Minimal Length Scale Scenarios for Quantum Gravity

Abstract

We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.

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] ).…”

The Geometry of Noncommutative Spacetimes

“…Most of them are connected with some quantum gravity theory and founded on the postulate that there exists a fundamental length-scale in Nature, which is of the order of Planck length λ P ∼ Ghc −3 1/2 ≈ 1.6 × 10 −35 m (see, for instance, [14] for a comprehensive review).…”

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

“…Furthermore, it has been generalized to describe a minimal length as a minimal uncertainty in position measurement [14]- [18] through the modification of Heisenberg commutation relation into a generalized form. The existence of a minimal length has long been suggested in quantum gravity and string theory [19]- [24], and has been proposed to describe, as an effective theory, non-point like particles like hadrons, quasi-particles or collective excitations [25]. In its original formulation, HUP is expressed in terms of variances of position and momentum of a particle.…”