Several comments are in order. First, the projective decompositions of the identity at different times need not be the same. Thus for a spin half particle one could have the \(S_z=\pm 1/2\) decomposition at one time and the \(S_x=\pm 1/2\) decomposition at some later time. And more complicated history-dependent decompositions of \(\breve I\) are possible; see the  Further Reading supplement. Griffiths (2002a). --> Second, there is no reference to measurements. Events occur or do not occur; whether a measuring apparatus is involved is entirely irrelevant, although histories can be used to discuss what goes on in a measuring process; see section 7. Third, the projectors in a history can be coarse-grained and specify only a small amount of information, e.g., the spin degree of freedom of an atom without reference to its position; they do not and generally will not project onto pure states. Fourth, there is no direct connection between the choice of projectors entering a history and Schrödinger’s time-dependent equation, although in appropriate circumstances the latter can be used to assign probabilities to the different histories in a family, as discussed next.