ARTICLE | doi:10.20944/preprints202110.0452.v2
Subject: Physical Sciences, Astronomy & Astrophysics Keywords: Lorentz invariance violation; FRW metric; general relativity; quantum mechanics; uncertainty principle; quantum gravity
Online: 7 December 2021 (11:37:55 CET)
Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.
ARTICLE | doi:10.20944/preprints202107.0646.v3
Subject: Physical Sciences, General & Theoretical Physics Keywords: General relativity; Uncertainty principle; Geodesics; Black hole singularity; vacuum energy; Quantum gravity; Planck star
Online: 25 August 2021 (09:01:26 CEST)
The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.
REVIEW | doi:10.20944/preprints202208.0347.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: General relativity; uncertainty principle; geodesics; black hole singularity; quantum gravity; Planck star; Lorentz invariance violations.
Online: 18 August 2022 (11:06:06 CEST)
Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.