A Constrained Helical Worldline Model: Unifying Mass-Frequency Equivalence, Zitterbewegung, and Spin Quantization

The wave-particle duality and the origin of spin remain central mysteries in quantum mechanics. Building on the mass-frequency equivalence principle ħω₀ = m₀c² and the force-gradient relation F = m₀c² dγ/dx, we construct a classical relativistic action for a point particle with an internal rotational degree of freedom. A kinematic constraint fixes the mechanical rotation frequency to the Compton frequency Ω₀ = 2ω₀, reflecting the spinor nature of fermions. Rest-frame analysis yields spin s = ħ/2, the reduced Compton wavelength r_c = ħ/(2m₀c), and an internal transverse speed c. In a moving frame, the worldline becomes a regular helix whose instantaneous path speed remains exactly c for all center-of-mass velocities—a geometric realization of u_μ u^μ = c². The force-gradient relation connects external influences to helix deformation: a spatially varying Lorentz factor γ(x) changes the local pitch and rotation frequency, with force as the measure of deformation. Applications reproduce Newtonian gravity, tidal effects, and the Lorentz force. The magnetic moment gives g = 1, indicating full quantization is needed to recover the Dirac value g = 2. This paper includes 4 figures.