Planck scale effects on some low energy quantum phenomena

TL;DR

This paper explores how Planck scale modifications to quantum mechanics, predicted by quantum gravity theories, can influence low-energy phenomena like superconductivity, quantum Hall effect, and muon magnetic moments, providing empirical bounds on quantum gravity effects.

Contribution

It applies the Generalized Uncertainty Principle to low-energy quantum phenomena and derives potential observable effects and bounds from current experiments.

Findings

Planck scale corrections affect superconductivity and quantum Hall effect.

Possible contribution to the anomalous magnetic moment of the muon.

Empirical bounds on GUP parameters from existing experiments.

Abstract

Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.