The Scalar Field Extension of Bohmian Mechanics: An Effective Field Theory with Laboratory-Testable Predictions

We propose a minimal effective field theory extension of Bohmian mechanics via a weak real Lorentz-scalar field φ coupled to the Dirac bilinear ψ-barψ through a strictly dimensionless Yukawa coupling g. In the non-relativistic limit this adds a classical term gφ (x) directly to the Bohmian quantum potential, Qₑff = Q + gφ (x). The model is fully relativistic, Lagrangian-based, and observationally equivalent to standard quantum mechanics plus a classical Yukawa fifth force. The paper derives the field equations, exact sourced scalar field, conservation laws, and realistic laboratory predictions for atom/neutron interferometry (μeV benchmark) and Casimir forces (meV benchmark). Current bounds already constrain |g| ≲ 10^-12–10^-15; next-generation experiments can test the predictions. This construction — giving the quantum potential an explicit hidden-sector scalar origin while remaining fully testable by existing fifth-force searches — is original and has not appeared in the literature.