A Unified Geodesic Guidance Theory of Wave–Particle Duality

This paper presents a geometric reinterpretation of quantum mechanics that eliminates wave-particle duality. By deriving a single geometric law from the Schrödinger equation, the author argues that quantum entities—such as photons and electrons—always follow definite trajectories as particles, but are guided by a curvature field. Key features of this framework include: Geometric Guidance: Replacing the dual-description framework with a "curvature tube" derived from quantum amplitude, analogous to how spacetime curvature shapes geodesics in General Relativity. Unified Evolution Law: The construction of a dual-mode state tensor that replaces the standard wavefunction and eliminates the need for the collapse postulate. Deterministic Results: Reproducing standard quantum phenomena through covariant conservation laws, with classical mechanics emerging as the limit where. Experimental Validation: The model is applied to six core scenarios, including double-slit interference, quantum tunnelling, and the Aharonov-Bohm effect. The text also provides comparative analyses with Bohmian mechanics, general relativity, and quantum field theory.