Constructing and constraining wave functions for identical quantum particles

•The symmetry dichotomy is explained in Bohmian mechanics from the guidance equation.•A superior explanation is given in Newtonian quantum mechanics.•This explanation appeals to the non-fundamental nature of the wave function.•Both explanations are then recast in reduced configuration space.•Relevance to debates about the ontological status of the wave function is discussed.

I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which include particles following definite trajectories in addition to, or in lieu of, the wave function: Bohmian mechanics and Newtonian quantum mechanics (a.k.a. many interacting worlds). In both cases I argue that, if the interpretation is formulated properly, the symmetry dichotomy can be derived and need not be postulated.