The Fermion as a Möbius LC Circuit: Inductive Mass, Capacitive Charge, and the Fine Structure Constant as an Impedance Ratio

This paper identifies the fermion (Möbius (n=3) standing wave) as a topological LC circuit. By separating the wave into an inductive inner layer and a capacitive outer layer, we derive the fine structure constant (α) as a fundamental impedance ratio. Key Findings Mass as Inductance: The inertial mass (m) is identified as the inductive impedance of the inner Möbius layer. Newton’s second law is shown to be the frequency-domain equivalent of an inductor's response. m ≡ L The Fine Structure Constant: (α) is derived as the exact ratio between the vacuum characteristic impedance ((Z_0)) and twice the von Klitzing quantum resistance ((R_K)), arising from the (4π) topology of the Möbius circuit. α = Z₀/2RK LC Resonance and Stability: The upper wave-particle threshold (E/f^2 = 4π^2) is shown to be the resonance condition of the fermion's LC circuit. ω₀ = 1√LC Quality Factor and Lifetime: The particle lifetime is determined by the circuit's quality factor, explaining the electron's stability through an ideal resonance. Q = 2/α ≈ 274 Conclusion This circuit-based model provides a classical intuitive framework for quantum electrodynamics, unifying mass, charge, and interaction strength through topological impedance matching.