  Suppose that we have a system \(S\) and a device \(S^*\) which measures an observable \(A\) on \(S\) with values \(\{a_1, a_2, a_3, ...\}\). Then there is some state of \(S^*\) (the ‘ground state’), and some observable \(B\) with values \(\{b_1, b_2, b_3, ...\}\) pertaining to \(S^*\) (its ‘pointer observable’, so called because it is whatever plays the role of the pointer on a dial on the front of a schematic measuring instrument in registering the result of the experiment), which are such that, if \(S^*\) is started in its ground state and interacts in an appropriate way with \(S\), and if the value of \(A\) immediately before the interaction is \(a_1\), then \(B\)’s value immediately thereafter is \(b_1\). If, however, \(A\)’s value immediately before the interaction is \(a_2\), then \(B\)’s value afterwards is \(b_2\); if the value of \(A\) immediately before the interaction is \(a_3\), then \(B\)’s value immediately after is \(b_3\), and so on. That is just what it means to say that \(S^*\) measures \(A\). So, if we represent the joint, partial state of \(S\) and \(S^*\) (just the part of it which specifies the value of [\(A\) on \(S\) &amp; \(B\) on \(S^*\)], the observable whose values correspond to joint assignments of values to the measured observable on \(S\) and the pointer observable on \(S^*\)) by the vector \(\ket{A=a_i}_s \ket{B=b_i}_{s^*}\), and let “\(\rightarrow\)” stand in for the dynamical description of the interaction between the two, to say that \(S^*\) is a measuring instrument for \(A\) is to say that the dynamical laws entail that,