Generalized Uncertainty Principle: Approaches and Applications

Abdel Nasser Tawfik (Egyptian Ctr. Theor. Phys., Cairo, WLCAPP, Cairo), Abdel Magied Diab (WLCAPP, Cairo)

(Submitted on 29 Sep 2014)

http://arxiv.org/abs/1410.0206

We review some highlights from the String theory, the black hole physics and the doubly special relativity and some thought experiments which were suggested to probe the shortest distances and/or maximum momentum at the Planck scale. Furthermore, all models developed in order to implement the minimal length scale and/or the maximum momentum in different physical systems are analysed. We compare between them. They entered the literature as the Generalized Uncertainty Principle (GUP) assuming modified dispersion relation, and therefore are allowed 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 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. A second 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 existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. 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.

Comments:	An invited Review to appear in the International Journal of Modern Physics D, 159 pages, 16 figures with 20 eps-graphs. arXiv admin note: text overlap with arXiv:0906.2108, arXiv:1403.5319, arXiv:1205.0158, arXiv:0811.0212,arXiv:1110.5550, arXiv:hep-th/9412167, arXiv:1005.2996, arXiv:1303.1256, arXiv:1110.2999, arXiv:1203.6191,arXiv:hep-th/9404123, arXiv:astro-ph/0406514, arXiv:hep-th/9904025 by other authors
Subjects:	General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
Report number:	ECTP-2013-09b, WLCAPP-2013-06b
Cite as:	arXiv:1410.0206 [gr-qc]
	(or arXiv:1410.0206v1 [gr-qc] for this version)