 For concreteness, suppose that have a system whose observables include a position, \(x\), and momentum, \(p\), with respect to some frame of reference. There is a sense in which, for two distinct times, \(t\) and \(t'\), position at time \(t\) and position at time \(t'\) are distinct observables, and also a sense in which they are values, at different times, of the same observable. Once we have settled on operators \(\hat{X}\) and \(\hat{P}\) to represent position and momentum at time \(t\), we still have a choice of which operators represent the corresponding quantities at time \(t.\)  On the Schrödinger picture, the same operators \(\hat{X}\) and \(\hat{P}\) are used to represent position and momentum, whatever time is considered.  As the probabilities for results of experiments involving these quantities may be changing with time, different vectors must be used to represent the state at different times.