of the theories of chemistry with the quantum and relativity theories of physics; formulates a consistent theory, based on clear physical pictures and manageable mathematics, to account for chemical concepts such as the structure and stability of atoms and molecules, the periodicity of nuclides and elements, valence states, activation and chemical reactivity, electronegativity and general covalency, the exclusion principle, electronic energy, orbital angular momentum and spin in relation to molecular shape, torsional rigidity, chirality and molecular modeling; explains the self-similarity between space-time, nuclear structure, covalent assembly, biological growth, planetary systems and galactic conformation. Chemistry from First Principles is an essential guide for students of chemistry who lack the knowledge in higher mathematics considered necessary to grasp the basic principles of chemical theory, teachers of chemistry who are forced to preach concepts which they poorly understand, and any scientist who is seeking a true understanding of chemistry through logical concepts.
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.
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 general law restricts the number of what may be considered as natural elements to 100 and is based on a proton:neutron ratio that matches the golden ratio, characteristic of biological and crystal growth structures. Different forms of the periodic table inferred at other proton:neutron ratios indicate that the electronic configuration of atoms is variable and may be a function of environmental pressure. Cosmic consequences of this postulate are examined.
One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the "three-box" quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315-2328] by using state-of-the-art control and measurement of the nitrogen vacancy center in diamond. In this protocol, the back-action of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurement-induced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59-87] that successfully addresses the measurement detectability loophole.
This introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4 - 12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.
The spacetime two-wave description of a massive particle presented earlier is considered in the context of the nonlinear wave hypothesis and tachyon theory. It is shown that the description implies that the massive particle in motion can be regarded as a system composed of both bradyonic and pseudotachyonic components. A physical interpretation of the pseudotachyonic component is proposed.
We consider the possibility of describing, within the special theory of relativity, particles with spacelike four-momentum, which therefore have velocities greater than that of light in vacuum. The usual objections to such particles are discussed, and they are found to be unconvincing within the framework of relativistic quantum theory. A quantum field theory of noninteracting, spinless, faster-than-light particles is described. The field theory is Lorentz-invariant, but must be quantized with Fermi statistics. The associated particle theory has the property that the particle number is not Lorentz-invariant, and the no-particle state is not Lorentz-invariant either. Nevertheless, the principle of relativity is satisfied. The Lorentz invariance implies a relation between emission and absorption processes, in contradiction to the usual case. Some comments are made about the problem of introducing interactions into the field theory. The limiting velocity is c, but a limit has two sides.
The Dirac equations for a free electron in a cosmological space are solved by means of separation of variables. It is shown that the wave functions depend on the angles θ and ϕ in the same manner as those of a free electron in flat space time. The radial functions are obtained and it is shown that they go over into the usual ones in the limit. The explicit form of the time dependence of the wave functions cannot be obtained until an arbitrary function R(t) is specified. Three different cases are discussed. The energy of the free electron is then determined for each of these. Finally the connection between the equation used here and that proposed by Dirac for the DeSitter space is discussed. It is shown that they are similar and that the imaginary part of the complex mass that he was forced to introduce has a geometrical origin.
In this paper we show that the formalism of O. Klein's version of the five-dimensional relativity can be interpreted as a four-dimensional theory based on projective instead of affine geometry. The most natural field equations for the empty space-time case are a combination into a single invariant set of the gravitational and electromagnetic field equations of the classical relativity without modification. This seems to be the simplest possible solution of the unification problem. When we drop a restriction on the fundamental projective tensor which was imposed in order to reduce our theory to that of Klein a new set of field equations is obtained which includes a wave equation of the type already studied by various authors. The use of projective tensors and projective geometry in relativity theory therefore seems to make it possible to bring wave mechanics into the relativity scheme.
IN the last century, the idea of a universal and all-pervading æther was popular as a foundation on which to build the theory of electromagnetic phenomena. The situation was profoundly influenced in 1905 by Einstein's discovery of the principle of relativity, leading to the requirement of a four-dimensional formulation of all natural laws. It was soon found that the existence of an æther could not be fitted in with relativity, and since relativity was well established, the æther was abandoned.
Current theories of the origin of inertia aer reviewed. An alternative treatment is given. This recognizes the physical extent of even the smallest masses and the interaction effects of physical measurement. It is shown that there are very good physical reasons for identifying the origin of inertia with the local system and that this simultaneously accounts for quantization and the units of length and time. Two experiments are described which illustrate some of the properties under discussion.
Kap. I.Kap. II. Die Undulationsrnechanik conde Broglie nnd die Theorie ron Weyl.§ 1. Die Identitat von y und Weyls Eichstrecke.§ 2. Nichtintegrabilitat schlie5t Eindentigkeit nicht aus.Kap. III. Quantenmechanische IJmdeutung der Theorie von We yl.
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"Together with his four lectures on wave mechanics" Incluye bibliografía e índice
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