Mathematical model of the structure of elementary particles in space

Mathematical model of the structure of elementary particles in space

(zenodo.org) Introduction In this paper we construct a mathematical apparatus according to which elementary particles can be described through standing waves with different number of nodes. This allows to connect their properties with scaling in multidimensional space and interaction through wave resonance between fractal levels. The wave nature of elementary particles Here under elementary particles we understand only long-lived particles: neutrino (standing wave with one node), electron (two nodes), neutron (three nodes), proton (four nodes), as well as their antiparticles. Standing waves are formed on the basis of wave resonance between different fractal levels. In the previous article (https://zenodo.org/records/15094660) it was shown that scaling occurs in multiples: where| ℏ|ₙᵤₘ is the theoretically calculated analogue of Planck's reduced constant, and c is the speed of light. This suggests that the scaling of wave resonance occurs as a function of size by a multiple of the fourth power of the speed of light. We also know that wavelength is related to mass through the same Planck constant. So...
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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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