Review on Generalized Uncertainty Principle

Abstract

Based on string theory, black hole physics, doubly special relativity and some "thought" experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified dispersion relation, the space noncommutativity, the Lorentz invariance violation, and the quantum-gravity-induced birefringence effects are summarized. The origin of minimal measurable quantities and the different GUP approaches are reviewed and the corresponding observations are analysed. Bounds on the GUP parameter are discussed and implemented in understanding recent PLANCK observations on the cosmic inflation. The higher-order GUP approaches predict minimal length uncertainty with and without maximum momenta.

37 pages, 3 figures and 2 tables, an invited review for Reports on Progress in Physics (ROPP). arXiv admin note: substantial text overlap with arXiv:1410.0206

References in corpus (18)

• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• General Very Special Relativity is Finsler Geometry
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Minimal Length Uncertainty Relation and gravitational quantum well
• Noncommutative Inspired Black Holes in Extra Dimensions
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• Short-range gravity and Lorentz violation
• Minimal Length and Bouncing Particle Spectrum
• Corrections to entropy and thermodynamics of charged black hole using generalized uncertainty principle
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Thermodynamics of an Evaporating Schwarzschild Black Hole in Noncommutative Space
• Quantum gravity, minimum length and Keplerian orbits
• Effects of the Generalized Uncertainty Principle on Compact Stars
• Is the Equivalence Principle violated by Generalized Uncertainty Principles and Holography in a brane-world?
• Modified clock inequalities and modified black hole lifetime
• Newton's Law Modifications due to a Sol Manifold Extra Dimensional Space

Cited by in corpus (71)

• Challenges for $\Lambda$CDM: An update
• Investigating the Connection between Generalized Uncertainty Principle and Asymptotically Safe Gravity in Black Hole Signatures through Shadow and Quasinormal Modes
• Generalised uncertainty relations from superpositions of geometries
• Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
• The Effect of GUP to Massive Vector and Scalar Particles Tunneling From a Warped DGP Gravity Black Hole
• Cosmological constraints on the Generalized Uncertainty Principle from modified Friedmann equations
• Generalised uncertainty relations for angular momentum and spin in quantum geometry
• Nonclassicality versus entanglement in a noncommutative space
• Near horizon thermodynamics of hairy black holes from gravitational decoupling
• Quantum theory of the Generalised Uncertainty Principle
• Uncertainty Relations for coarse-grained measurements: an overview
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Dark Energy within the Generalized Uncertainty Principle in Light of DESI DR2
• The minimum mass of a charged spherically symmetric object in $D$ dimensions, its implications for fundamental particles, and holography
• GUP black hole remnants in quadratic gravity
• Gravitational bending angle with finite distances by Casimir wormholes
• A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations
• New higher-order generalized uncertainty principle: Applications
• Generalized Uncertainty Principle and Black Holes in Higher Dimensional Self-Complete Gravity
• The GUP effect on tunnelling of massive vector bosons from the 2+1 dimensional black hole
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Eruptive Massive Vector Particles of 5-Dimensional Kerr-Gödel Spacetime
• Unveiling Phase Space Modifications: A Clash of Modified Gravity and the Generalized Uncertainty Principle
• Consequences of Minimal Length Discretization on Line Element, Metric Tensor and Geodesic Equation
• Dispersion relations in finite-boost DSR
• Generalized Extended Momentum Operator
• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
• Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method
• Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)
• The effect of modified dispersion relations on the thermodynamics of Schwarzschild black hole surrounded by quintessence
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• A new mass scale, implications on black hole evaporation and holography
• Testing Short Distance Anisotropy in Space
• Schwinger's Model of Angular Momentum with GUP
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Generalized entropic gravity from modified Unruh temperature
• Quantum oscillations in the black hole horizon
• Exotic fermionic fields and minimal length
• Generalised Uncertainty Relations from Finite-Accuracy Measurements
• Generalized Uncertainty principle and momentum-dependent effective mass Schrodinger equation
• Generalized uncertainty principle in quantum cosmology for the maximally symmetric space
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• Nonlinear Schrödinger equation from generalized exact uncertainty principle
• Another look on the connections of Hubble tension with the Heisenberg Uncertainty Principle
• Radial Oscillations and Dynamical Instability Analysis for Linear-Quadratic GUP-modified White Dwarfs
• On the algebraic approach to GUP in anisotropic space
• A minimal Length Uncertainty Approach to Cosmological Constant Problem
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Covariant Predictions for Planck-Scale Features in Primordial Power Spectra
• Removing the divergence of Chandrasekhar limit caused by generalized uncertainty principle
• Noisy effects in interferometric quantum gravity tests
• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• Problems with Modified Commutators
• Fractal properties of particle paths due to generalised uncertainty relations
• Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics
• Remarks on the quasi-position representation in models of generalized uncertainty principle
• Towards a Quantum Erlangen Program
• Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory
• The Derivation of Phase-Space Metric in a Geometric Quantization Approach: General Relativity with Quantized Phase-Space Metric and Relative Spacetime
• From minimal-length quantum theory to modified gravity
• Non-local imprints of gravity on quantum theory
• Relativistic generalised uncertainty and the corrected vacuum energy
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• Generalized imaginary units in quantum mechanics
• An algebraic approach to gravitational quantum mechanics
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Probing Planck scale effects on absolute mass limit in neutrino flavor evolution
• Quantum geometry from commutators: a Heisenberg-picture framework and a toy application to early structure