The symmetries of the wavefunction for identical particles, including anyons, are given a rigorous non-relativistic generalisation within pilot-wave formulations of quantum mechanics. In particular, parastatistics are excluded. The result has a rigorous generalisation to _n_ particles and to spinorial wavefunctions. The relation to other non-relativistic approaches is briefly discussed.

Many phenomena in the world display a striking time-asymmetry: the forwards transition frequencies are approximately invariant while the backwards ones are not. I argue in this paper that theories of such phenomena will entail that time has a direction, and that quantum mechanics in particular entails that the future is objectively different from the past.