Mathematical model of the structure of elementary particles in space

Mathematical model of the structure of elementary particles in space

(zenodo.org) Correction dated 2025.06.18 Corrected the fractalization formula (recently there was an incorrect entry). Changed the fractalization formula, now it depends not on h, but on ħ (reduced the coefficient 2π, since it is a consequence of geometry, not the processes themselves, which leads to its reduction). This increased the coincidence for the size and mass of the Milky Way when transitioning from neutron parameters. Accordingly, changed the applications and conclusion. Annotation This paper presents a theoretical model describing matter, fundamental interactions and the structure of the Universe on the basis of unified wave principles and the concept of fractality. The paper aims to overcome the fragmentation of modern physical theories by offering an alternative approach to explain the nature of mass, electric charge, gravitation and the origin of fundamental constants. The model is based on the idea that elementary particles are stable standing waves formed in Euclidean space, considered as an energy-rich medium. Interactions between particles and formation of all fundamental forces are interpreted...
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Standing waves of energy density and particle structure

Standing waves of energy density and particle structure

(zenodo.org) Introduction Modern physics describes elementary particles as point objects or perturbations of quantum fields, but another interpretation is possible. This chapter considers the hypothesis that particles are standing waves of energy density and their properties can be explained through de Broglie waves. We will also consider how particle birth can be explained within this model and why the law of conservation of energy leads to the symmetry of matter and antimatter. Standing waves of energy density and particles To date, science does not describe the origin of electric charge. What is its nature? Why is its value constant for elementary particles? Charge does not change its sign or its value regardless of the environment. Why does the mass of a body change when the speed of motion changes, but nothing happens to the charge? What is this parameter - charge? It is known that: 1/c = αћ/e² where e is the charge of the electron, ћ is the reduced Planck constant, c is the speed of light. One constant is expressed...
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Energy Density Theory

Energy Density Theory

(zenodo.org) Introduction This paper explores the hypothesis that the mass of elementary particles is a consequence of variations in energy density within space. This approach provides a new perspective on fundamental interactions, explains anomalies related to dark matter and dark energy, addresses Heisenberg's uncertainty principle, and offers an alternative to the concepts of space-time curvature and the Higgs field. 1. Mass as a Consequence of Energy Density In classical physics, mass is considered a fundamental property of matter. However, if mass is assumed to be a manifestation of energy density, its origin can be explained without invoking the Higgs field. In this case, the mass of charged particles results from uniform changes in energy density, whereas neutral particles may exhibit vortex-like variations in energy density. 1.1. Relationship Between Mass and Wavelength Consider the behavior of mass at the speed of light limit. There is a direct dependence between wavelength and mass. If this dependence is fundamental, then variations in energy density in space determine the inertial...
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The Electromagnetic Nature of Mass: Rethinking Fundamental Interactions

The Electromagnetic Nature of Mass: Rethinking Fundamental Interactions

(zenodo.org) Introduction Modern physics classifies fundamental interactions into four main forces: gravity, electromagnetism, the strong interaction, and the weak interaction. However, recent studies and hypotheses suggest that electromagnetic waves  may play a more fundamental role in the structure of matter than previously assumed. This work presents an alternative perspective on the nature of mass and charge through the lens of electromagnetic processes, supported by mathematical derivations. 1. Mass as a Manifestation of Electromagnetic Wave Energy According to Einstein’s mass-energy equivalence principle:     E = mc² mass is a form of energy. However, the question remains as to how this energy is structured.     If an elementary particle is considered not as a point object but as a complex lectromagnetic wave confined within a spherical or toroidal structure, its mass may result from the energy contained in this form. Mass can also be examined in the relativistic limit through the energy of a photon:     E = hc / λ and expressed as a function of wavelength at the speed of...
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The Fundamental Connection Between Electromagnetic Waves and the Mass of an Elementary Particle

The Fundamental Connection Between Electromagnetic Waves and the Mass of an Elementary Particle

(zenodo.org) Introduction Modern physics considers mass and electromagnetic radiation as two distinct entities. However, by analyzing fundamental principles, one can conclude that the mass of an elementary particle is directly related to the characteristics of the electromagnetic wave that confines its structure. In this article, we examine the physical foundations of this connection and its possible implications. The Wave Nature of Elementary Particles The idea of the wave nature of matter was first proposed by Louis de Broglie. According to his hypothesis, a particle can be associated with a wavelength:     λ = h / p where:- λ is the de Broglie wavelength, - h is Planck’s constant, - p is the momentum of the particle. In relativistic mechanics, the total energy of a particle is given by the equation:     E² = (pc)² + (mc²)² Here, the rest mass m plays a crucial role, but at high energies, its contribution becomes small compared to the momentum term. This means that as an elementary particle moves, its mass and the associated...
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Dependence of Mass on Wavelength in the Relativistic Limit

Dependence of Mass on Wavelength in the Relativistic Limit

(zenodo.org) Introduction This paper examines the relationship between a particle’s mass and its wavelength based on the relativistic energy equation. In the case of high-energy particles, the rest mass transitions into a change in wavelength, allowing us to derive a mathematical dependence between these quantities. 1. Fundamental Equations The relativistic expression for the total energy of a particle with nonzero rest mass is given by:     E² = p²c² + m²c⁴  where:- E is the total energy of the particle, - p is the particle’s momentum, - m is the rest mass of the particle, - c is the speed of light. According to de Broglie’s relation, momentum is connected to wavelength λ as follows:     p = h / λ where h is Planck’s constant. 2. Expressing Mass Through Wavelength Substituting the expression for momentum into the energy equation, we obtain:     E² = (hc / λ)² + m²c⁴     Solving for mass:     m²c⁴ = E² - (hc / λ)²     m = (1 / c²) * sqrt(E² - (hc / λ)²) 3. High-Energy Limit At high energies,...
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