Mathematical model of the structure of elementary particles in space

Mathematical model of the structure of elementary particles in space

(zenodo.org) Mail.ru Correction dated 2025.06.20 An unfortunate error was discovered in the size scaling formula; however, a solution has been found which still leads to the desired result when scaling the size. Appendix 8, therefore, remains unchanged. The postulates have been slightly amended (specifically 3.3). The calculation in Appendix 8 for the scaling of the interaction speed has been corrected. 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 as a result of resonance processes in this medium. The existence of...
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Wave resonance and scaling. Speed of light as a boundary of physical interactions.

Wave resonance and scaling. Speed of light as a boundary of physical interactions.

(zenodo.org) Introduction Modern physics operates with a number of fundamental constants, among which Planck's constant h occupies a special place. However, if we consider the process of scaling physical quantities through resonant waves, we can assume that Planck's constant is not an independent quantity, but is derived from the speed of light and geometrical characteristics of wave processes. Linking wave processes and scaling Many physical phenomena are based on resonance. If we consider standing waves at different scales, we can identify their common patterns. One of the key factors is that when scaling the wavelength, the number of nodes is preserved, while the frequency changes inversely proportional to the scale. The speed of light plays here the role of a fundamental parameter determining the interaction of waves. It is important to note that the interaction velocity remains constant, but it can be decomposed into two components: along the x-axis (spatial scale that defines the size); along the y-axis (energy-related oscillation frequency). This leads to a fundamental relationship between...
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