 In any case there is no need to set \(\ket{w^j}\) equal to \(\ket{s^j}\) in order to discuss quantum measurements, and a better way of viewing the family \(\FC_p\) in \eqref{eqn27} is as a model of a quantum preparation process in which the macroscopic pointer position tells one the future rather than the past state of the particle. The conditional probability in \eqref{eqn29} refers specifically to properties at the time \(t_2\), but given the assumption that \(T(t',t)\) is trivial for times after \(t_2\), the argument leading to \eqref{eqn29} is easily extended to \([v^l]\) and \([m^j]\) at any times (not necessarily the same) later than \(t_2\). In general the outcome \([m^j]\) is random, and if the wrong \(j\) occurs \(\ket{w^j}\) may not be the desired state.  But then the preparer can throw the particle away (run it into a baffle) and repeat the experiment until the desired outcome occurs. There are more sophisticated ways to do preparations, but our model illustrates the general idea, and in fact discarding unwanted outcomes is a procedure often used in quantum optics.  The essential point is that an apparatus can be constructed using quantum principles to prepare a particle whose future state is known on the basis of macroscopic (pointer) information.