Generalized Uncertainty Principle: Approaches and Applications

Abstract

We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which are designed to implement the minimal length scale and/or the maximum momentum in different physical systems are analysed entered the literature as the Generalized Uncertainty Principle (GUP). We compare between them. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. Furthermore, assuming modified dispersion relation allows for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker-Wigner inequalities, entropic nature of the gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. Another one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.

Invited Review Article to appear in International Journal of Modern Physics D, 151 pages, 16 figures with 20 eps-graphs. arXiv admin note: text overlap with arXiv:1403.5319, arXiv:0910.2808, arXiv:1205.0158 by other authors

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• Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
• Quantum Tunneling of Massive Spin-1 Particles From Non-stationary Metrics
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• Upper bound on the GUP parameter using the black hole shadow
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• PV criticality of Achucarro-Ortiz black hole in the presence of higher order quantum and GUP corrections
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• Observational Tests of the Generalized Uncertainty Principle: Shapiro Time Delay, Gravitational Redshift, and Geodetic Precession
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• Type V singularities in non-standard cosmological backgrounds
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• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
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• Uncertainty Principles and Non-local Black Holes
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• Relativistic generalised uncertainty and the corrected vacuum energy
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• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• Compactification, T-Duality and Quantum Erasers
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