  Now, if the only possible states of the system were    and    (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state  1 is impossible. For if  1 interacts with  3 then it will develop into  2, which, during time travel, will develop into  3, which inconsistent with the assumed state  3. Similarly if  1 interacts with  3 it will develop into  2, which will then develop into  3 which is also inconsistent. Thus the system can not start in state  1.