QUANTUM GRAVITY AND MINIMUM LENGTH

GARAY, LUIS J.

doi:10.1142/s0217751x95000085

Cited by 1,371Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

QUANTUM GRAVITY AND MINIMUM LENGTH

Open access

GARAY, LUIS J.·1995·International Journal of Modern Physics A

DOI 10.1142/s0217751x95000085

Open this paper in CoChat — free account Open PDF

Abstract

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1142/s0217751x95000085

Cites

81 of 81 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

In many approaches to quantum gravity, the Planck length LP should play the role of a minimal observable length.
“A Planck-scale minimal observable length appears in many approaches to quantum gravity.”
From Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction (2003) · cites this paper as [1]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

The quantum theory of radiation
Heitler, W. (1936) · doi:10.2307/3607790 · Cited by 2,880
On the quantum structure of a black hole
't Hooft, G. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90418-3 · Cited by 1,311 · see citing works
Can spacetime be probed below the string size
Amati, D., Ciafaloni, M., & Veneziano, G. (1989) · Physics Letters B · doi:10.1016/0370-2693(89)91366-x · Cited by 1,151 · see citing works
String Theory Beyond the Planck Scale
Gross, D., & Mende, P. F. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90390-2 · Cited by 1,150 · cited 1× · see citing works
“This may be one of the reasons for the exponential damping that high-energy fixed-angle scattering amplitudes suffer [ 38 ,39], and for the slower growth of thermal partition functions at high temperature [40].”
Background
The stretched horizon and black hole complementarity
Susskind, L., Thorlacius, L., & Uglum, J. (1993) · Physical Review D · doi:10.1103/physrevd.48.3743 · Cited by 1,081 · see citing works
A generalized uncertainty principle in quantum gravity
Maggiore, M. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91401-8 · Cited by 1,019 · cited 1× · see citing works
“Quite recently, Maggiore [ 53 ] has found that an uncertainty relation that gives rise to a minimum length can also be derived from the measurement of the radius of a black hole.”
Background
Why there is nothing rather than something: A theory of the cosmological constant
Coleman, S. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90097-1 · Cited by 852 · see citing works
Superstrings in the Early Universe
Brandenberger, R., & Vafa, C. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90037-0 · Cited by 835 · see citing works
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806 · see citing works
Quantum Groups
Kassel, C. (1994) · doi:10.1007/978-1-4612-0783-2 · Cited by 780
The Hagedorn Transition and the Number of Degrees of Freedom of String Theory
Atick, J., & Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90151-4 · Cited by 761 · see citing works
The High-Energy Behavior of String Scattering Amplitudes
Gross, D., & Mende, P. F. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)90355-8 · Cited by 720 · see citing works
MINIMUM PHYSICAL LENGTH AND THE GENERALIZED UNCERTAINTY PRINCIPLE IN STRING THEORY
Konishi, K., Paffuti, G., & Provero, P. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)91927-4 · Cited by 672 · cited 2× · see citing works
“Through a detailed analysis of thought-experiments involving high energy string collisions [25,26], and also through a renormalization group type analysis in string theory [ 24 ,27,28] it was found that this result could be qualitatively written in the form (see, for instance, Refs.”
BackgroundMethod
On the nature of quantum geometrodynamics
Wheeler, J. (1957) · Annals of Physics · doi:10.1016/0003-4916(57)90050-7 · Cited by 584 · see citing works
A Stringy Nature Needs Just Two Constants
VENEZIANO, G. (1986) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/2/3/006 · Cited by 576 · see citing works
The algebraic structure of the generalized uncertainty principle
Maggiore, M. (1993) · doi:10.1016/0370-2693(93)90785-g · Cited by 537
Knot Theory and Quantum Gravity
Rovelli, C., & Smolin, L. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1155 · Cited by 463 · see citing works
Quantum groups, gravity, and the generalized uncertainty principle.
Maggiore, M. (1993) · Physical Review D, Particles and fields · doi:10.1103/physrevd.49.5182 · Cited by 446 · see citing works
Wormholes in spacetime
Hawking, S. W. (1988) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.37.904 · Cited by 412 · see citing works
Weaving a classical metric with quantum threads
Ashtekar, A., Rovelli, C., & Smolin, L. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.237 · Cited by 399 · see citing works
On localized states for elementary systems
Biritz, H. (1971) · doi:10.1007/bf02728594 · Cited by 396 · cited 1×
“In fact, an essentially unique position operator was defined by Newton and Wigner [ 4 ].”
Background
Possible Connection Between Gravitation and Fundamental Length
Mead, C. (1964) · Physical Review · doi:10.1103/physrev.135.b849 · Cited by 358 · cited 1× · see citing works
“The process of detecting a particle with a microscope and some related thoughtexperiments were carefully analyzed by Mead [ 12 ].”
Method
Black-hole evaporation and ultrashort distances
Jacobson, T. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.44.1731 · Cited by 352 · cited 1× · see citing works
“[ 82 ]). However, this membrane would be real only for this observer at rest (its reality would be dramatically shown if this observer were too close to the membrane since its extremely high temperature would burn him to ashes).”
Background
LIMITATIONS ON THE STATISTICAL DESCRIPTION OF BLACK HOLES
Preskill, J. P., Schwarz, P. M., Shapere, A. D., Trivedi, S. P., & Wilczek, F. A. (1991) · Modern Physics Letters A · doi:10.1142/s0217732391002773 · Cited by 287 · cited 1× · see citing works
“Note that this assumption is plausible since the emission produced by a nearly extremal black hole need not be thermal [ 54 ].”
Background
Compactification of the twisted heterotic string
Nair, V. P., Shapere, A. D., Strominger, A., & Wilczek, F. A. (1987) · Nuclear Physics B · doi:10.1016/0550-3213(87)90112-x · Cited by 254 · see citing works
On quantization of fields
Rosenfeld, L. (1963) · Nuclear Physics · doi:10.1016/0029-5582(63)90279-7 · Cited by 251 · see citing works
Quantum reference systems
Rovelli, C. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/2/012 · Cited by 250 · see citing works
String theory and the principle of black hole complementarity
Susskind, L. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.2367 · Cited by 232 · cited 1× · see citing works
“Due to the existence of a minimum proper interval, the notion of event loses one of its characteristic features: it is no longer an invariant concept [ 79 ,80,81].”
Background
Ashtekar formulation of general relativity and loop-space nonperturbative quantum gravity: a report
Rovelli, C. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/9/002 · Cited by 221 · see citing works
Limitations on the operational definition of spacetime events and quantum gravity
Padmanabhan, Τ. (1987) · Classical and Quantum Gravity · doi:10.1088/0264-9381/4/4/007 · Cited by 213 · see citing works
Wormholes and the cosmological constant
Klebanov, I. R., Susskind, L., & Banks, T. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90538-5 · Cited by 201 · see citing works
The path-integral approach to quantum gravity
Hawking, S. W. (1993) · Advanced series in astrophysics and cosmology · doi:10.1142/9789812384935_0012 · Cited by 190 · see citing works
On quantum field theory with nonzero minimal uncertainties in positions and momenta
Kempf, A. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531814 · Cited by 158 · cited 1× · see citing works
“[63, 64 ]) has pushed this kind of arguments further and has found an algebra that gives rise to the generalized uncertainty relations and that, under quite general assumptions, is essentially unique.”
Background
Field and Charge Measurements in Quantum Electrodynamics
Bohr, N., & Rosenfeld, L. (1950) · doi:10.1103/physrev.78.794 · Cited by 154 · cited 1×
“Based on the work by Bohr and Rosenfeld [65,66, 67 ,68] (see e.g.”
Method
Small-scale structure of spacetime as the origin of the gravitational constant
Townsend, P. (1977) · doi:10.1103/physrevd.15.2795 · Cited by 152 · cited 1×
“By considering gravity as the gauge theory of the deSitter group, Townsend [ 60 ] introduced Planck’s length into gravity kinematically.”
Method
Semiclassical gravity theory and quantum fluctuations.
Kuo, C.-I., & Ford, L. (1993) · Physical Review D, Particles and fields · doi:10.1103/physrevd.47.4510 · Cited by 145 · cited 1× · see citing works
“However, there is another source of uncertainty that will not be considered here: the quantum fluctuations of the gravitational field due to the Heisenberg uncertainty relations that affect the source of the gravitational field [9,10, 11 ].”
Background
Spectrum of wormholes
Hawking, S. W., & Page, D. N. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.2655 · Cited by 141 · see citing works
Measuring small distances in N=2 sigma models
Aspinwall, P., Greene, B., & Morrison, D. (1993) · doi:10.1016/0550-3213(94)90379-4 · Cited by 128
On the interpretation of minimal length in string theories
Yoneya, T. (1989) · doi:10.1142/s0217732389001817 · Cited by 128 · cited 1×
“Through a detailed analysis of thought-experiments involving high energy string collisions [25,26], and also through a renormalization group type analysis in string theory [24, 27 ,28] it was found that this result could be qualitatively written in the form (see, for instance, Refs.”
Method
Lattice gravity near the continuum limit
Feinberg, G., Friedberg, R. M., Lee, T. D., & Ren, H.-C. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90436-x · Cited by 118 · see citing works
Prima facie questions in quantum gravity
Isham, C. J. (2008) · Springer eBooks · doi:10.1007/3-540-58339-4_13 · Cited by 111 · see citing works
Study of Three Dimensional Quantum Black Holes
Satoh, Y. (1997) · doi:10.48550/arxiv.hep-th/9705209 · Cited by 107
Physical significance of planck length
Padmanabhan, T. (1985) · Annals of Physics · doi:10.1016/s0003-4916(85)80004-x · Cited by 107 · see citing works
Particle theories with minimum observable length and open string theory
Kato, M. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)90162-y · Cited by 101 · cited 2× · see citing works
“However, this non-local change of variables will turn the action non-local and non-local actions contain a minimum length in them [ 23 ].”
Background
General Relativity and the Divergence Problem in Quantum Field Theory
Deser, S. (1957) · doi:10.1103/revmodphys.29.417 · Cited by 98 · cited 2×
“Let us illustrate this issue in the case of a massless scalar field in curved spacetime [ 55 ,14] (see also Ref.”
Background
Continuum strings from discrete field theories
Klebanov, I., & Susskind, L. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90237-4 · Cited by 95 · see citing works
Planck length as the lower bound to all physical length scales
Padmanabhan, T. (1985) · General Relativity and Gravitation · doi:10.1007/bf00760244 · Cited by 89 · cited 1× · see citing works
“From different points of view, both Padmanabhan [14, 15 ,16,17] and Greensite [18] inferred the existence of a minimum length within a path integral formulation of quantum gravity; namely, the former worked in a theory in which the conformal factor is quantized [19] and the latter in lattice quantum gravity (see also…”
Background
Wormholes in spacetime and the constants of nature
Preskill, J. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90592-0 · Cited by 87 · see citing works
The Σ±-particles
Dreizin, E. L. (1957) · doi:10.1007/bf02824505 · Cited by 75
The meaning of quantum gravity
von Borzeszkowski, H., & Treder, H. (1987) · doi:10.1007/978-94-009-3893-9 · Cited by 70
A generally covariant quantum field theory and a prediction on quantum measurements of geometry
Rovelli, C. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90567-9 · Cited by 66 · cited 1× · see citing works
“it is an integer multiple of the elementary Planck’s area [46, 47 ].”
Background
Observable Consequences of Fundamental-Length Hypotheses
Mead, C. (1966) · Physical Review · doi:10.1103/physrev.143.990 · Cited by 61 · cited 1× · see citing works
“An early attempt to give a kinematical meaning to the generalized uncertainty relations was made by Mead [ 58 ] (see also Ref.”
Background
Quantum-mechanical histories and the uncertainty principle. II. Fluctuations about classical predictability
Halliwell, J. J. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.48.4785 · Cited by 48 · see citing works
Acceptable density perturbations from inflation due to quantum gravitational damping.
Padmanabhan, T. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.2229 · Cited by 37 · cited 1× · see citing works
“[ 57 ]). The Green function evaluated in a classical spacetime has the well-known form”
Background
Quantum cosmology via path integrals
Narlikar, J., & Padmanabhan, T. (1983) · Physics Reports · doi:10.1016/0370-1573(83)90098-4 · Cited by 34 · cited 1× · see citing works
“From different points of view, both Padmanabhan [14,15,16,17] and Greensite [18] inferred the existence of a minimum length within a path integral formulation of quantum gravity; namely, the former worked in a theory in which the conformal factor is quantized [ 19 ] and the latter in lattice quantum gravity (see also…”
Background
Is there a minimum length in D=4 lattice quantum gravity?☆
Greensite, J. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90781-k · Cited by 31 · see citing works
Baby Universes II
Hawking, S. (1990) · Modern Physics Letters A · doi:10.1142/s0217732390000524 · Cited by 31 · see citing works
Black hole complementarity and the physical origin of the stretched horizon
Maggiore, M. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.2918 · Cited by 28 · see citing works
UNCERTAINTY PRINCIPLE AND THE QUANTUM FLUCTUATIONS OF THE SCHWARZSCHILD LIGHT CONES
Padmanabhan, T., Seshadri, T., & Singh, T. P. (1986) · doi:10.1142/s0217751x86000216 · Cited by 24
Minimum distances in non-trivial string target spaces
Aspinwall, P. S. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90098-1 · Cited by 20 · see citing works
Quantum state of wormholes and path integral.
Garay, L. J. (1991) · Physical Review D, Particles and fields · doi:10.1103/physrevd.44.1059 · Cited by 20 · cited 1×
“[92,93,94]). They admit also a full quantum treatment in terms of wave functions [91,95, 96 ,97].”
BackgroundSelf-citation
The role of general relativity in the uncertainty principle
Padmanabhan, T. (1986) · doi:10.1088/0264-9381/3/5/020 · Cited by 19
The planckions as largest elementary particles and as smallest test bodies
Treder, H. (1985) · doi:10.1007/bf00735287 · Cited by 19
Hilbert space of wormholes.
Garay, L. (1993) · Physical Review D, Particles and fields · doi:10.1103/physrevd.48.1710 · Cited by 17 · see citing works
Self-citation
String theory at short distance and the principle of equivalence
Mende, P. F. (1992) · doi:10.48550/arxiv.hep-th/9210001 · Cited by 16
Quantum theory and Einstein's general relativity
Borzeszkowski, H.-H., & Treder, H. (1982) · doi:10.1007/bf01300549 · Cited by 15
Time measurement in quantum gravity
Itzhaki, N. (1994) · doi:10.1016/0370-2693(94)91479-6 · Cited by 12 · cited 1×
“[ 13 ]). We will make use of the full general relativity theory (rather than the Newtonian limit).”
Method
Phase structure of SU(2) lattice gauge theory with quantum gravity
Berg, B., & Krishnan, B. (1993) · doi:10.1016/0370-2693(93)91784-k · Cited by 12 · cited 1×
“[20, 21 ,22]). They both reached the result that the coincidence limit, in which the difference between coordinates of two events in a given frame or the separation between lattice points goes to zero, of the proper interval between them is not zero but Planck’s length.”
Background
Quantum Gravity and String Theory, What Have We Learned?
Strominger, A. (1991) · doi:10.48550/arxiv.hep-th/9110011 · Cited by 10 · see citing works
The action uncertainty principle in continuous quantum measurements
Mensky, M. (1991) · doi:10.1016/0375-9601(91)90474-m · Cited by 10 · cited 2×
“The probability amplitude for an output α can be written in terms of path integrals [ 76 ]:”
Background
Asymptotic freedom and euclidean quantum gravity
Berg, B., Krishnan, B., & Katoot, M. (1992) · doi:10.1016/0550-3213(93)90484-7 · Cited by 9
Quantum Dust Black HolesPreprint
Peleg, Y. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9307057 · Cited by 9 · see citing works
Uncertainty Principle and the Quantum Fluctuations of the Light Cones in the Static Space-times
Daftardar, V., & Dadhich, N. (1986) · doi:10.1142/s0217751x86000289 · Cited by 6
The action uncertainty principle and quantum gravity
Mensky, M. (1992) · doi:10.1016/0375-9601(92)90436-p · Cited by 5
Small-distance derivatives
Gonzalez-diaz, P. (1984) · doi:10.1007/bf02748388 · Cited by 5
The R→α′/R Space-Time Duality from the 2+1 Point of View
Gan, Y.-K. I. (1991) · doi:10.1142/s0217732391000518 · Cited by 4
Quantum Black HolesPreprint
García-Bellido, J. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9302127 · Cited by 4 · see citing works
Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and MomentaPreprint
Kempf, A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9405067
Prima Facie Questions in Quantum Gravity
Isham, C. J. (1993) · arXiv · doi:10.48550/arxiv.gr-qc/9310031
Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
Kempf, A. (1993) · arXiv · doi:10.48550/arxiv.hep-th/9311147
Minimum Distances in Non-Trivial String Target Spaces
Aspinwall, P. (1994) · arXiv · doi:10.48550/arxiv.hep-th/9404060

Flagged first, then by citations

18 of the 99 references couldn’t be matched to a known paper.

Research works printed but not linked: 10

[2][2] V. B. Berestetskiˇ ı, E. M. Lifshitz and L. P. Pitaevskiˇ ı, Relativistic Quantum Theory (Pergamon, Oxford, 1971). -
[6][6] M. A. Markov, Preprint P-0187 of the Inst. Nucl. Res., Moscow (1980). On quantum violation of topology in small spatial regions. -
[7][7] M. A. Markov, Preprint P-0208 of the Inst. Nucl. Res., Moscow (1981). On the maximon and the concept of elementary particle. -
[44][44] L. Smolin, in Quantum Gravity and Cosmology , eds. J. P´ erez-Mercader et al. (World Scientific, Singapore, 1992). Recent developments in nonperturbative quantum gravity. -
[65][65] N. Bohr and L. Rosenfeld, Det. Kgl. Danske Videnskabernes Selskab., Math.-fys. Medd. 12 , 8 (1933); in Selected Papers of L` eon Rosenfeld , eds. Cohen and Stachel (Reidel, Dordrecht, 1979); in Quantum Theory and Measurement , eds. J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1983). On the question of measurability of electromagnetic field quantities. -
[71][71] B. S. DeWitt, in Gravitation: An Introduction to Current Research , ed. L. Witten (Wiley, New York, 1962). The quantization of gravity. -
[75][75] L. Landau and R. Peierls, Z. Phys. 69 , 56 (1931); in Collected Papers of Landau , ed. D. ter Haar (Gordon and Breach, New York, 1965); in Quantum Theory and Measurement , eds. J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1983). Extension of the uncertainty principle to the relativistic quantum theory. -
[87][87] J. J. Halliwell, in Quantum Cosmology and Baby Universes , eds. S. Coleman et al. (World Scientific, Singapore, 1990). Introductory lectures on quantum cosmology. -
[89][89] J. A. Wheeler, Geometrodynamics (Ac. Press, London, 1962). -
[94][94] A. Strominger, in Particles, Strings and Supernovae , eds. A. Jevicki and C. I. Tan (World Scientific, Singapore, 1989). Baby universes. -

Sorted by citations

Hilbert space representation of the minimal length uncertainty relation
Kempf, A., Mangano, G., & Mann, R. B. (1995) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.52.1108 · Cited by 1,968 · see citing works
Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · see citing works
Analogue Gravity
Barceló, C., Liberati, S., & Visser, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-12 · Cited by 1,163 · see citing works
Modern Tests of Lorentz Invariance
Mattingly, D. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-5 · Cited by 1,061 · see citing works
Thermodynamical aspects of gravity: new insights
Padmanabhan, Τ. (2010) · Reports on Progress in Physics · doi:10.1088/0034-4885/73/4/046901 · Cited by 1,046 · see citing works
Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment
Scardigli, F. (1999) · Physics Letters B · doi:10.1016/s0370-2693(99)00167-7 · Cited by 889 · see citing works
The Asymptotic Safety Scenario in Quantum Gravity
Niedermaier, M. R., & Reuter, M. (2006) · Living Reviews in Relativity · doi:10.12942/lrr-2006-5 · Cited by 733 · see citing works
Minimal Length Scale Scenarios for Quantum Gravity
Hossenfelder, S. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-2 · Cited by 818 · see citing works
Quantum-Spacetime Phenomenology
Giovanni Amelino-camelia, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-5 · Cited by 799 · see citing works
Universality of Quantum Gravity Corrections
Das, S., & Vagenas, E. C. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.221301 · Cited by 664 · see citing works
NONCOMMUTATIVE BLACK HOLES, THE FINAL APPEAL TO QUANTUM GRAVITY: A REVIEW
Nicolini, P. (2009) · International Journal of Modern Physics A · doi:10.1142/s0217751x09043353 · Cited by 641 · see citing works
Discreteness of space from the generalized uncertainty principle
Ali, A. F., Das, S., & Vagenas, E. C. (2009) · Physics Letters B · doi:10.1016/j.physletb.2009.06.061 · Cited by 604 · see citing works
Probing Planck-scale physics with quantum optics
Pikovski, I., Vanner, M. R., Aspelmeyer, M., Kim, M. S., & Brukner, Č. (2012) · Nature Physics · doi:10.1038/nphys2262 · Cited by 597 · see citing works
Analogue Gravity
Barceló, C., Liberati, S., & Visser, M. (2011) · Living Reviews in Relativity · doi:10.12942/lrr-2011-3 · Cited by 598 · see citing works
Entanglement Entropy of Black Holes
Solodukhin, S. N. (2011) · Living Reviews in Relativity · doi:10.12942/lrr-2011-8 · Cited by 539 · see citing works
The Spectral Dimension of the Universe is Scale Dependent
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.171301 · Cited by 523 · see citing works
“the nonperturbative formulation of quantum gravity employed here, causal dynamical triangulations, evades the ultraviolet inﬁnities of perturbative quantum gravity. Contrary to current folklore (see [17] for a review), this is done without appealing to short-scale discreteness or abandoning geometric concepts altogeth…”
Background
Holographic dark energy model from Ricci scalar curvature
Gao, C., Wu, F., Chen, X., & Shen, Y.-G. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.043511 · Cited by 490 · see citing works
Non-pointlike particles in harmonic oscillators
Kempf, A. (1997) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/30/6/030 · Cited by 467 · see citing works
Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken ExperimentPreprint
Scardigli, F. (1999) · Cited by 459 · see citing works
Tests of Lorentz invariance: a 2013 update
Liberati, S. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/13/133001 · Cited by 447 · see citing works
Quantum gravity: a progress report
Carlip, S. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/8/301 · Cited by 449 · see citing works
Proposal for testing quantum gravity in the lab
Ali, A. F., Das, S., & Vagenas, E. C. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.044013 · Cited by 436 · see citing works
Quantum gravity phenomenology at the dawn of the multi-messenger era—A review
Jetzer, P., Álvarez-Muñiz, J., Batista, R. A., et al. (2022) · Zurich Open Repository and Archive (University of Zurich) · doi:10.5167/uzh-230734 · Cited by 439 · see citing works
Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints
Ted Jacobson, A., Liberati, S., & Mattingly, D. (2005) · Annals of Physics · doi:10.1016/j.aop.2005.06.004 · Cited by 369 · see citing works
Minimal Length Scale Scenarios for Quantum Gravity
Hossenfelder, S. (2013) · DOAJ (DOAJ: Directory of Open Access Journals) · Cited by 329 · see citing works
Dark energy and gravity
Padmanabhan, Τ. (2007) · General Relativity and Gravitation · doi:10.1007/s10714-007-0555-7 · Cited by 393 · see citing works
When conceptual worlds collide: The generalized uncertainty principle and the Bekenstein-Hawking entropy
Medved, A. J. M., & Vagenas, E. C. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.124021 · Cited by 330 · see citing works
EQUIPARTITION OF ENERGY IN THE HORIZON DEGREES OF FREEDOM AND THE EMERGENCE OF GRAVITY
Padmanabhan, Τ. (2010) · Modern Physics Letters A · doi:10.1142/s021773231003313x · Cited by 317 · see citing works
Discreteness of space from GUP II: Relativistic wave equations
Das, S., Vagenas, E. C., & Ali, A. F. (2010) · Physics Letters B · doi:10.1016/j.physletb.2010.05.052 · Cited by 309 · see citing works
Signatures in the Planck regime
Hossenfelder, S., Bleicher, M., Hofmann, S., Ruppert, J., Scherer, S., & Horst Stöcker, B. (2003) · Physics Letters B · doi:10.1016/j.physletb.2003.09.040 · Cited by 305 · see citing works
Lorentz violation at high energy: concepts, phenomena and astrophysical constraintsPreprint
Ted Jacobson, A., Liberati, S., & Mattingly, D. (2005) · Cited by 266 · see citing works
The asymptotic safety scenario in quantum gravity: an introduction
Niedermaier, M. R. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/18/r01 · Cited by 263 · see citing works
Phenomenological implications of the generalized uncertainty principleThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.
Das, S., & Vagenas, E. C. (2009) · Canadian Journal of Physics · doi:10.1139/p08-105 · Cited by 261 · see citing works
Planck-scale modified dispersion relations and Finsler geometry
Girelli, F., Liberati, S., & Sindoni, L. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.064015 · Cited by 249 · see citing works
Stellar structure models in modified theories of gravity: Lessons and challenges
Olmo, G. J., Rubiera-García, D., & Wojnar, A. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.07.001 · Cited by 255 · see citing works
Gravity-wave interferometers as quantum-gravity detectors
Giovanni Amelino-camelia, A. (1999) · Nature · doi:10.1038/18377 · Cited by 250 · see citing works
Quantum superposition of massive objects and the quantization of gravity
Belenchia, A., Wald, R. M., Giacomini, F., et al. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.126009 · Cited by 247 · see citing works
“sion that localization of any body cannot be achieved to better than a Planck length—a conclusion that has been previously reached by many authors; see [34], [35, 36] and references therein.”
Result
Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles
Giovanni Amelino-camelia, A., Arzano, M., Ling, Y., & Mandanici, G. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/7/022 · Cited by 243 · see citing works
Generalized uncertainty principle: Approaches and applications
Tawfik, A. N., & Diab, A. M. (2014) · International Journal of Modern Physics D · doi:10.1142/s0218271814300250 · Cited by 241 · see citing works
Quantum-corrected black hole thermodynamics to all orders in the Planck length
Nouicer, K. (2007) · Physics Letters B · doi:10.1016/j.physletb.2006.12.072 · Cited by 240 · see citing works
Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation
Benczik, S., Chang, L. N., Minić, D., Okamura, N., Rayyan, S., & Takeuchi, T. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.026003 · Cited by 236 · see citing works
Maximal localization in the presence of minimal uncertainties in positions and in momenta
Hinrichsen, H., & Kempf, A. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531501 · Cited by 236 · see citing works
Deformed boost transformations that saturate at the Planck scale
Bruno, N. R., Giovanni Amelino-camelia, A., & Kowalski-Glikman, J. (2001) · Physics Letters B · doi:10.1016/s0370-2693(01)01264-3 · Cited by 248 · see citing works
Non-commutative geometry inspired higher-dimensional charged black holes
Spallucci, E., Smailagic, A., & Nicolini, P. (2008) · Physics Letters B · doi:10.1016/j.physletb.2008.11.030 · Cited by 225 · see citing works
Quantum uncertainty in doubly special relativity
Cortés, J. L., & Gamboa, J. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.065015 · Cited by 223 · see citing works
Mode generating mechanism in inflation with a cutoff
Kempf, A. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.083514 · Cited by 220 · see citing works
Stellar structure models in modified theories of gravity: lessons and challenges.
Olmo, G. J., Rubiera-García, D., & Wojnar, A. (2020) · Library Open Repository (Universidad Complutense Madrid) · Cited by 206 · see citing works
The generalized uncertainty principle in (A)dS space and the modification of Hawking temperature from the minimal length
Park, M.-I. (2007) · Physics Letters B · doi:10.1016/j.physletb.2007.11.090 · Cited by 207 · see citing works
A higher order GUP with minimal length uncertainty and maximal momentum
Pedram, P. (2012) · Physics Letters B · doi:10.1016/j.physletb.2012.07.005 · Cited by 196 · see citing works
Will we observe black holes at the LHC?
Cavaglià, M., Das, S., & Maartens, R. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/15/101 · Cited by 190 · see citing works
Gravitational decoherence
Bassi, A., Großardt, A., & Ulbricht, H. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa864f · Cited by 190 · see citing works
Minimal length, maximal momentum, and Hilbert space representation of quantum mechanics
Nozari, K., & Etemadi, A. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.104029 · Cited by 189 · see citing works
A review of the generalized uncertainty principle
Tawfik, A. N., & Diab, A. M. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/12/126001 · Cited by 205 · see citing works
The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
Pedram, P., Nozari, K., & Taheri, S. H. (2011) · Journal of High Energy Physics · doi:10.1007/jhep03(2011)093 · Cited by 185 · see citing works
Uncertainty relation on a world crystal and its applications to micro black holes
Petr Jizba, B., Kleinert, H. M., & Scardigli, F. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.084030 · Cited by 170 · see citing works
On quantum field theory with nonzero minimal uncertainties in positions and momenta
Kempf, A. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531814 · Cited by 158 · see citing works
Entropy of null surfaces and dynamics of spacetime
Padmanabhan, Τ., & Paranjape, A. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.064004 · Cited by 169 · see citing works
Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
Kothawala, D., Sarkar, S., & Padmanabhan, Τ. (2007) · Physics Letters B · doi:10.1016/j.physletb.2007.07.021 · Cited by 163 · see citing works
Probing deformed commutators with macroscopic harmonic oscillators
Bawaj, M., Biancofiore, C., Bonaldi, M., et al. (2015) · Nature Communications · doi:10.1038/ncomms8503 · Cited by 160 · see citing works
Six easy roads to the Planck scale
Adler, R. (2010) · American Journal of Physics · doi:10.1119/1.3439650 · Cited by 132 · see citing works
Doubly special relativity and de Sitter space
Kowalski-Glikman, J., & Nowak, S. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/22/006 · Cited by 153 · see citing works
Black hole thermodynamics with generalized uncertainty principle
Myung, Y. S., Kim, Y., & Park, Y.-J. (2007) · Physics Letters B · doi:10.1016/j.physletb.2006.12.062 · Cited by 150 · see citing works
Minimum Length from Quantum Mechanics and Classical General Relativity
Xavier Calmet, A., Graesser, M. L., & Hsu, S. D. H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.211101 · Cited by 152 · see citing works
Local D=4 field theory on κ -deformed Minkowski space
Kosiński, P., Lukierski, J., & Maślanka, P. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.025004 · Cited by 146 · see citing works
Gravitational bar detectors set limits to Planck-scale physics on macroscopic variables
Marin, F., Marino, F., Bonaldi, M., CERDONIO, M., Conti, L., Falferi, P., Mezzena, R., Ortolan, A., Prodi, G. A., Taffarello, L., et al. (2012) · Nature Physics · doi:10.1038/nphys2503 · Cited by 141 · see citing works
Quantum Metrology with Indefinite Causal Order
Zhao, X., Yang, Y., & Chiribella, G. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.190503 · Cited by 141 · see citing works
Interpretation of quantum field theories with a minimal length scale
Hossenfelder, S. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.105013 · Cited by 139 · see citing works
Spacetime Foam as a Quantum Thermal Bath
Garay, L. J. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2508 · Cited by 139 · see citing works
Self-citation
Quantum corrections to the thermodynamics of Schwarzschild–Tangherlini black hole and the generalized uncertainty principle
Feng, Z.-W., Li, H. L., Zu, X., & Yang, S. (2016) · The European Physical Journal C · doi:10.1140/epjc/s10052-016-4057-1 · Cited by 136 · see citing works
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
Rovelli, C., & Speziale, S. (2003) · Physical Review D · doi:10.1103/physrevd.67.064019 · Cited by 136 · see citing works
“Kerrr” black hole: The lord of the string
Smailagic, A., & Spallucci, E. (2010) · Physics Letters B · doi:10.1016/j.physletb.2010.03.075 · Cited by 131 · see citing works
Dimension and dimensional reduction in quantum gravity
Carlip, S. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa8535 · Cited by 141 · see citing works
Remnant for all black objects due to gravity's rainbow
Ali, A. F., Faizal, M., & Khalil, M. (2015) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2015.03.014 · Cited by 129 · see citing works
Nonsingular rainbow universes
Awad, A., Ali, A. F., & Majumder, B. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/10/052 · Cited by 129 · see citing works
Displacement operator for quantum systems with position-dependent mass
Filho, R. N. C., de Almeida, M. P., Farias, G. A., et al. (2011) · Physical Review A · doi:10.1103/physreva.84.050102 · Cited by 126 · see citing works
A heuristic analysis of black hole thermodynamics with generalized uncertainty principle
Xiang, L., & Wen, X. (2009) · Journal of High Energy Physics · doi:10.1088/1126-6708/2009/10/046 · Cited by 126 · see citing works
“This term is also attributed to gravity in some gedanken experiments [7, 8, 10, 12].”
Some consequences of the generalised uncertainty principle: statistical mechanical, cosmological, and varying speed of light
Rama, S. K. (2001) · Physics Letters B · doi:10.1016/s0370-2693(01)01091-7 · Cited by 125 · see citing works
A higher order GUP with minimal length uncertainty and maximal momentum II: Applications
Pedram, P. (2012) · Physics Letters B · doi:10.1016/j.physletb.2012.10.059 · Cited by 125 · see citing works
A note on theories with a minimal length
Hossenfelder, S. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/5/n01 · Cited by 127 · see citing works
Black hole entropy without brick walls
Xiang, L. (2002) · Physics Letters B · doi:10.1016/s0370-2693(02)02123-8 · Cited by 121 · see citing works
Some aspects of gravitational quantum mechanics
Nozari, K., & Azizi, T. (2006) · General Relativity and Gravitation · doi:10.1007/s10714-006-0262-9 · Cited by 117 · see citing works
Absence of black holes at LHC due to gravity's rainbow
Ali, A. F., Faizal, M., & Khalil, M. (2015) · Physics Letters B · doi:10.1016/j.physletb.2015.02.065 · Cited by 116 · see citing works
Classical and quantum mechanics of the nonrelativistic Snyder model
Mignemi, S. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.025021 · Cited by 116 · see citing works
Is gravitational entropy quantized?
Kothawala, D., Padmanabhan, Τ., & Sarkar, S. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.104018 · Cited by 113 · see citing works
New approach to nonperturbative quantum mechanics with minimal length uncertainty
Pedram, P. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.024016 · Cited by 112 · see citing works
Pointlike D-brane Dynamics and Space-Time Uncertainty Relation
Li, M., & Yoneya, T. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.1219 · Cited by 113 · see citing works
Trans-Planckian effects in inflationary cosmology and the modified uncertainty principle
Hassan, S. F., & Sloth, M. S. (2003) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2003.09.041 · Cited by 112 · see citing works
Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle
Setare, M. R. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.087501 · Cited by 109 · see citing works
Minimal length in quantum gravity, equivalence principle and holographic entropy bound
Ali, A. F. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/6/065013 · Cited by 109 · see citing works
Natural cutoffs and quantum tunneling from black hole horizon
Nozari, K., & Saghafi, S. (2012) · Journal of High Energy Physics · doi:10.1007/jhep11(2012)005 · Cited by 108 · see citing works
GUP-corrected thermodynamics for all black objects and the existence of remnants
Faizal, M., & Khalil, M. M. (2015) · International Journal of Modern Physics A · doi:10.1142/s0217751x15501444 · Cited by 106 · see citing works
Doubly Special Relativity and de Sitter spacePreprint
Kowalski-Glikman, J., & Nowak, S. (2003) · Cited by 104 · see citing works
Absence of an effective Horizon for black holes in Gravity's Rainbow
Ali, A. F., Faizal, M., & Majumder, B. (2015) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/109/20001 · Cited by 104 · see citing works
Regularization of the singular inverse square potential in quantum mechanics with a minimal length
Bouaziz, D., & Bawin, M. (2007) · Physical Review A · doi:10.1103/physreva.76.032112 · Cited by 102 · see citing works
SPACE–TIME IN LIGHT OF KÁROLYHÁZY UNCERTAINTY RELATION
Maziashvili, M. (2007) · International Journal of Modern Physics D · doi:10.1142/s0218271807010870 · Cited by 104 · see citing works
Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality
Ng, Y. J. (2008) · Entropy · doi:10.3390/e10040441 · Cited by 159 · see citing works
Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal
El‐Nabulsi, R. A. (2018) · Journal of Statistical Physics · doi:10.1007/s10955-018-2116-8 · Cited by 99 · see citing works
The Casimir effect in the presence of a minimal length
Harbach, U., & Hossenfelder, S. (2005) · Physics Letters B · doi:10.1016/j.physletb.2005.10.045 · Cited by 99 · see citing works
Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums
Bushev, P. A., Bourhill, J., Goryachev, M., et al. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.066020 · Cited by 97 · see citing works
Quantum gravity and recovery of information in black hole evaporation
Nozari, K., & Mehdipour, S. H. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/84/20008 · Cited by 97 · see citing works

Authors: GARAY, L. J.
Affiliations: Imperial College London (GB)
Corresponding author: GARAY, LUIS J.
Venue: International Journal of Modern Physics A
Publisher: World Scientific Pub Co Pte Ltd
Published: 1995-01-20
Volume: 10
Issue: 02
Pages: 145-165
ISSN: 0217-751X (ISSN-L)
1793-656X
DOI: 10.1142/s0217751x95000085
OpenAlex: W2170399496
Cited by: 1,371
References: 99
Citations by year: 2026: 45 · 2025: 66 · 2024: 57 · 2023: 69 · 2022: 68 · 2021: 81 · 2020: 61 · 2019: 63 · 2018: 46 · 2017: 62 · 2016: 90 · 2015: 66 · 2014: 64 · 2013: 66 · 2012: 55
FWCI: 11.29
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: International Journal of Modern Physics A (publishedVersion)
arXiv (Cornell University) (publishedVersion)
arXiv (Cornell University)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords: quantum gravity, minimal length, fundamental length scale, position measurement, quantum mechanics, special relativity, general relativity, causality, discrete spacetime

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

QUANTUM GRAVITY AND MINIMUM LENGTH

Abstract

Integrity signals

Claims the paper makes

Claims other papers make about this one

Self-check

Cites

Cited by

Record

About these checks