Abstract: Commutators and uncertainty relations have sparked much debate and confusion as to their physical meaning. As such, this chapter focuses partly on historical and interpretational aspects. Because it is central to the uncertainty relations, the commutator — including its manifestation in matrix mechanics — is introduced first. It is emphasized that the commutator of two operators is generally another operator. The general form of the uncertainty relations is then introduced. These relations reflect the fact that probability distributions for different observables are generally not independent. Moreover, application of the uncertainty relations generally requires knowledge of the quantum state — a fact that is obscured by the well known position-momentum uncertainty relation. Various proposed physical interpretations of the uncertainty relations are then discussed. The chapter concludes with a brief reflection on the significance of the uncertainty relations.

Keywords: matrix mechanics, observable, probability distribution, interpretation,