A dynamic programming interpretation of quantum mechanics

We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\logρ$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as stochastic Hamilton-Jacobi-Bellman equations. The system of equations provide a local description of quantum mechanics, which is enabled by the inherently retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also investigate the stochastic transformation of the classical system, where is it shown that quantum mechanics with the quantum potential reduced by a factor of $\frac{1}{2}$ has a classical representation, which may have interesting implications. Finally, we discuss the notion of a subsystem correspondence principle, which constrains the ontology of the total quantum system.

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