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.

Black hole corrections due to minimal length and modified dispersion relation

“…• Secondly, we revise the physical concept of the higher order GUP in the momentum space and give the maximum momentum measurable at the uncertainty of minimal length, which apparently agrees with the predication of Double special relativity (DSR) [21] and Hilbert space [4,5] and other results estimated from the different behaviors given in section (VI).…”

“…The latter one was introduced by Doubly Special Relativity (DSR). DSR suggests minimal uncertainty in position and maximum measurable momentum [4,5,[20][21][22][23]. Furthermore, DSR gives a linear combination of the last two approaches and amazingly agrees well with the predications of string theory, black hole physics and Loop quantum gravity.…”

“…The uncharged black holes are of de-Sitter-Schwarzschild-type, while the charged ones can be characterized by Reissner -Nordström metric. There are various quantum gravity approaches designed to study the quantum description of some problems in presence of gravitational fields [4,5]. We limit the discussion to the effects of minimal length and/or maximal momentum which are likely applicable at Planck scale which lead to modifications in Heisenberg uncertainty principle in form of quadratic and/or linear terms of momentum.…”

“…Accordingly, a minimum measurable length and a maximum measurable momentum [24][25][26] are simultaneously likely. This offers a major revision of quantum phenomena [4,5,[27][28][29]. These approaches have the genetic name, Generalized (gravitational) Uncertainty Principle (GUP).…”

Bouncing universe with modified dispersion relation

“…The forms of the modified dispersion relation (MDR) and ones of GUP can be viewed as the alternative mechanisms to handle the black hole problems, such as the singularity, the "thermodynamics", the evaporation and the "information paradox" and so on. In the recent years, the implication and application of the effects of quantum gravity have attracted a great deal of attentions ( for recent reviews we refer to [33][34][35] ).…”