Experimental Verification of the Minimal Length Hypothesis

Determine an experimental verification of the existence of a minimal spatial length predicted by generalized uncertainty principles and the deformed Heisenberg algebra characterized by deformation parameters β and β′, by identifying and conducting empirical tests that can confirm or refute such a minimal length in nature.

Background

The paper studies classical Keplerian scattering and gravitational lensing under a deformed Heisenberg algebra that implies a minimal spatial length, a concept motivated by quantum gravity and generalized uncertainty principles. While numerous theoretical works explore minimal-length effects across systems, a decisive experimental test has not yet been established.

Here, the authors derive corrections to scattering angles using the precession of the Hamilton vector and argue that minimal-length effects reduce gravitational deflection, including for photons. They use Einstein ring observations to place bounds on deformation parameters, but emphasize that a direct experimental verification of the minimal length hypothesis is still lacking.