Abstract

The arguments presented by Gibbins in his Note are based on a sharp distinction between the product Δx·Δp, which refers to the ranges of position and momentum of an individual system, and the uncertainty principle ΔX·ΔP ≥ ħ/2, which expresses a statistical relation for an ensemble of systems. A critical role in Gibbins’ reasoning is played by the theorem T which states that the restriction of the dynamical variable of position x of an individual system to a finite range Δx excludes the possibility of restricting the canonically conjugate dynamical variable of momentum p to a finite range Δp.