Discreteness of space from the generalized uncertainty principle

By A. Ali, Saurya Das, E. Vagenas. 2009

533 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a41e99977f7ac9f7b84b77b99952cde6ba9e8454

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Citations in the corpus

Probing Planck-scale physics with quantum optics (2011, background): “Among the various proposals for different commutator deformations, we choose as a last example the recently proposed commutator (15) which also accounts for a maximum momentum that is present in several approaches to quantum gravity (6, 7)”
The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field (2011, methodology): “In this paper, we consider a recently proposed GUP which is consistent with string theory, doubly special relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum [21, 22, 23].”
Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “In this fashion, in the leading-order approximation, the harmonic oscillator in one dimension has been studied in [184, 167, 8, 125], the harmonic oscillator in arbitrary dimensions in [83, 177, 85, 93], the energy levels of the hydrogen atom in [167, 69, 296, 67, 258], the particle in a box in [7],”
Generalized Uncertainty Principle: Approaches and Applications (2014, methodology): “Comparison KMM [29] ADV [63, 113] Pedram [64]”