A framework for nonrelativistic isotropic models based on generalized uncertainty principles

TL;DR

This paper develops a unified theoretical framework for isotropic generalized uncertainty principles in nonrelativistic quantum mechanics, enabling systematic analysis of quantum gravity effects related to a fundamental length scale.

Contribution

It introduces a minimal assumptions-based framework that encompasses various GUP models and translates experimental bounds into this unified context.

Findings

Unified framework for isotropic GUP models

Analysis of popular GUP models within the framework

Bounds on GUP parameters derived from current experiments

Abstract

The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so called generalized uncertainty principles (GUP). In this work we provide such framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show simple dimensional analysis allows for building a unified framework containing any isotropic generalized uncertainty principle (iGUP) and discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such unified iGUP framework.