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.
In this study, I argue that the future is not open if quantum mechanics is complete. An open future means that the value observed when measuring a physical quantity in the future is not determined. At first glance, quantum mechanics seems to support the open future thesis, because it cannot always predict measurement value with certainty. However, many interpretations regard quantum mechanics as deterministic. These interpretations only suggest that the quantum mechanical world can be deterministic. I argue that, although quantum mechanics cannot predict the future with certainty, the quantum mechanical world must bedeterministic, and the value observed by the observer is determined. I examine the following two cases: (1) the wave-function completely describes the physical state and (2) the wave-function does not describe the physical state. Then, I argue that the future cannot be open in either case when quantum mechanics is complete.