scholarly journals EXTENDED UNCERTAINTY PRINCIPLE AND THE GEOMETRY OF (ANTI)-DE SITTER SPACE

2010 ◽  
Vol 25 (20) ◽  
pp. 1697-1703 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Sitter Spacetime ◽  
Heisenberg Uncertainty ◽  
Sitter Background ◽  
Extended Uncertainty

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.

scholarly journals Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
Cosmological Constant ◽  
Pair Production ◽  
Uncertainty Principle ◽  
Correction Term ◽  
Correct Result ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Extended Uncertainty ◽  
Background Curvature

Abstract The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the “extended uncertainty principle” (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de Sitter case). We compare the results with previous works in the EUP literature, which are not all consistent. Our result further highlights an important issue in the literature of generalizations of the uncertainty principle: how much can heuristic derivations be trusted?

scholarly journals Modified inertia from extended uncertainty principle(s) and its relation to MoND

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Jaume Giné ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Direct Consequence ◽  
Natural Generalization ◽  
Alternative Theories Of Gravity ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Sitter Spacetime ◽  
Heisenberg Uncertainty ◽  
Theories Of Gravity ◽  
Extended Uncertainty

AbstractIn this paper we show that Modified Inertia, i.e., the modification of inertia predicted by some alternative theories of gravity at cosmic scales, can be naturally derived within the framework of the extended uncertainty principle (EUP). Specifically, we consider two possible extensions of the Heisenberg uncertainty principle (HUP), corresponding to two different deformations of the fundamental commutator: the first one provides the natural generalization of the HUP to the (anti)-de Sitter spacetime and is endowed with only a quadratic correction in the uncertainty position. On the other hand, the second model contains both linear and quadratic extra terms. We prove that modified inertia is a direct consequence of the minimal acceleration experienced by any body due to the cosmic expansion. The obtained results are then discussed in connection with the empirical predictions of Modified Newtonian dynamics (MoND). The requirement of consistency between the two approaches allows us to fix the adjustable constant which marks the transition between the Newtonian and deep-MoND regimes.

scholarly journals Hawking temperature for various kinds of black holes from Heisenberg uncertainty principle

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040004 ◽  
Author(s):  
Fabio Scardigli
Keyword(s):  
Black Holes ◽  
Large Class ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Classical Physics ◽  
Heisenberg Uncertainty ◽  
Extended Uncertainty

Hawking temperature for a large class of black holes (Schwarzschild, Reissner–Nordström, (Anti) de Sitter, with spherical, toroidal and hyperboloidal topologies) is computed using only laws of classical physics plus the “classical” Heisenberg Uncertainty Principle. This principle is shown to be fully sufficient to get the result, and there is no need to this scope of a Generalized Uncertainty Principle or an Extended Uncertainty Principle.

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals Relationship between Bondi–Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

2018 ◽  
Vol 27 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Xiaokai He ◽  
Jiliang Jing ◽  
Zhoujian Cao
Keyword(s):  
Cosmological Constant ◽  
Gravitational Wave ◽  
Gravitational Radiation ◽  
The Other ◽  
Perturbation Approach ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Sitter Spacetime ◽  
Explicit Expressions

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi–Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

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