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We present a local-realistic description of both wave-particle duality andBohmian trajectories. Our approach is relativistic and based on Hamilton'sprinciple of classical mechanics, but departs from its standard setting in tworespects. First, we address an ensemble of extremal curves, the so-called Mayerfield, instead of focusing on a single extremal curve. Second, we assume thatthere is a scale, below which we can only probabilistically assess whichextremal curve in the ensemble is actually realized. The continuity equationruling the conservation of probability represents a subsidiary condition forHamilton's principle. As a consequence, the ensemble of extremals acquires adynamics that is ruled by Maxwell equations. These equations are thus shown toalso rule some non-electromagnetic phenomena. While particles followwell-defined trajectories, the field of extremals can display wave behavior.

Local-realistic Bohmian trajectories: a non-Bohmian approach to wave-particle duality