Minimal length in quantum gravity and gravitational measurements

Ali, Ahmed Farag; Khalil, Mohammed M.; Vagenas, Elias C.

doi:10.1209/0295-5075/112/20005

Cited by 31 publications

(15 citation statements)

References 81 publications

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“…5 Recently, it was argued that in the special case in which ǫ(r) ∼ 1/r 2 , the specific metric (20) could have some drawbacks in the context of GUP formalism [31]. However, none of those drawbacks appear here and, thus, there is no problem to employ (20) in our present study.…”

Section: Computing βmentioning

confidence: 72%

GUP parameter from quantum corrections to the Newtonian potential

2017

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We propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter

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Section: Computing βmentioning

confidence: 72%

GUP parameter from quantum corrections to the Newtonian potential

2017

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“…Both operator representations may be used to construct and solve a generalized Schrodinger equation for simple quantum mechanical systems [18,[39][40][41][42][43][44] in one space dimension leading to generalized spectra that are consistent with the existence of a fundamental minimum lengthscale [17]. They may also be used to derive thermodynamics properties of gravity and black holes [26,[45][46][47][48][49][50][51] The operator representation (2.7)-(2.8) is more suitable for perturbative analysis of quantum systems while in the representation (2.9)-(2.10) the Hamiltonian eigenvalue problems may usually be expressed as a relatively simpler second order ODE in momentum space which may lead to exact generalized solutions [17].…”

Section: Ii1 One Space Dimensionmentioning

confidence: 99%

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Perivolaropoulos¹

2017

Phys. Rev. D

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The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to non-locality of quantum mechanics, the global properties of the Universe could produce a signature on the behaviour of local quantum systems. A Generalized Uncertainty Principle (GUP) that is consistent with the existence of such a maximum observable length scale lmax is ∆x∆p ≥ 2 √ α. Using appropriate representation of the position and momentum quantum operators we show that the spectrum of the one dimensional harmonic oscillator becomesĒn = 2n + 1 + λnᾱ whereĒn ≡ 2En/ ω is the dimensionless properly normalized n th energy level,ᾱ is a dimensionless parameter withᾱ ≡ α /mω and λn ∼ n 2 for n 1 (we show the full form of λn in the text). For a typical vibrating diatomic molecule and lmax = c/H0 we findᾱ ∼ 10 −77 and therefore for such a system, this effect is beyond reach of current experiments. However, this effect could be more important in the early universe and could produce signatures in the primordial perturbation spectrum induced by quantum fluctuations of the inflaton field.

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“…The important contribution of the GUP is to remove the divergences in physics. On the other hand, GUP can be used to modify Proca equation and Klein-Gordon equation to obtain the effects of the GUP on the Hawking temperature and check if it leaves remnants [50][51][52][53]. Nozari and Mehdipour [54] have discussed BH remnants and their cosmological constraints.…”

Section: Introductionmentioning

confidence: 99%

Tunneling Glashow-Weinberg-Salam Model Particles from Black Hole Solutions in Rastall Theory

Овгун

Javed

Ali

2018

Advances in High Energy Physics

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Using the semiclassical WKB approximation and Hamilton-Jacobi method, we solve an equation of motion for the Glashow-Weinberg-Salam model, which is important for understanding the unified gauge-theory of weak and electromagnetic interactions. We calculate the tunneling rate of the massive charged W-bosons in a background of electromagnetic field to investigate the Hawking temperature of black holes surrounded by perfect fluid in Rastall theory. Then, we study the quantum gravity effects on the generalized Proca equation with generalized uncertainty principle (GUP) on this background. We show that quantum gravity effects leave the remnants on the Hawking temperature and the Hawking radiation becomes nonthermal.

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Minimal length in quantum gravity and gravitational measurements

Cited by 31 publications

References 81 publications

GUP parameter from quantum corrections to the Newtonian potential

GUP parameter from quantum corrections to the Newtonian potential

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

Tunneling Glashow-Weinberg-Salam Model Particles from Black Hole Solutions in Rastall Theory

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