A note on the uncertainty principle

Peter Gibbins

It is shown that the uncertainty principle has nothing directly to do with the non-localisability of position and momentum for an individual system on the quantum logical view. The product Δx·Δp for localisation of the ranges of position and momentum of an individual system → ∞, while the quantities ΔX and ΔP in the uncertainty principle ΔX·ΔP ≥ ħ/2, must be given a statistical interpretation on the quantum logical view.

A. Gamba

Max Jammer

The arguments presented by Gibbins (1981) 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.

Steven Matthysse

P Marquardt, G. Galeczki

R. C. Harney

The concept of the uncertainty principle that position and momentum cannot be simultaneously specified to arbitrary accuracy is somewhat difficult to reconcile with experience. This note describes order-of-magnitude calculations which quantify the inadequacy of human perception with regards to direct observation of the breakdown of the trajectory concept implied by the uncertainty principle. Even with the best optical microscope, human vision is inadequate by three orders of magnitude. 1 figure. (RWR)