Remarks on Uncertainty Principles

Abstract

Since the publication of Heisenberg’s paper¹ on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality,

$$ \Delta p\Delta q>\frac{h}{{2\pi}} $$

((1))

This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.