Universality of Quantum Gravity Corrections

TL;DR

This paper explores how quantum gravity effects, predicted by the Generalized Uncertainty Principle, modify quantum phenomena like the Lamb Shift and Landau levels, providing potential experimental bounds on quantum gravity parameters.

Contribution

It demonstrates that quantum gravity corrections influence all quantum Hamiltonians and offers a way to test or constrain these effects through precise experiments.

Findings

Quantum gravity corrections affect quantum Hamiltonians.

Corrections are either too small or set bounds on quantum gravity parameters.

Future experiments could test these predictions or refine bounds.

Abstract

We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb Shift, the Landau levels and the tunnelling current in a Scanning Tunnelling Microscope (STM). We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the quantum gravity parameter in the GUP, compatible with experiments at the electroweak scale. Thus, more accurate measurements in the future should either be able to test these predictions, or further tighten the above bounds and predict an intermediate length scale, between the electroweak and the Planck scale.