  Now, it follows from (3.1), above, that there are states of \(S\) (too many to count) which are not eigenstates of \(A\), and if we consider what Schrödinger’s equation tells us about the joint evolution of \(S\) and \(S^*\) when \(S\) is started out in one of these, we find that the state of the pair after interaction is a superposition of eigenstates of [\(A\) on \(S\) &amp; \(B\) on \(S^*\)]. It doesn’t matter what observable on \(S\) is being measured, and it doesn’t matter what particular superposition \(S\) starts out in; when it is fed into a measuring instrument for that observable, if the interaction is correctly described by Schrödinger’s equation, it follows just from the linearity of the \(U\) in that equation, the operator that effects the transformation from the earlier to the later state of the pair, that the joint state of \(S\) and the apparatus after the interaction is a superposition of eigenstates of this observable on the joint system.