Year: 2025
Type: article
Abstract: We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width Δx or a geodesic ball of radius R. Using Hermitian momentum operators consistent with the EUP algebra, we prove a sharp lower bound on the product of momentum spread and preparation size in one dimension and show that it reduces smoothly to the standard quantum limit as the deformation vanishes. We then extend the construction to dimensions two and three on spaces of constant curvature and obtain the corresponding bound for spherical confinement, clarifying its geometric meaning via an isometry to S2 and S3. The framework links curvature-scale effects to operational momentum floors and suggests concrete tests in diffraction, cold-atom, and optomechanical settings.
Source: Foundations
Author: Thomas Schürmann
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W4413893154