Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation

TL;DR

This paper explores how deformed quantum commutation relations, inspired by string theory, affect classical particle orbits and uses observational data to constrain the minimal length scale implied by these relations.

Contribution

It analyzes the classical implications of minimal length uncertainty relations derived from deformed commutation relations, linking quantum string-inspired concepts to observable classical phenomena.

Findings

Severe constraints on the minimal length scale from classical orbit observations

Deformed commutation relations influence classical particle trajectories

Results limit the possible size of the minimal length in quantum gravity theories

Abstract

We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.