Natural extension of the generalized uncertainty principle

Bambi, Cosimo; Urban, Federico R.

doi:10.1088/0264-9381/25/9/095006

Cited by 218 publications

(204 citation statements)

References 21 publications

Supporting

Mentioning

199

Contrasting

Unclassified

Order By: Relevance

“…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%

“…We first review briefly the Generalized uncertainty principle (GUP) [14][15][16][17][18][19][20][21] and secondly we review its effect on the area-entropy law [7][8][9][10][11][12][13]. 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].…”

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%

See 3 more Smart Citations

Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…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%

Section: Jhep06(2014)093mentioning

confidence: 99%

Section: Jhep06(2014)093mentioning

confidence: 99%

See 2 more Smart Citations

Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…However, the deformation of the uncertainty principle leads to the deformation of the Heisenberg algebra, and this in turn deforms the coordinate representation of the momentum operators [7,9,10,11,12,13,14,15]. The deformation of the coordinate representation of the momentum operator produces correction terms for all quantum mechanical systems.…”

Section: Introductionmentioning

confidence: 99%

Constraints on the Generalized Uncertainty Principle from black-hole thermodynamics

Gangopadhyay¹,

Dutta²,

Faizal³

2015

EPL

View full text Add to dashboard Cite

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.

show abstract

The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field

Pedram

Nozari

Taheri

2011

J. High Energ. Phys.

194

139

View full text Add to dashboard Cite

The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In this scenario, the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP) which results in modification of all Hamiltonians in quantum mechanics. In this paper, following a recently proposed GUP which is consistent with quantum gravity theories, we study the quantum mechanical systems in the presence of both a minimum length and a maximum momentum. The generalized Hamiltonian contains two additional terms which are proportional to αp 3 and α 2 p 4 where α ∼ 1/M P l c is the GUP parameter. For the case of a quantum bouncer, we solve the generalized Schrödinger equation in the momentum space and find the modified energy eigenvalues and eigenfunctions up to the secondorder in GUP parameter. The effects of the GUP on the transition rate of ultra cold neutrons in gravitational spectrometers are discussed finally.

show abstract

Natural extension of the generalized uncertainty principle

Cited by 218 publications

References 21 publications

Minimal length, Friedmann equations and maximum density

Minimal length, Friedmann equations and maximum density

Constraints on the Generalized Uncertainty Principle from black-hole thermodynamics

The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field

Contact Info

Product

Resources

About