Constructing and Constraining Wave Functions for Identical Quantum Particles

TL;DR

This paper explores how the symmetry properties of wave functions for identical particles can be derived within certain interpretations of quantum mechanics, rather than assumed, by properly formulating these theories.

Contribution

It demonstrates that the symmetry dichotomy of wave functions can be derived from the foundations of Bohmian and Newtonian quantum mechanics, not just postulated.

Findings

The symmetry dichotomy can be derived from proper formulations of Bohmian mechanics.

The symmetry dichotomy can be derived from proper formulations of Newtonian quantum mechanics.

Wave function symmetry need not be an ad hoc assumption in these interpretations.

Abstract

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.