A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structures aimed at clarifying their physical content.
A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structuresaimed at clarifying their physical content.
This work develops a relational helical formulation of quantum mechanics in which the complex structure of the wavefunction acquires a concrete geometric interpretation. The imaginary unit i is identified as the generator of helical transport across a foliation of discrete hypersurfaces, transforming quantum phase into an angular coordinate and amplitude into a radial coordinate on a logarithmic spiral. Within this framework, standard quantum mechanics emerges as the projection of a deeper helical symmetry, revealing that its complex structure already encodes an intrinsic relativistic geometry. Building on this foundation, the construction incorporates a spiral mass equation, a modified ER-analogue metric, and a hypersurface-discrete spacetime, yielding a relational Hilbert- bundle structure governed by a least-action principle defined between layers. The resulting dual gravitational system, combining geometric (spiral) and energetic (mass/curvature) components, introduces canonical variables such as the spiral pitch a(λ) and the helical connection A(λ,x), each admitting well-defined conjugate momenta. These variables satisfy canonical commutation relations and form the operator algebra required for a quantum-gravity-like dynamics. The string-length postulate, identifying hypersurface circumferences as fundamental geometric quanta, further discretizes the underlying geometry. Together, these elements constitute a coherent proto-quantum-gravity framework in which the conceptual tension between quantum mechanics and relativity is dissolved, and the quantization of geometric degrees of freedom arises organically from the relational helical structure.