An Ontological Interpretation of Photon Wave-Particle Duality via Complex-Space Trajectories

Abstract

Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum Hamilton Jacobi framework. In this approach, photon motion is represented by complex trajectories whose real projections describe propagation, while imaginary components encode oscillatory structure. We show that momentum eigenstates correspond to straight line trajectories with uniform propagation at the speed of light, whereas superposition states lead to nontrivial quantum potentials and oscillatory motion in the complex plane. Extending the analysis to complex two dimensional space reveals richer dynamical behavior, including propagating wave like trajectories and standing wave like patterns in real projections. Energy momentum consistency is verified through an internal coherence analysis based on projected standing wave wavelengths. Rather than introducing new dynamical laws or additional physical dimensions, the complex space is employed as an interpretational framework that renders wave like and particle like aspects as complementary projections of a single underlying motion. The results suggest a unified geometric perspective on wave particle duality, while remaining fully compatible with standard quantum mechanics.