Discreteness of space from the generalized uncertainty principle

Ahmed Farag Ali,Saurya Das,Elias C Vagenas

doi:10.1016/j.physletb.2009.06.061

Ahmed Farag Ali, Saurya Das + Show 1 more

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https://doi.org/10.1016/j.physletb.2009.06.061

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Journal: Physics Letters B	Publication Date: Jul 3, 2009
Citations: 486	License type: cc-by

Affiliation: University of Lethbridge, Academy of Athens

Abstract

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.

Highlights

An intriguing prediction of various theories of quantum gravity and black hole physics is the existence of a minimum measurable length
The commutators which are consistent with String Theory, Black Holes Physics, DSR, and which ensure [xi, xj] = 0 = [pi, pj] have the following form [4] 1
We do not impose this condition a priori, and note that this may signal the existence of a new physical length scale of the order of α = αolP l

Summary

Introduction

An intriguing prediction of various theories of quantum gravity (such as String Theory) and black hole physics is the existence of a minimum measurable length. This has given rise to the so-called Generalized Uncertainty Principle, or GUP, or equivalently, modified commutation relations between position coordinates and momenta [1]. The recently proposed Doubly Special Relativity (or DSR) theories on the other hand (which predict maximum observable momenta), suggest a similar modification of commutators [2, 3].

Results

Conclusion