Mathematics of the crystal model

Author: Hatem Saleh S Alwardi

Alwardi, Hatem Saleh S, 2022 Mathematics of the crystal model, Flinders University, College of Science and Engineering

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In this thesis we investigate a new geometrical model of elementary particles derived in a unified way from the fundamental electromagnetic and spin fields. In basic physical phenomenology it thus has the characteristic features of a compound-particle model, but unlike most of the existing theories, dynamical treatment of the interaction makes up an essential part of the model. The scheme is motivated by the observation of an interesting analogy between the properties of particles. Maxwell’s equations, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Departing from this point we establish a steady-state model to describe most experimentally established subatomic particles, but also enigmas such as dark matter and the Higgs boson. In addition, we use a fixed crystalline structure as a scaffold for the elements’ atoms including their electrons. This novel crystal theory aims to explain quantum mechanics and phenomena such as dark matter and teleportation, basing it on the known properties of atoms, their electronic shells, and nuclei. The crystalline symmetries, rotations, reflections, translations, and changes of colour are calculated and explained. They relate to transitions in the physics, such as matter to anti-matter, protons to neutrons, magnetic to electric, or invariant properties related to time and motion. The classical “standard model” concepts or reasoning via fields or forces, or less intuitive classes of particles such as quarks and gluons are replaced by a kind of simplified structure in a fixed “Parmenidean” crystal comprised of congruent tetrahedra in colours red, yellow, and black which represent axiomatically the positive, negative, and neutral charges. Basic physical ideas such as Pauli’s exclusion principle, Hund’s rule in atomic chemistry, the rules for sizes of electron shells and the need for excess neutrons in many stable nuclides are given reasons within the crystal model. Finally, a theorem about the spin of a particle is proved, that it can be calculated from the surface properties.

Keywords: Atom, nucleus, Coxeter group, subgroup, shell, subshell, orbital, quantum mechanics, spin, charge, physics, mathematics, honeycomb, lattice, graph, tetrahedron, proton, neutron, electron, deuteron, particle, quantum number, symmetry, left-handed, graph paper, electromagnetism.

Subject: Mathematics thesis

Thesis type: Masters
Completed: 2022
School: College of Science and Engineering
Supervisor: Prof. David G. Glynn