An examination of the limitations placed by the conceptual structure of quantum mechanics on the simultaneous measurement of two or more observables leads, for the case of an even number $m=2k$ of observables, to a quantitative estimate, depending only on the mean values of their commutators in the state in question, of the least value which the product of their $m$ uncertanties may assume. This indeterminacy relation is interpreted classically to mean that, by measurement of these observables alone, a point ($p, q$) in phase space can be determined only to within a certain channel whose normal cross section, as measured by the value of the $k\mathrm{th}$ integral invariant taken over it, must be at least of order $h^k$.

• Received 10 September 1934

DOI:https://doi.org/10.1103/PhysRev.46.794