# Change of basis in the many worlds interpretation?

Say we have two orthogonal states $$|A\rangle$$ and $$|B\rangle$$. In the many worlds interpretation, we can imagine two parallel universes in which we are either in state $$A$$ or $$B$$.

But now if we change the basis so that we have:

$$|C\rangle = \frac{1}{\sqrt{2}}(|A\rangle+|B\rangle)$$ and $$|D\rangle = \frac{1}{\sqrt{2}}(|A\rangle-|B\rangle)$$

It seems we have to then adjust our interpretation of the parallel universes. The only way out of seems to be if the universes $$A$$ and $$B$$ correspond to a universe with person with a brain beleiving or disbelieving a true/false statement. Since one cannot both believe something is true and false. But then don't we arrive back at the copenhegen interpretation with an observer collapsing a wave function?

• There seem to be three unrelated ideas here: (1) the phase relationship between A and B (which ends up being irrelevant because of decoherence), (2) the preferred basis problem, and (3) the fact that an observer can't consciously experience the fact of being in a superposition of states. One could certainly draw connections among these ideas, but it's not obvious to me from reading the question what connection you have in mind. – user4552 Jun 18 '19 at 13:30