The DOI matches its Crossref record; 6 of the 14 references it cites were found in a registry or an index, and 8 are not checked yet; none of the 11 sources its claims cite is checked for support yet.
Nonstandard optics from quantum space-time
Open accessAbstract
We study light propagation in the picture of semiclassical space-time that emerges in canonical quantum gravity in the loop representation. In such a picture, where space-time exhibits a polymerlike structure at microscales, it is natural to expect departures from the perfect nondispersiveness of an ordinary vacuum. We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity and showing that under certain circumstances nonvanishing corrections appear that depend on the helicity of propagating waves. These effects could lead to observable cosmological predictions of the discrete nature of quantum space-time. In particular, recent observations of nondispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semiclassical state that describes the universe.
Checked 2026-10-06 · 8 references not checked yet
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper computes quantum-gravity corrections to Maxwell propagation in a loop-quantum-gravity weave state and finds a helicity-dependent birefringence, with a group-velocity splitting of order one Planck length per wavelength. The effect is parity-violating and could be constrained by gamma-ray-burst observations, though the predicted delay is about two orders of magnitude below current sensitivity.
Key findings
- Loop quantum gravity’s polymer-like semi-classical spacetime can modify Maxwell’s equations by a term proportional to the Laplacian of the fields, producing helicity-dependent propagation and “intrinsic birefringence.”
- The correction is rotationally invariant but parity-violating; it vanishes if the weave is parity-invariant or if regions of size Δ have random orientations in parity violation.
- For a gamma-ray burst at about \(10^{10}\) light years and frequencies of order 200 keV, the delay between the two polarization group velocities is \(10^{-5}\) s, while observed burst widths are about 0.1 s with features as small as 1 ms, leaving observations two orders of magnitude away.
- The effect is distinct from other quantum-gravity dispersion proposals because it is helicity-dependent and absent for scalar fields; the shift is of order one Planck length per wavelength.
Methods
- Theoretical calculation in canonical loop quantum gravity: Maxwell fields are treated as close to coherent states approximating a classical travelling wave of wavelength λ much larger than the Planck length, while gravity is in a weave state \(|Δ\rangle\) approximating flat geometry on scales larger than Δ.
- The Hamiltonian constraint coupling Maxwell fields to gravity is regulated using Thiemann’s proposal for the metric divided by the determinant, with point-splitting and expansion of the electric field around a central point P in Δ/λ.
- Summing over weave vertices yields a leading rotational-invariant, parity-violating correction \(\chi \epsilon_{abc} \ell_P/\Delta\); modified Maxwell equations are then combined to seek helicity solutions and derive two group-velocity branches.
Limitations
- The paper states that there is no agreement on a precise dynamics for loop quantum gravity, no detailed prescription for constructing the semi-classical limit, and the discussion is intentionally loose.
- It states that weave states are not yet fully constructed in the spin network representation, and the predicted effects depend on the type of semi-classical state chosen.
- The paper states it does not present a detailed calculation of the magnitude of the effects; it also notes the observational delay is two orders of magnitude below current burst timing sensitivity.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 11 cited sources checked · 0 supported · 0 flagged
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity, and showing that under certain circumstances, non-vanishing corrections appear that depend on the helicity of propagating waves.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The group velocity has two branches, and the effect is of the order of a shift of one Planck length per wavelength.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As we see the equations gain a correction proportional to the Laplacian ∆ 2 of the fields, the correction is symmetrical in both fields, but is not Lorentz covariant.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It should be noticed that the additional term we found is rotationally invariant, i.e., it respects the original spirit of the weave construction.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“in the model considered it is violated.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This quantity averages out to zero in a first approximation, since one is summing over an isotropic set of vertices.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“the correction is symmetrical in both fields, but is not Lorentz covariant.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the example considered we see that this invariance is broken simultaneously with parity invariance.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We have therefore found a correction to the Maxwell Hamiltonian arising from the discrete nature of the weave construction.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Assuming a non-parity invariant weave, the resulting equations of motion from the above Hamiltonian can be viewed as corrections to the Maxwell equations,”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The weave is non-parity invariant.
- It may state two separate claims as one. 9
- Probably not a substantial claim. 7
- The quote only partly states this claim. 2
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We therefore see the emergence of a birefringence effect, associated with quantum gravity corrections. The group velocity has two branches, and the effect is of the order of a shift of one Planck length per wavelength.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We consider the leading contribution to this term, which should be a rotational invariant tensor of three indices, i.e., it is given by χǫ abc ℓ P / ∆ with χ a proportionality constant of order one (that can be positive or negative).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Due to the definition of the weave state, the sum just yields the classical metric and we recover the usual Maxwell Hamiltonian in flat space.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“in reference [1] it was shown that the simultaneity of time structures in the patterns of light received gamma ray bursts are possible candidates to set limits on these models.”
What the sources say
- Not checked yetcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“Various models of string quantum gravity imply dispersive frequency wavelength relations for light propagation”
What the sources say
- Not checked yetcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“This kinematic framework is widely accepted throughout various formulations of the theory, and has led to several physical predictions associated with the 'polymer-like' structure of quantum space-time [4].”
What the sources say
- Not checked yetcites [4] A. Ashtekar, J. Lewandowski, Class.Quant.Grav. 14 , A55 (1997); Adv. Theor. Math. Phys. 1 , 388 (1998). source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“What these authors point out is that the light coming from gamma-ray bursts travels very large distances before being detected on Earth, and is therefore quite sensitive to departures from orthodox theories.”
What the sources say
- Not checked yetcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This already suggests that there will be modifications to the usual dispersion relation for light propagation.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If one were to assume that the weaves are parity-invariant, the term would vanish.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“The observed width of the bursts appears to be of the order of 0 . 1 s , with features like a rising edge as small as 1 ms .”
What the sources say
- Not checked yetcites [2] C. Bhat et al, Nature, 359 , 217 (1992); J. Scargle, J. Norris, J. Bonnell, astro-ph/9712016. source
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“If we compare with the proposals considered by Amelino-Camelia et al [1], in their case they find only a change in the dispersion relation, whereas here we in addition see a helicity-dependent effect.”
What the sources say
- Not checked yetcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“This is in line with the observations of ref. [1], that quantum gravity effects will increase with the frequency, the opposite being expected for other more standard sources of cosmological dispersion or birefringence.”
What the sources say
- Not checked yetcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our effect is also absent for scalar fields, whereas other quantum gravity corrections are all-encompassing (they can be viewed as corrections to quantum mechanics itself).”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is because the kind of corrective terms we are introducing in Maxwell theory, although linear in the fields, are higher order in the derivatives.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The term would also vanish -on average- if one assumes that the different regions of size ∆ have 'random orientations' in their parity violation.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
In the paper
“The only feature we will need of these operators is that acting on spin network states they are finite and only give contributions at intersections.”
What the sources say
- Not checked yetcites [7] T. Thiemann, Class. Quan. Grav. 15 , 1281 (1998). source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
The authors state this as an assumption.
The Maxwell fields operate as classical fields at the level of equations of motion.
“we will assume that the Maxwell fields operate as classical fields at the level of equations of motion”
The authors state this as an assumption.
The coherent state chosen approximates a classical travelling wave of wavelength λ, and λ is much larger than the Planck length.
“The coherent state chosen will be one that approximates a classical travelling wave of wavelength λ , which we assume to be much larger than the Planck length.”
The authors state this as an assumption.
The gravitational degrees of freedom are in a 'weave' state |Δ>.
“For the gravitational degrees of freedom we will assume we are in a 'weave' state [8] | ∆ > , such that,”
The authors state this as an assumption.
The weave considered approximates a flat geometry for lengths larger than Δ.
“The weave we will consider approximates a flat geometry for lengths larger than ∆.”
The authors state this as an assumption.
The weave is non-parity invariant.
“Assuming a non-parity invariant weave, the resulting equations of motion from the above Hamiltonian can be viewed as corrections to the Maxwell equations,”
The authors state this as an assumption.
Rotational invariance is locally preserved in the construction of the weave.
“In the construction of the weave, we have assumed that rotational invariance is locally preserved.”
The paper relies on this without support.
The universe is non-parity invariant.
“The fact that we live in a non-parity invariant universe suggests that parity invariant weaves might not necessarily be the most natural ones to consider in constructing a semiclassical state of cosmological interest.”
The paper relies on this without support.
The coupling term in the Hamiltonian constraint is the usual E^2+B^2 term in a curved background.
“The term in the Hamiltonian constraint coupling Maxwell fields to gravity is the usual ' E 2 + B 2 ' term, but in a curved background,”
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 the citing paper
“In the absence of detailed formulations, certain early pioneering model calculations [192] (see also general treatment [340, 341]) indicate the possibility for certain Lorentz-invariance-violation (LIV) effects associated to a quantum-gravity granularity of spacetime measured at rest by a preferred frame of observers.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [192]
Citations
Cites
Lorentz-violating extension of the standard model
Colladay, D., & Kostelecký, V. A. (1998) · Physical Review D · doi:10.1103/physrevd.58.116002 · Cited by 2,403
Tests of quantum gravity from observations of γ-ray bursts
Amelino-Camelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, D. V., & Sarkar, S. (1998) · Nature · doi:10.1038/31647 · Cited by 1,430
Quantum geometry and black hole entropy
Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105
Quantum theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852
Quantum theory of geometry II: Volume operators
Ashtekar, A., & Lewandowski, J. (1997) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1997.v1.n2.a8 · Cited by 580
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/012 · Cited by 416
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
Evidence for sub-millisecond structure in a γ-ray burst
Bhat, P. N., Fishman, G. J., Meegan, C. A., Wilson, R. B., Brock, M. N., & Paciesas, W. S. (1992) · Nature · doi:10.1038/359217a0 · Cited by 92
ON THE CONSISTENCY OF THE CONSTRAINT ALGEBRA IN SPIN NETWORK QUANTUM GRAVITY
GAMBINI, R., LEWANDOWSKI, J., MAROLF, D., & PULLIN, J. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000103 · Cited by 77
Self-citationLOOP CONSTRAINTS: A HABITAT AND THEIR ALGEBRA
LEWANDOWSKI, J., & MAROLF, D. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000231 · Cited by 76
Flagged first, then by citations
Research works printed but not linked: 1
- J. Iwasaki, 1993, Int. J. Mod. Phys. D, 1, 53
Cited by
Sorted by citations
Lorentz Invariance with an Invariant Energy Scale
Magueijo, J., & Smolin, L. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.190403 · Cited by 1,226
Barceló, C., Liberati, S., & Visser, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-12 · Cited by 1,163
“Interest in this question is reinforced by a specific analysis in the “loop quantum gravity” approach to quantizing gravity that points towards the the existence of fundamental MDR at high energies [135].”
BackgroundModern Tests of Lorentz Invariance
Mattingly, D. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-5 · Cited by 1,061
“The possibility of four-dimensional Lorentz invariance violation has been investigated in different quantum gravity models (including string theory [185, 107], warped brane worlds [70], and loop quantum gravity [120]), although no quantum gravity model predicts Lorentz violation conclusively.”
BackgroundTestable scenario for relativity with minimum length
Giovanni Amelino-camelia, A. (2001) · Physics Letters B · doi:10.1016/s0370-2693(01)00506-8 · Cited by 803
Quantum-Spacetime Phenomenology
Giovanni Amelino-camelia, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-5 · Cited by 886
“[247, 33]), there are some candidate mechanisms (see, e.”
BackgroundMethodInfluentialGeneralized Lorentz invariance with an invariant energy scale
Magueijo, J., & Smolin, L. (2003) · Physical Review D · doi:10.1103/physrevd.67.044017 · Cited by 691
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677
“In the absence of detailed formulations, certain early pioneering model calculations [192] (see also general treatment [340, 341]) indicate the possibility for certain Lorentz-invariance–violation (LIV) effects associated to a quantum-gravity granularity of spacetime measured at rest by a preferred frame of observers.”
BackgroundBarceló, C., Liberati, S., & Visser, M. (2011) · Living Reviews in Relativity · doi:10.12942/lrr-2011-3 · Cited by 598
Martin Bojowald, A. (2005) · Living Reviews in Relativity · doi:10.1142/9789812700988_0014 · Cited by 628
Ultraviolet Modifications of Dispersion Relations in Effective Field Theory
Myers, R. C., & Pospelov, M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.211601 · Cited by 499
Electrodynamics with Lorentz-violating operators of arbitrary dimension
Kostelecký, V. A., & Mewes, M. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.015020 · Cited by 518
Bojowald, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-11 · Cited by 723
“This can be used to study modified dispersion relations to the extent that the result agrees with preliminary calculations performed in the full theory [115, 3, 4, 181, 182] even at a quantitative level.”
Quantum Gravity Corrections to Neutrino Propagation
Alfaro, J., Morales-Técotl, H. A., & Urrutia, L. F. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2318 · Cited by 522
Quantum gravity: a progress report
Carlip, S. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/8/301 · Cited by 449
Tests of Lorentz invariance: a 2013 update
Liberati, S. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/13/133001 · Cited by 492
Quantum gravity phenomenology at the dawn of the multi-messenger era—A review
Addazi, A., Álvarez-Muñiz, J., Batista, R. A., Giovanni Amelino-camelia, A., Antonelli, V., Arzano, M., Asorey, M., Atteia, J. L., Bahamonde, S., Bajardi, F., et al. (2022) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2022.103948 · Cited by 580
Amelino-Camelia, G., & Piran, T. (2001) · Physical Review D · doi:10.1103/physrevd.64.036005 · Cited by 375
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
“[6] appeared, Gambini and Pullin [7] argued that semiclassical loop quantum gravity suggests just such LV. 2 Following this work, a very strong constraint on photon birefringence was obtained by Gleiser and Kozameh [42] using UV light from distant galaxies.”
BackgroundLoop quantum gravity and light propagation
Alfaro, J., Morales-Técotl, H. A., & Urrutia, L. F. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.103509 · Cited by 366
Lorentz Invariance and Quantum Gravity: An Additional Fine-Tuning Problem?
Collins, J., Perez, A., Sudarsky, D., Urrutia, L., & Vucetich, H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.191301 · Cited by 312
Modern Michelson-Morley Experiment using Cryogenic Optical Resonators
Müller, H., Herrmann, S., Braxmaier, C., Schiller, S., & Peters, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.020401 · Cited by 311
Carlo Rovelli, C. (2006) · The frontiers collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 504
DOUBLY-SPECIAL RELATIVITY: FIRST RESULTS AND KEY OPEN PROBLEMS
Giovanni Amelino-camelia, A. (2002) · International Journal of Modern Physics D · doi:10.1142/s021827180200302x · Cited by 292
A strong astrophysical constraint on the violation of special relativity by quantum gravity
Jacobson, T., Liberati, S., & Mattingly, D. (2003) · Nature · doi:10.1038/nature01882 · Cited by 277
“Several approaches to quantum gravity, however, suggest that there may be a Lorentz violating microscopic structure of spacetime, for example discreteness [1], non-commutativity [2], or extra dimensions [3].”
BackgroundNew varying speed of light theories
Magueijo, J. (2003) · Reports on Progress in Physics · doi:10.1088/0034-4885/66/11/r04 · Cited by 314
Biller, S. D., Breslin, A. C., Buckley, J., Catanese, M., Carson, M., Carter-Lewis, D. A., Cawley, M. F., Fegan, D. J., Finley, J. P., Gaidos, J. A., et al. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.2108 · Cited by 269
Lorentz violation at high energy: concepts, phenomena and astrophysical constraintsPreprint
Ted Jacobson, A., Liberati, S., & Mattingly, D. (2005) · Cited by 266
Hawking radiation as tunneling through the quantum horizon
Arzano, M., Medved, A. J. M., & Vagenas, E. C. (2005) · Journal of High Energy Physics · doi:10.1088/1126-6708/2005/09/037 · Cited by 265
Lectures on Loop Quantum GravityPreprint
Thiemann, T. (2003) · Cited by 286
Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
Giovanni Amelino-camelia, A. (2010) · Symmetry · doi:10.3390/sym2010230 · Cited by 257
Exact Schwarzschild-like solution in a bumblebee gravity model
Casana, R., Cavalcante, A., Poulis, F. P., & Santos, A. C. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.104001 · Cited by 309
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 276
“A succinct list includes: arguments based on string field theory tensor VEVs [10], cosmologically varying moduli scenarios [11], spacetime foam models [12], semiclassical spin-network calculations in Loop QG [13, 14], as well as non-commutative geometry studies [15, 16, 17, 18] and some brane-world scenarios [19].”
BackgroundBlack-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
Jacobson, T., Liberati, S., & Mattingly, D. (2003) · Physical Review D · doi:10.1103/physrevd.67.124011 · Cited by 240
Precision Measurement of the Hydrogen 1 S − 2 S Frequency via a 920-km Fiber Link
Matveev, A., Parthey, C. G., Predehl, K., Alnis, J., Beyer, A., Holzwarth, R., Udem, T., Wilken, T., Kolachevsky, N., Abgrall, M., et al. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.230801 · Cited by 228
A Search in Gamma‐Ray Burst Data for Nonconstancy of the Velocity of Light
Ellis, J. R., Farakos, K., Mavromatos, N. E., Mitsou, V. A., & Nanopoulos, D. V. (2000) · The Astrophysical Journal · doi:10.1086/308825 · Cited by 226
“Another possible example of such behavior has been proposed within a canonical approach to quantum gravity (Gambini & Pullin 1999), and it has also been observed that quantum Ñuctuations in the light cone are to be expected (Yu & Ford 1999).”
BackgroundQuantum symmetry, the cosmological constant and Planck-scale phenomenology
Amelino-Camelia, G., Smolin, L., & Starodubtsev, A. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/13/002 · Cited by 228
Albert, J., Aliu, E., Anderhub, H., Antonelli, L. A., Antoranz, P., Backes, M., Baixeras-Aiguabella, C., Barrio, J. A., Bartko, H., Bastieri, D., et al. (2008) · Physics Letters B · doi:10.1016/j.physletb.2008.08.053 · Cited by 222
Rosi, G., D’Amico, G., Cacciapuoti, L., Sorrentino, F., Prevedelli, M., Zych, M., Brukner, Č., & Tino, G. M. (2017) · Nature Communications · doi:10.1038/ncomms15529 · Cited by 217
Robust limits on Lorentz violation from gamma-ray bursts
Ellis, J. R., Mavromatos, N. E., Nanopoulos, D. V., Sakharov, A., & Sarkisyan, E. K. G. (2006) · Astroparticle Physics · doi:10.1016/j.astropartphys.2006.04.001 · Cited by 215
Probing the structure of space-time with cosmic rays
Aloisio, R., Pasquale Blasi, A., Ghia, P. L., & Grillo, A. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.053010 · Cited by 213
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
Gauge field theory coherent states (GCS): I. General properties
Thiemann, T. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/11/304 · Cited by 272
Quantum tests of the Einstein Equivalence Principle with the STE–QUEST space mission
Altschul, B., Bailey, Q. G., Blanchet, L., Bongs, K., Bouyer, P., Cacciapuoti, L., Capozziello, S., Gaaloul, N., Giulini, D., Hartwig, J., et al. (2015) · Advances in Space Research · doi:10.1016/j.asr.2014.07.014 · Cited by 204
TeV astrophysics constraints on Planck scale Lorentz violation
Jacobson, T., Liberati, S., & Mattingly, D. (2002) · Physical Review D · doi:10.1103/physrevd.66.081302 · Cited by 204
Searching for C P T Violation with Cosmic Microwave Background Data from WMAP and BOOMERANG
Feng, B., Li, M., Xia, J., Chen, X., & Zhang, X. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.221302 · Cited by 190
Allmendinger, F., Heil, W., Karpuk, S., Kilian, W., Scharth, A., Schmidt, U., Schnabel, A., Sobolev, Y., & Tullney, K. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.110801 · Cited by 188
Rotating optical cavity experiment testing Lorentz invariance at the 10 − 17 level
Herrmann, S., Senger, A., Möhle, K., Nagel, M., Kovalchuk, E. V., & Peters, A. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.105011 · Cited by 198
Cold Atom Clock Test of Lorentz Invariance in the Matter Sector
Wolf, P., Chapelet, F., Bize, S., & Clairon, A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.060801 · Cited by 180
Black holes with a cosmological constant in bumblebee gravity
Maluf, R. V., & Neves, J. C. S. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.044002 · Cited by 176
Giovanni Amelino-camelia, A., Arzano, M., & Procaccini, A. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.107501 · Cited by 174
New varying speed of light theoriesPreprint
Magueijo, J. (2003) · Cited by 197
Uncertainty relation on a world crystal and its applications to micro black holes
Jizba, P., 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 173
New physics from the polarized light of the cosmic microwave background
Komatsu, E. (2022) · Nature Reviews Physics · doi:10.1038/s42254-022-00452-4 · Cited by 164
“Lorentz and CPT breaking terms in the effective Lagrangian can give β ( k ) ∝ k n with n = 1 97 and 2 38,98 .”
BackgroundProspects for constraining quantum gravity dispersion with near term observations
Giovanni Amelino-camelia, A., & Smolin, L. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.084017 · Cited by 162
“Soon after the first papers on the NLSB scenario, Gambini and Pullin produced [7] a first attempt of formalization within low-energy effective field theory.”
BackgroundQuantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light
Ellis, J. R., Mavromatos, N. E., & Nanopoulos, D. V. (2000) · General Relativity and Gravitation · doi:10.1023/a:1001852601248 · Cited by 161
Astrophysical limits on quantum gravity motivated birefringence
Gleiser, R., & Kozameh, C. (2001) · Physical Review D · doi:10.1103/physrevd.64.083007 · Cited by 156
Test of relativistic time dilation with fast optical atomic clocks at different velocities
Reinhardt, S., Saathoff, G., Buhr, H., Carlson, L. A., Wolf, A., Schwalm, D., Karpuk, S., Novotny, C., Huber, G., Zimmermann, M., et al. (2007) · Nature Physics · doi:10.1038/nphys778 · Cited by 154
“In string theory and also in the quest for a quantum theory of gravity, which unifies the standard model of particle physics with general relativity in a ‘theory of everything’, Lorentz violation is frequently assume”
BackgroundLorentz Violation: Motivation and New Constraints
Liberati, S., & Maccione, L. (2009) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev.nucl.010909.083640 · Cited by 155
XIPE: the x-ray imaging polarimetry explorer
Paolo Soffitta, A., Bellazzini, R., Bozzo, E., Burwitz, V., Castro-Tirado, A. J., Costa, E., Courvoisier, T. J.-L., Feng, H., Gburek, S., Goosmann, R. W., et al. (2016) · Space Telescopes and Instrumentation: Ultraviolet to Gamma Ray · doi:10.1117/12.2233046 · Cited by 147
Coherent states for canonical quantum general relativity and the infinite tensor product extension
Sahlmann, H., Thiemann, T., & Winkler, O. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00226-7 · Cited by 168
Gauge Field Theory Coherent States (GCS): I. General Properties
Thiemann, T. (2000) · Cited by 147
McGlynn, S., Clark, D. J., Dean, A. J., Hanlon, L., McBreen, S., Willis, D. R., McBreen, B., Bird, A. J., & Foley, S. (2007) · Astronomy and Astrophysics · doi:10.1051/0004-6361:20066179 · Cited by 145
“GRBs and their afterglows can also be used to place constraints on Quantum Gravity (QG) because of a birefringence effect on photon propagation, caused by the difference in light velocity for the two states of circular polarisation (Gambini & Pullin 1999).”
BackgroundTHERMODYNAMICS OF MODIFIED BLACK HOLES FROM GRAVITY'S RAINBOW
LING, Y., LI, X., & ZHANG, H. (2007) · Modern Physics Letters A · doi:10.1142/s0217732307022931 · Cited by 142
Overview of the Standard Model Extension: Implications and Phenomenology of Lorentz Violation
Bluhm, R. (2006) · Springer eBooks · doi:10.1007/3-540-34523-x_8 · Cited by 148
Quantization ambiguities in isotropic quantum geometry
Martin Bojowald, A. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/20/306 · Cited by 148
“However, if one does not introduce parity violating terms into the semiclassical states used for the calculation [26], the corrections start at second or fourth order [28],”
BackgroundMethodAN INVITATION TO LOOP QUANTUM GRAVITY
Smolin, L. (2004) · International Symposium on Quantum Theory and Symmetries (QTS) · doi:10.1142/9789812702340_0078 · Cited by 185
Loop Quantum Gravity: An Inside View
Thiemann, T. (2007) · Lecture notes in physics · doi:10.1007/978-3-540-71117-9_10 · Cited by 153
“For first steps towards a systematic derivation from LQG see [120, 121].”
BackgroundCharged dilatonic black holes in gravity’s rainbow
Hendi, S. H., Faizal, M., Panah, B. E., & Panahiyan, S. (2016) · The European Physical Journal C · doi:10.1140/epjc/s10052-016-4119-4 · Cited by 136
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
“This departure could also be a result of spacetime [7] discreteness, spontaneous symmetry breaking of Lorentz invariance in string field theory[8], spacetime foam models [9] or spinnetwork in Loop quantum gravity (LQG) [10].”
Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
Thiemann, T., & Winkler, O. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/23/302 · Cited by 149
“In [45] we will explicitly compute the size of this effect from first principles by a down-to-the-ground-computation, thereby significantly improving the results of [ 46 ].”
BackgroundMethodResultInfluentialRemnant 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
“In fact, the modification of the standard energy-momentum dispersion relation seems to be an almost universal feature of all models of quantum gravity, such as spacetime discreteness [9], spontaneous symmetry breaking of Lorentz invariance in string field theory [10], spacetime foam models [11] and spin-network in loo…”
BackgroundAbramowski, A., Acero, F., Aharonian, F., Akhperjanian, A. G., Anton, G., Barnacka, A., de Almeida, U. B., Bazer‐Bachi, A. R., Becherini, Y., Tjus, J. B., et al. (2011) · Astroparticle Physics · doi:10.1016/j.astropartphys.2011.01.007 · Cited by 125
Causal structure and electrodynamics on Finsler spacetimes
Pfeifer, C., & Wohlfarth, M. N. R. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.044039 · Cited by 125
Quantum gravity with a positive cosmological constantPreprint
Smolin, L. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0209079 · Cited by 181
“ightforward toextend these results to photons and other fields, these results will be reported elsewhere. It is very interesting to note that similar corrections have been derived by Gambini and Pullin[83] and by Alfaro, Morales-Tecotl and Urrutia[84] from loop quantum gravity, using a different approach in which they s…”
Observational Bounds on Quantum Gravity Signals using Existing Data
Sudarsky, D., Urrutia, L. F., & Vucetich, H. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.231301 · Cited by 123
XIPE: the X-ray imaging polarimetry explorer
Paolo Soffitta, A., Barcons, X., Bellazzini, R., Braga, J., Costa, E., Fraser, G. W., Gburek, S., Huovelin, J., Matt, G., Pearce, M., et al. (2013) · Experimental Astronomy · doi:10.1007/s10686-013-9344-3 · Cited by 120
Tests of Relativity Using a Cryogenic Optical Resonator
Braxmaier, C., Müller, H., Pradl, O., Mlynek, J., Peters, A., & Schiller, S. (2001) · Physical Review Letters · doi:10.1103/physrevlett.88.010401 · Cited by 120
Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product ExtensionPreprint
Sahlmann, H., Thiemann, T., & Winkler, O. (2001) · Cited by 133
Synchrotron radiation from the Crab Nebula discriminates between models of space–time foam
Ellis, J. R., Mavromatos, N. E., & Sakharov, A. S. (2004) · Astroparticle Physics · doi:10.1016/j.astropartphys.2003.12.001 · Cited by 116
Microscopic recoil model for light-cone fluctuations in quantum gravity
Ellis, J. R., Mavromatos, N. E., & Nanopoulos, D. V. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.027503 · Cited by 117
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
“This deformation of the energy-momentum relation has been predicted from spacetime discreteness [9], spontaneous symmetry breaking of Lorentz invariance in string field theory [10], spacetime foam models [11], spin-network in loop quantum gravity (LQG) [12], non-commutative geometry [13], and Horava-Lifshitz gravity […”
MethodComparison of approaches to quantum correction of black hole thermodynamics
Nozari, K., & Sefiedgar, A. S. (2006) · Physics Letters B · doi:10.1016/j.physletb.2006.02.043 · Cited by 117
Vacuum solutions of a gravity model with vector-induced spontaneous Lorentz symmetry breaking
Orfeu Bertolami, A., & Páramos, J. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.044001 · Cited by 145
Quantum gravity and spin-1/2 particle effective dynamics
Alfaro, J., Morales-Técotl, H. A., & Urrutia, L. F. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.124006 · Cited by 118
Observational limits on quantum geometry effects
Konopka, T. J., & Major, S. A. (2002) · New Journal of Physics · doi:10.1088/1367-2630/4/1/357 · Cited by 112
The Search for Quantum Gravity Signals
Giovanni Amelino-camelia, A. (2005) · AIP conference proceedings · doi:10.1063/1.1900507 · Cited by 122
“This has been attempted for the “Liouville String” scenario [22, 23] as well as for the loop quantum gravity approach [16, 17, 18, 19].”
BackgroundMethodInfluentialModified TOV in gravity's rainbow: properties of neutron stars and dynamical stability conditions
Hendi, S. H., Bordbar, G. H., Panah, B. E., & Panahiyan, S. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/09/013 · Cited by 112
“Such modification is also observed in discrete spacetime [12], spacetime foam [13], spin-network in loop quantum gravity (LQG) [3], ghost condensation [14] and non-commutative geometry [4].”
BackgroundPhenomenology of Planck-scale Lorentz-symmetry test theories
Giovanni Amelino-camelia, A. (2004) · New Journal of Physics · doi:10.1088/1367-2630/6/1/188 · Cited by 111
Tests of Local Lorentz Invariance Violation of Gravity in the Standard Model Extension with Pulsars
Shao, L. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.111103 · Cited by 102
Thermodynamic phase transition of a black hole in rainbow gravity
Feng, Z.-W., & Yang, S.-Z. (2017) · Physics Letters B · doi:10.1016/j.physletb.2017.07.057 · Cited by 107
Improved test of Lorentz invariance in electrodynamics
Wolf, P., Bize, S., Clairon, A., Santarelli, G., Tobar, M. E., & Luiten, A. N. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.051902 · Cited by 108
Hendi, S. H., Panah, B. E., & Panahiyan, S. (2017) · Physics Letters B · doi:10.1016/j.physletb.2017.03.051 · Cited by 105
PHENOMENOLOGY OF DOUBLY SPECIAL RELATIVITY
Giovanni Amelino-camelia, A., Mandanici, G., Procaccini, A., & Kowalski-Glikman, J. (2005) · International Journal of Modern Physics A · doi:10.1142/s0217751x05028569 · Cited by 123
Strong field effects on binary systems in Einstein-aether theory
Foster, B. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.084033 · Cited by 76
Topics in Noncommutative Geometry Inspired Physics
Banerjee, R., Chakraborty, B., Ghosh, S., Mukherjee, P., & Samanta, S. (2009) · Foundations of Physics · doi:10.1007/s10701-009-9349-y · Cited by 104
In vacuo dispersion features for gamma-ray-burst neutrinos and photons
Giovanni Amelino-camelia, A., D’Amico, G., Rosati, G., & Loret, N. (2017) · Nature Astronomy · doi:10.1038/s41550-017-0139 · Cited by 101
“z t M D E z M D E z 1 (1) (1 ) (1) (1 ) (5) off X”
MethodOptical cavity tests of Lorentz invariance for the electron
Müller, H., Herrmann, S., Sáenz, A., Peters, A., & Lämmerzahl, C. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.68.116006 · Cited by 99
Belenchia, A., Carlesso, M., Bayraktar, Ö., Dequal, D., Derkach, I. D., Gasbarri, G., Herr, W., Li, Y. L., Rademacher, M., Sidhu, J. S., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2021.11.004 · Cited by 109
Spacetime foam, CPT anomaly, and photon propagation
Klinkhamer, F. R., & Rupp, C. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.045020 · Cited by 98
Metadata
- Authors
- Gambini, R., & Pullin, J.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1999-05-21
- Volume
- 59
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2594004064
- Semantic Scholar
- 6d77e7089d7b5cc0af79c78c61702a7873eda39c
- Cited by
- 960
- References
- 14
- Citations by year
- 2026: 27 · 2025: 37 · 2024: 35 · 2023: 28 · 2022: 34 · 2021: 35 · 2020: 28 · 2019: 38 · 2018: 45 · 2017: 51 · 2016: 54 · 2015: 39 · 2014: 31 · 2013: 33 · 2012: 41
- FWCI
- 19.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Civil War Book Review (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- quantum spacetime, loop quantum gravity, light propagation, modified dispersion relations, modified Maxwell's equations, gamma-ray bursts, discrete spacetime, cosmological constraints
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.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
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
