Utilizing Theory and Experiment to Search for new structures of Fundamental Particles
Our current understanding of the Big Bang indicates that the universe was not a dimensionless point at $t=0$ but already had four dimensions. This work, exploring physics beyond the Standard Model, abandons the point-like nature of fundamental particles. It comprises theoretical and experimental parts. Theoretically, we present the Empirical Toy Ansatz about a Microstructure of Fundamental Particles (ETAMFP), using the numerical coincidence of strong, weak, and electromagnetic interactions and their corresponding charges (color, weak, electric) to develop a common ground state for all fundamental particles. The time coordinate is used to interpret higher states as vibrational modes of $x, y, z$ (monopole, dipole, quadrupole). We focus on the electron, with lifetime $6.6\times10^{28}$ years, longer than the universe's age. We investigate a Lorentz-contracted gyroscope, a soliton in GR, and the Gross--Pitaevskii equation to derive an electron wave function, yielding an upper size limit, while ETAMFP gives a lower limit. Experimentally, the $e^+e^-\to γγ$ reaction probes long-range QED, and the $e^+e^-\to e^+e^-(γ)$ Bhabha reaction probes short-range weak interaction. The theoretical outer electron radius is $3.2\times10^{-14}$~m, experimental $3.18\times10^{-14}$~m; the inner kernel radius is theoretically $3.3\times10^{-15}$~m and experimentally $3.9\times10^{-15}$~m. The agreement between our investigations in the theoretical and experimental domains of our work generally shows that it is possible to combine all fundamental particles into a common scheme--the ETAMPF model, especially the electron as a geometrically extended object with two fundamental boundaries. These findings open a window to the fusion of General Relativity and Quantum Mechanics and an explanation of the wave-particle duality.