Why Quantum Measurements Yield Single Values

Abstract

It is shown that the Born Rule probabilities, i.e. the squares of the moduli of the coefficients in a pure state superposition, refer to mutually exclusive events consequent on measurement. It is also shown that the eigenstates in a pure state superposition are not mutually exclusive events. If the Born Rule is to be retained as the fundamental interpretative postulate of quantum mechanics then it follows, firstly, that the probabilities necessarily refer not to the eigenstates but to the eigenvalues to which the eigenstates belong and, secondly, that the eigenvalues are necessarily mutually exclusive events. This means that to ask why a measurement of an observable on a system in a pure state superposition of eigenstates yields a single state rather than all the states in the superposition is to ill-pose the quantum measurement problem. The events the Born Rule probabilities properly refer to are not states but values. And it also means that the correctly-posed measurement problem, why does a measurement of an observable in a pure state superposition of the eigenstates of the observable yield a single eigenvalue rather than all the eigenvalues implicit in the superposition, admits of the answer: the values, being mutually exclusive events, constitute a statistical mixture of values, and as such, a measurement will yield just one of them.