A Three–Dimensional Ontological Formulation of Bohmian Mechanics

We present a three–dimensional field ontology for Bohmian mechanics in which the single-particle wave functions defined in ordinary physical space are taken as ontological elements alongside particle positions. In this view, each particle is associated with a wave function in three–dimensional space conditioned on the actual positions of the remaining particles. The universal wave function on configuration space is retained within the formalism, but its role is interpreted as nomological: it determines the coupled evolution of the three–dimensional fields without itself being treated as a fundamental physical field. The corresponding evolution equations for the conditioned three–dimensional wave functions follow from the standard Bohmian formalism and, together with the guidance equation, yield dynamics fully equivalent to those of the conventional theory. The empirical and predictive content of Bohmian mechanics is thereby preserved, while its ontological structure is expressed in explicitly three–dimensional terms. Within a $\psi$-ontic perspective, this proposal makes explicit an ontological organization of Bohmian mechanics in which the dynamical fields are defined on physical space. While fully equivalent to the conventional formulation, expressing the theory in these terms may facilitate interpretation, visualization, and pedagogical presentation.