2011/12/05 by Martin Bojowald, Achim Kempf · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Epistemology #GRASP #Mathematics #Noncommutative and Quantum Gravity Theories #Phenomenology (philosophy) #Physics #Quantum #Quantum Mechanics and Applications #Quantum gravity #Quantum mechanics #Space (punctuation) #Statistical physics #Theoretical physics #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.86.085017
published as Phys. Rev. D 86 (2012) 085017 · 26 pages
arxiv created 2011/12/05 · openalex publication_date 2012/10/08 · arxiv updated 2015/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on nontrivial space-time structures such as a fundamental discreteness of space, a universal band limit or an irreducible extendedness of elementary particles. In this article, uncertainty relations for single-particle quantum mechanics are derived by a moment expansion of states for quantum systems with a discrete coordinate and, correspondingly, a periodic momentum. Corrections to standard uncertainty relations are found, with some similarities but also key differences to what is often assumed in this context. The relations provided can be applied to discrete models of matter or space-time, including loop quantum cosmology.