 Indeed, as pointed out already by von Neumann (1932, Section VI.3), one cannot reproduce the correct probabilities by assuming that they arise because we are ignorant of the exact state of a macroscopic apparatus. But whatever the exact initial state of the apparatus, if the system (say, an electron) is described by a superposition of two given states, say, spin in \(x\)-direction equal \(+\frac{1}{2}\) and spin in \(x\)-direction equal \(-\frac{1}{2}\), and we let it interact with a measuring apparatus that couples to these states, the final quantum state of the composite will be a sum of two components, one in which the apparatus has coupled to (has registered) \(x\)-spin \(= +\frac{1}{2}\), and one in which the apparatus has coupled to (has registered) \(x\)-spin \(= -\frac{1}{2}\).[13]  This is the measurement problem in the narrow sense of the term. 