  If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state  3 or in state  3 prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state  1 in all worlds. In some of the many worlds the older system will be in the  3 state, let us call them A-worlds, and in some worlds, B-worlds, it will be in the  3 state. Thus in A-worlds after interaction we will have state  2 , and in B-worlds we will have state  2. During time travel the  2 state will remain the same, i.e., turn into state  3, but the systems in question will travel from A-worlds to B-worlds. Similarly the  2 states will travel from the B-worlds to the A-worlds, thus preserving consistency.