30 years in: Quo vadis generalized uncertainty principle?

Abstract

According to a number of arguments in quantum gravity, both model-dependent and model-independent, Heisenberg's uncertainty principle is modified when approaching the Planck scale. This deformation is attributed to the existence of a minimal length. The ensuing models have found entry into the literature under the term generalized uncertainty principle. In this work, we discuss several conceptual shortcomings of the underlying framework and critically review recent developments in the field. In particular, we touch upon the issues of relativistic and field theoretical generalizations, the classical limit and the application to composite systems. Furthermore, we comment on subtleties involving the use of heuristic arguments instead of explicit calculations. Finally, we present an extensive list of constraints on the model parameter β, classifying them on the basis of the degree of rigor in their derivation and reconsidering the ones subject to problems associated with composites.

The authors acknowledge networking support by the COST Action CA18108. G G L is grateful to the Spanish ‘Ministerio de Universidades’ for the awarded Maria Zambrano fellowship and funding received from the European Union—NextGenerationEU. L P acknowledges support by MUR (Ministero dell‘Universit`a e della Ricerca) via the Project PRIN 2017 ‘Taming complexity via QUantum Strategies: a Hybrid Integrated Photonic approach’ (QUSHIP) Id. 2017SRNBRK and is grateful to the ‘Angelo Della Riccia’ foundation for the awarded fellowship received to support the study at Universität Ulm.