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Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1134-1162页

作者： declan traill Melbourne Australia

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

关键词： Electron Positron Wave Function Solution Electromagnetic Spin Mass Charge Proof Fundamental Particle Properties Quantum Mechanics Classical Physics Computer 3D Model Schrödinger Equation RMS Klein Gordon Electric Magnetic Lorentz Invariant Hertzian Vector Point Potential Field Density Phase Flow Attraction Repulsion Shell Theorem Ehrenfest Virial Normalization Harmonic Oscillator

The Light Timing Calculations of the Interferometer in the Quest to Detect Light Speed Anisotropy and a Case Study of the Michelson-Morley and Miller Mt Wilson Experiments

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Journal of Applied Mathematics and Physics 2022年第3期10卷 802-827页

作者： declan traill Melbourne Australia

This paper formulates the light timing calculations for each interferometer arm;one that is parallel to the direction of motion of the interferometer through space and the other that is perpendicular. The calculations are done for a vacuum-mode interferometer and then for a gas-mode interferometer. The calculations show that no light timing difference is detectable in a vacuum-mode interferometer, but once an optical medium is present in the light path down the arms of the interferometer, this is no longer the case and a timing difference is detectable. Further to this, the timing equations obtained from the analysis are used to model the historical experiments of Michelson-Morley and Miller (Mt Wilson) and predictions are made by the model that accurately match the actual recorded results from those experiments. Thus, this timing analysis confirms that there is a light speed anisotropy in a reference frame that is moving through space, indicating the presence of a preferred Aether reference frame through which the Earth is moving.

关键词： Interferometer Luminiferous Aether Michelson Morley Miller Wilson Light Interference Fringe Timing Isotropic Anisotropic Preferred Reference Frame NASA Doppler Anomaly Cahill Computer Model Gas Mode Vacuum

The Delayed Quantum Eraser Experiment Explained Classically

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Journal of Modern Physics 2021年第9期12卷 1183-1189页

作者： declan traill Independent Researcher Melbourne Australia

This paper discusses the well-known delayed choice Quantum Eraser experiment performed by Kim et al. in 2000 and analyzes it from a Classical Physics perspective. I have included a diagram of the setup used in the experiment. I show that the result of the experiment can be explained by Classical Physics and does not require “Spooky action at a distance” due to entangled particles, as Einstein famously once put it, nor events modifying the past due to the delayed choice aspect of the experiment.

关键词： Delayed Choice Quantum Eraser Photon Laser EPR Entangled Classical Physics Polarizing Beam Splitter Coincidence SPDC

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1050-1062页

作者： declan traill Melbourne Australia

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

关键词： Electrostatic Electron Positron Coulomb Force Attraction Repulsion Wave Function Electric Magnetic Radiation Pressure Shell Theorem 3D Computer Model Quantum

Fresnel Dragging Explained by a Classical Model of Light Transmission in Optical Media

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Journal of Applied Mathematics and Physics 2021年第8期9卷 1883-1889页

作者： declan traill Melbourne Australia

The original mathematical treatment used in the analysis of the Fizeau experiment of 1851, which measured the relative speed of light in a moving medium, assumes that light travels through the water in a smooth continuous flow, at a speed less than the speed of light in a vacuum (relative to the water). Thus, it assumes that the water’s velocity vector can simply be added to that of the light. However, light is transmitted through optical media, such as water, by a continuous process of charge excitation (semi-absorption) and re-emission by the water molecules;but travels between them at the full speed of light (in a vacuum). Thus, the mathematics describing the process of Fresnel dragging must be formulated differently and can then be explained by classical physics, allowing the entire process to be fully visualized.

关键词： Fresnel Dragging Optical Fizeau Absorption Emission Delay Refrac-tive Index Relativity Classical Physics