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On the Periodic Table of Fundamental Particles: The Vibrational Structure of Spacetime and Torsion (A Unified Model)

November 2024

DOI:10.13140/RG.2.2.16556.68487

Authors:

Alessandro Rizzo

C.I. Labs

Preprints and early-stage research may not have been peer reviewed yet.

We present a comprehensive development of the Einstein-Cartan-Kaluza-Klein (ECKK) theory as a unified framework that extends General Relativity by incorporating spacetime torsion and extra compact dimensions. This theory aims to derive the fundamental properties of particles—spin, mass, and charge—from a purely geometric perspective. We rigorously formulate the fundamental equations of the ECKK theory, including the effects of torsion and the Kaluza-Klein decomposition, to establish connections between higher-dimensional geometry and four-dimensional physical phenomena. By integrating the Higgs mechanism into this framework, we derive the masses of fermions and gauge bosons and address the quantization of electric charge, including the fractional charges observed in quarks. We perform detailed calculations of the spin, mass, and charge for all known fundamental particles and compare these results with experimental data. Our findings show remarkable consistency between the theoretical predictions and observed particle properties, validating the ECKK model's potential as a unified theory. Additionally, we explore the application of the ECKK model to hadronic mass spectra, providing insights into the quantization patterns observed in baryons and mesons. We address theoretical challenges such as anomaly cancellation, compatibility with the Standard Model, and the hierarchy problem, offering resolutions within the ECKK framework. Finally, we introduce a novel periodic table of fundamental particles derived from the ECKK model, highlighting the geometric origin of their properties.

Visualization of the mass redistribution in a droplet after an interaction. The initial mass 1 splits into 1 − x, representing the remaining mass, and x, the dispersed mass. This branching structure illustrates the recursive nature of interactions, where mass and energy are redistributed across scales, forming a cascade of smaller impacts.

Formation of a Majorana Fermion through Spacetime Torsion. The sequence illustrates the emergence of a Majorana fermion from spacetime deformations. Initially, a saddle-like spacetime configuration allows free photon propagation. As torsion and metric asymmetry grow, spacetime begins to twist, forming a non-orientable topology analogous to a Klein bottle. Further deformation leads to quantized vortices, associated with torsion singularities, where zero-energy Majorana modes emerge. In the final stage, the structure stabilizes into a twisted, toroidal topology, representing a stable Majorana fermion. This progression highlights the role of spacetime torsion and topology in generating dark matter candidates.

The evolution of spacetime geometry under varying conditions. (Left) A representation of flat spacetime, characterized by the absence of curvature in the absence of mass or energy. (Center) Spacetime curvature induced by the presence of mass, consistent with the predictions of General Relativity (GR). The deformation of the spacetime continuum illustrates how mass distorts the geometry of spacetime. (Right) The combined effects of mass and an electromagnetic field, introducing both curvature and torsion into the spacetime fabric. This configuration exemplifies a more complex geometric distortion, where torsion plays a critical role in shaping spacetime structure and potentially preventing singularities through the interplay of gravitational and electromagnetic effects.

Visualization of a water droplet's mass dispersion following an impact. The droplet represents a localized high-density interaction, while the surrounding blurred region illustrates the gradient of interaction density and the concept of a blurred compactification radius. This demonstrates the recursive, fluid-like nature of space as a continuum of energy interactions, where the spatial structure emerges from overlapping scales of interaction.

Visualization of a particle's mass dispersion following an interaction. The central region, being less dynamic than the outer region, exhibits inertial characteristics due to the stabilization of mass and energy density. In contrast, the outer region is more dynamic, reflecting a gradient of interaction density that extends across larger scales. This structure illustrates the concept of a blurred compactification radius. It demonstrates the recursive, fluid-like nature of space as a continuum of interactions and an energetic background, where the spatial structure emerges from overlapping scales of interaction. The model also highlights the equivalence of space and energy, suggesting that energy is an intrinsic property of space itself, with the outer regions potentially manifesting unseen or dark mass through gradients of interaction density.

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Content uploaded by Alessandro Rizzo

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Content uploaded by Alessandro Rizzo

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Content uploaded by Alessandro Rizzo

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Content uploaded by Alessandro Rizzo

Content may be subject to copyright.