Generalized Uncertainty Principle and Quantum Gravity Phenomenology

TL;DR

This paper explores the implications of the Generalized Uncertainty Principle for quantum systems, providing calculations of Planck-scale corrections and proposing experimental schemes to test quantum gravity effects in laboratory settings.

Contribution

It offers detailed computations of quantum corrections due to GUP and introduces experimental strategies to detect quantum gravity phenomena.

Findings

Planck-scale corrections to atomic and angular momentum spectra

Analysis of GUP-perturbed harmonic oscillator and new quantum states

Proposed optomechanical experiments to test quantum gravity effects

Abstract

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canon ical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.