Geometric Unification of Quantum Reality: Particles as Knots, Probability as Topological Entropy

This paper proposes a unified geometric framework for fundamental particle physics, positing that elementary particles are topological manifestations of a single, complexly knotted cosmic worldline. A central achievement of this framework is a detailed proposed resolution to the long-standing muon g-2 anomaly. The theory derives a specific topological contribution to the muon's anomalous magnetic moment, Δaμtopo=+2.99±0.42×10−9, which quantitatively addresses the experimental discrepancy and explains the anomaly's selectivity for the muon via knot chirality. Building on Wheeler's "one-electron universe" hypothesis, the work develops a two-tier unification. At the microscopic level, beyond the g-2 resolution, particle masses are derived from knot invariants using twistor geometry. This approach claims to reproduce all known charged lepton masses (electron, muon, tau) with an accuracy of up to 0.03%. The framework reduces the 19 free parameters of the Standard Model in the lepton sector to two fundamental scales (α≈100.47 MeV, λ1=−0.05 MeV) plus a cosmologically determined effective temperature (Teff≈100 MeV). At the macroscopic level, the theory suggests that quantum statistics and gravitational phenomena emerge from thermodynamic ensembles of these knotted configurations. The paper also makes falsifiable predictions for new physics, including fourth-generation (L4 at 1.985±0.049 GeV) and fifth-generation (L5 at 4.178±0.050 GeV) leptons. The work aims to provide a geometric foundation for quantum reality, offering concrete pathways to experimental validation for its predictions, including the g-2 mechanism.