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 (GUP). 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 $\beta$, classifying them on the basis of the degree of rigour in their derivation and reconsidering the ones subject to problems associated with composites.

38 pages. Accepted for publication in Classical and Quantum Gravity, "Special Issue: Focus on Quantum Gravity Phenomenology in the Multi-Messenger Era: Challenges and Perspectives"

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Cited by in corpus (32)

• $\alpha$-attractor inflation modified by GUP in light of ACT observations
• Kaniadakis entropy in extreme gravitational and cosmological environments: a review on the state-of-the-art and future prospects
• Black hole interior quantization: a minimal uncertainty approach
• Unveiling Phase Space Modifications: A Clash of Modified Gravity and the Generalized Uncertainty Principle
• Constraining Snyder and GUP models with low-mass stars
• A generalized uncertainty-inspired quantum black hole
• n-dimensional non-commutative GUP quantization and application to the Bianchi I model
• Challenging $\Lambda$CDM with Higher-Order GUP Corrections
• Extended Uncertainty Principle: A Deeper Insight into the Hubble Tension?
• Generalized Uncertainty Principle theories and their classical interpretation
• Expectation value dynamics within real Hilbert space quantum mechanics
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Minimal-length quantum field theory: a first-principle approach
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
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• Product Entropic Uncertainty Principle
• Einstein crystals in Snyder and Snyder-de Sitter noncommutative backgrounds