The Generalized Uncertainty Principle and Quantum Gravity Phenomenology

TL;DR

This paper explores a modified uncertainty principle incorporating linear and quadratic momentum terms, affecting quantum Hamiltonians and suggesting space may be fundamentally discrete, with potential observable consequences.

Contribution

It introduces a generalized uncertainty principle with new terms and analyzes its implications for quantum Hamiltonians and the nature of space at fundamental levels.

Findings

Modified Hamiltonians due to the generalized uncertainty principle

Potential observational signatures in low energy experiments

Indication of space discreteness at fundamental scales

Abstract

In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this affects all Hamiltonians, and in particular those which describe low energy experiments. We discuss possible observational consequences. Further, we also show that this indicates that space may be discrete at the fundamental level.