Determine the dynamics of the Schrödinger source field

Determine whether the complex Schrödinger source field J(x,t) should obey a classical, quantum, or subquantum dynamical law, and formulate such a law if appropriate.

Background

The framework treats J(x,t) as an external complex scalar field that generates the pilot-wave field through the inhomogeneous Schrödinger equation. Unlike the wavefunction and particle distribution, J is not assigned an evolution equation and does not receive back-reaction from the system. A complete ontological theory therefore requires determining the physical status and autonomous dynamics of the source field.

References

Whether the dynamics of $J$ is ultimately classical, quantum, or subquantum is a question we leave open; a future theory may supply its equations of motion.

— de Broglie-Bohm Dynamics with Schrödinger Source Fields: A Framework for Subquantum Theory  (2608.13894 - Mikki, 14 Aug 2026) in Section 'The Extended Ontology: Three Fundamental Fields'

Whether the nonlinearity of~eq:nonlinear_schrodinger permits or suppresses specific quantum features such as long-range interference or superposition is a dynamical question that depends on the initial conditions and the self-consistent solution of the nonlinear equation.

— de Broglie-Bohm Dynamics with Schrödinger Source Fields: A Framework for Subquantum Theory  (2608.13894 - Mikki, 14 Aug 2026) in Section 5.2, 'Exact Cancellation of the Quantum Potential: Classicalization via the Source'; footnote in Section 5.3

The deterministic source term may be related to stochastic modifications of quantum mechanics; clarifying whether collapse dynamics can be recovered as a limit of source-driven evolution would connect the present framework to existing approaches to the measurement problem.

— de Broglie-Bohm Dynamics with Schrödinger Source Fields: A Framework for Subquantum Theory  (2608.13894 - Mikki, 14 Aug 2026) in Section 'Future Directions', subsection 'Relation to stochastic collapse models'

Can $J$ be understood as an effective description of an underlying classical or subquantum dynamics, in the sense that the Navier-Stokes equations emerge from kinetic theory?

— de Broglie-Bohm Dynamics with Schrödinger Source Fields: A Framework for Subquantum Theory  (2608.13894 - Mikki, 14 Aug 2026) in Section 'Future Directions', subsection 'Derivation from a deeper theory'