A thought experiment in many worlds

The many-worlds interpretation of quantum mechanics (MWI) is based on three key assumptions: (1) the completeness of the physical description by means of the wave function, (2) the linearity of the dynamics for the wave function, and (3) multiplicity. In this paper, I propose a new thought experiment in which a post-measurement superposition undergoes no net change while individual branches do change under certain unitary time evolution. Moreover, I argue that MWI gives contradictory predictions for this experiment. In order to avoid the contradiction and save many worlds, it seems that we must drop one or both of the first two assumptions