Non-Quantum Behaviors of Configuration-Space Density Formulations of quantum mechanics

The trajectories of the pilot-wave formulation of quantum mechanics and hence its empirical predictions may be recovered via the dynamics of a density function on the configuration space of a system, without reference to a physical wave function. We label such formulations `CSD frameworks.' But this result only holds if a particular, apparently ad hoc condition, broadly speaking equivalent to the single-valuedness of the wave function in standard quantum mechanics, is imposed. Here we relax this condition. We describe the types of scenarios in which this would lead to deviations from quantum mechanics. Using computational models we ask how the degree of `non-quantumness' of a state, suitably defined, changes with time. We find that it remains constant in time even under non-trivial dynamics, and argue that this implies that a dynamical justification of the Wallstrom condition is unlikely to be successful. However, we also make certain observations about stationary states in CSD frameworks, which may offer a way forward in justifying the Wallstrom condition.