A Three-Dimensional Ontological Formulation of Bohmian Mechanics

Area of Science:

• Quantum Mechanics
• Foundations of Physics

Background:

• Bohmian mechanics traditionally uses a high-dimensional configuration space.
• Interpreting the ontological status of the wave function remains a challenge.

Purpose of the Study:

• To develop a three-dimensional (3D) field ontology for Bohmian mechanics.
• To re-express Bohmian mechanics in terms of physically local, 3D wave functions.

Main Methods:

• Introducing single-particle wave functions in ordinary physical space as ontological elements.
• Interpreting the universal wave function as a nomological (law-like) entity governing field evolution.
• Deriving evolution equations for conditioned 3D wave functions from the standard Bohmian formalism.

Main Results:

• A novel 3D ontology for Bohmian mechanics is presented.
• The universal wave function's role is reinterpreted as nomological, not fundamental field.
• The theory remains empirically and predictively equivalent to the conventional formulation.

Conclusions:

• The proposed 3D ontology offers a spatially explicit framework for Bohmian mechanics.
• This formulation may enhance the interpretation, visualization, and pedagogical presentation of quantum theory.
• It provides a ψ-ontic perspective with dynamical fields defined on physical space.