What does this equation mean?

There is a fifth kind of answer to “where,” and it is worth stating precisely how it differs from all four above before using it. Prepare a system in a state |$\psi$$\rangle$ , couple it weakly to a pointer, and then postselect on a final state |f$\rangle$ measured after the coupling. The weak value of any observable $\hat A$ , position among them, conditioned on that postselection is $A_w = \frac{\langle f|\hat A|\psi\rangle}{\langle f|\psi\rangle}$. introduced by Aharonov, Albert, and Vaidman as the quantity a weakly coupled pointer’s mean shift actually reports, to leading order in the coupling strength, once the postselection has been performed [ 11 ] . $A_w$ is not an eigenvalue of $\hat A$ , not an expectation value in the ordinary sense, and not guaranteed to be real: it is built from an amplitude ratio over a sub-ensemble selected by an event, the postselection, that has not yet happened at the time the weak coupling acts.