2020
DOI: 10.48550/arxiv.2006.05781
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Discreteness of Space from GUP in Strong Gravitational Fields

Ashmita Das,
Saurya Das,
Elias C. Vagenas

Abstract: A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schrödinger equation and to the relativistic quantum mechanical equations. Some of these corrections give rise to potentially measurable effects in … Show more

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Cited by 6 publications
(8 citation statements)
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“…This is consistent with other cosmological studies using quadratic GUP 55 , non-trivial structures of space-time 8,16,55-57 and a crystal lattice considerations with GUP 56 . This can suggest that space-time can have a granular structure at the Planck scale 27,[58][59][60] .…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…This is consistent with other cosmological studies using quadratic GUP 55 , non-trivial structures of space-time 8,16,55-57 and a crystal lattice considerations with GUP 56 . This can suggest that space-time can have a granular structure at the Planck scale 27,[58][59][60] .…”
Section: Discussionmentioning
confidence: 99%
“…One such concept is the existence of a minimal measurable length, predicted my all or most models of QG. A natural way to incorporate minimal length in our considerations is to modify the Heisenberg uncertainty principle [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] . The modified Heisenberg uncertainty principle is called the Generalized Uncertainty Principle (GUP) and in the commutator form it reads as 21 [x i , p j ] = i δ ij − α pδ ij + p i p j p + β p 2 δ ij + 3p i p j (1) where α ≡ α 0 /(M P c), β ≡ β 0 /(M P c) 2 , α 0 , β 0 are the dimensionless linear and quadratic GUP parameters and M P = c/G is the Planck mass.…”
Section: Introductionmentioning
confidence: 99%
“…( 16), i.e., H SN = H. First, we consider the case λ 2 = 0 which can be found in Refs. [53][54][55]. From Eq.…”
Section: Gup and Hubble Parametermentioning
confidence: 99%
“…This means that space-time is believed to be fundamentally discrete. One of the phenomenological models, which describes such discreteness is the Generalized Uncertainty Principle (GUP), which has been studied in great detail [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The most general form of GUP in three spatial dimensions with linear plus quadratic terms in momentum is given by the commutator [21] [x i , p j ] = i δ ij − α pδ ij + p i p j p + β p 2 δ ij + 3p i p j…”
Section: Introductionmentioning
confidence: 99%