A Deterministic Space-Symmetry Approach to Quantum Spin Dynamics: Resolving the Superluminal Paradox through DualOscillator Geometric Representation

This paper presents a novel geometric and deterministic interpretation of quantum spin angular momentum for Spin-1/2 fermions, establishing a structural bridge between classical mechanics and relativistic quantum theory. We propose a fundamental formulation that defines the total spin vector magnitude (S) via rest mass properties and the reduced Compton wavelength, yielding S = mcλ c = ℏ. By aligning this intrinsic magnitude with the experimentally verified projectionS z = 0.5ℏ, a precise spatial symmetry angle of exactly 60° emerges via direct trigonometric formulation (cosθ = 0.5), substituting the probabilistic expectation values (√s(s+1)ℏ ≈ 0.866ℏ) of standard quantum mechanics. We demonstrate that this geometric framework serves as an Equivalent Representation, yielding a 100% numerical match with laboratory-measured energy splittings in both the Zeeman and Paschen-Back effects. Furthermore, this framework successfully resolves the historical Lorentz superluminal surface velocity paradox, proving that the localized oscillation propagates exactly at the speed of light (v = c) at the Compton radius boundary. Finally, we show a profound structural convergence between this deterministic model and the relativisticZitterbewegung (ZBW) dynamics derived from the Dirac equation. Keywords: Quantum Spin Geometry, Compton Wavelength, Zeeman Effect, Superluminal Paradox, Zitterbewegung, Space-Symmetry.