Volume 12, Issue 2, pages 150-178
A geometric interpretation of electron dynamics is presented based on phase-coherent helical motion constrained by relativistic kinematics. Building on de Broglie’s concept of internal periodicity and the Hamilton–Jacobi formulation of mechanics, the electron is modeled as an intrinsic light-speed helical trajectory whose axial pitch corresponds to the de Broglie wavelength and whose transverse scale is set by the reduced Compton length. Within this framework, spin-1/2 symmetry, magnetic moment, rest energy, and bound-state quantization emerge as interconnected consequences of phase closure and geometric constraints, rather than as independent postulates. The formal operator structure of quantum mechanics is recovered as a statistical description of ensembles of phase-coherent helical trajectories, with momentum and energy operators arising as generators of spatial and temporal phase evolution. The framework provides a geometric visualization of interference, tunneling, and quantum transitions, while remaining fully consistent with the standard probabilistic predictions of quantum mechanics and the Lorentz invariance of special relativity. The helical phase interpretation is intended as a conceptual and pedagogical complement to orthodox formalisms, offering physical intuition for otherwise abstract quantum structures without modifying their mathematical foundations. Thus, this work does not propose a modification of quantum theory, but offers a geometric interpretation of its formal structures aimed at clarifying their physical content.
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