Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment

Scardigli, Fabio

doi:10.1016/s0370-2693(99)00167-7

Cited by 878 publications

(753 citation statements)

References 11 publications

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“…The existence of Planck length as a minimal observable length l p is a universal feature among all approaches of QG [14][15][16][17][18][19][20][21][22]. This minimal length…”

Section: Jhep06(2014)093mentioning

confidence: 94%

“…A generalized uncertainty principle(GUP) was proposed by different approaches to quantum gravity such as string theory and black hole physics [14][15][16][17][18][19][20][21][22][23][24][25] in which Planck length plays an important role. The existence of Planck length as a minimal observable length l p is a universal feature among all approaches of QG [14][15][16][17][18][19][20][21][22].…”

Section: Jhep06(2014)093mentioning

confidence: 99%

“…The existence of a minimum measurable length originates as an intriguing prediction of various frameworks of quantum gravity such as string theory [14] and black hole physics [15][16][17][18][19][20][21]. This implies a direct modification of the standard uncertainty principle [14][15][16][17][18][19][20][21][22][23][24][25]:…”

Section: Jhep06(2014)093mentioning

confidence: 99%

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Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

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Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5,6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entropyarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.

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“…The existence of Planck length as a minimal observable length l p is a universal feature among all approaches of QG [14][15][16][17][18][19][20][21][22]. This minimal length…”

Section: Jhep06(2014)093mentioning

confidence: 94%

Section: Jhep06(2014)093mentioning

confidence: 99%

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Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

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“…[5]. When we measure a position with precision of order ∆x, we expect quantum fluctuations of the metric field around the measured position with energy amplitude…”

Section: Linear Gup In Four Dimensions From Micro Black Holesmentioning

confidence: 99%

Generalized uncertainty principle, extra-dimensions and holography

Scardigli¹,

Casadio²

2005

Braz. J. Phys.

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We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4 + n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.

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“…Consider a system which cannot be probed to distances smaller than some length scale. This phenomenon can be an intrinsic property of the system such as the minimal length scale in high energy physics which is of the order of the Planck length [2,6,9,10,[59][60][61][62][63]. On the other hand, it can be due to the size effect of the measurement apparatus.…”

Section: Introductionmentioning

confidence: 99%

The Minimal Length Uncertainty and the Nonextensive Thermodynamics

Shababi

Pedram

2016

Int J Theor Phys

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In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop quantum gravity, and black-hole physics. We analytically obtain the partition function, probability function, internal energy, and the specific heat capacity of the vibrational quantum system for 1 < q < 3 2 and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale.

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Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment

Cited by 878 publications

References 11 publications

Minimal length, Friedmann equations and maximum density

Minimal length, Friedmann equations and maximum density

Generalized uncertainty principle, extra-dimensions and holography

The Minimal Length Uncertainty and the Nonextensive Thermodynamics

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