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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.
Verified 2026-10-06 · 8 references not checked yet
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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.
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17 Own interpretation · 16 No basis given · 10 Not checked yet · 1 Supported · 1 Own result
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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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.”
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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.”
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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.”
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In the paper
“in the model considered it is violated.”
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In the paper
“This quantity averages out to zero in a first approximation, since one is summing over an isotropic set of vertices.”
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In the paper
“the correction is symmetrical in both fields, but is not Lorentz covariant.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“In the example considered we see that this invariance is broken simultaneously with parity invariance.”
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In the paper
“We have therefore found a correction to the Maxwell Hamiltonian arising from the discrete nature of the weave construction.”
plaindirect- Asserted: passes — The authors put it forward as true.
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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,”
plainconditional- Asserted: passes — The authors put it forward as true.
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- 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
Every source the paper cites for this claim was checked and supports it.
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
- Supportedcites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
The paper says that at least some GRBs are at cosmological distances and that their emissions are sensitive to possible departures from conventional electromagnetic-wave propagation (p. 1). It explains that a small departure can become observable when light travels a very long distance, making GRBs particularly promising for such tests (p. 3). (LLM, conf=0.92)
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It may state two separate claims as one.
- Supported
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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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It 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).”
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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.”
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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
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably 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
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably 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
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Probably not a substantial 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
“This already suggests that there will be modifications to the usual dispersion relation for light propagation.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“If one were to assume that the weaves are parity-invariant, the term would vanish.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably 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
hedged- Asserted: passes — The authors put it forward as true.
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It 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
plain- Asserted: passes — The authors put it forward as true.
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It 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
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably 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).”
plain- Asserted: passes — The authors put it forward as true.
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It 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.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It 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.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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- Based: fails — The paper may give no reason why it holds.
Probably 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
plain- Asserted: passes — The authors put it forward as true.
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Probably 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
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Aranda, J. I., Ramírez–Zavaleta, F., Tlachino, F. J., Toscano, J. J., & Tututi, E. S. (2014) · International Journal of Modern Physics A · doi:10.1142/s0217751x14501802 · Cited by 14
Experimental search for a Lorentz invariant spacetime granularity: Possibilities and bounds
Aguilar, P. M., Sudarsky, D., & Bonder, Y. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.064007 · Cited by 14
Rainbow Gravity Corrections to the Entropic Force
Feng, Z.-W., & Yang, S.-Z. (2018) · Advances in High Energy Physics · doi:10.1155/2018/5968284 · Cited by 14
Gravitational searches for Lorentz violation with ultracold neutrons
Escobar, C. A., & Martín-Ruiz, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.075032 · Cited by 14
Bernardini, A. E., & da Rocha, R. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/81/40010 · Cited by 14
Lorentz violation and Faddeev-Popov ghosts
Altschul, B. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.045004 · Cited by 15
Neutrino oscillations and Lorentz invariance breakdown
Lambiase, G. (2003) · Physics Letters B · doi:10.1016/s0370-2693(03)00379-4 · Cited by 14
Observational Constraints on Local Lorentz Invariance
Bluhm, R. (2014) · Springer handbooks · doi:10.1007/978-3-642-41992-8_23 · Cited by 21
Effective dissipative dynamics for polarized photons
Benatti, F., & Roberto Floreanini, B. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.125009 · Cited by 14
Lepton-Flavor Violating Decays as Probes of Quantum Gravity?
Silagadze, Z. K. (2001) · Physica Scripta · doi:10.1238/physica.regular.064a00128 · Cited by 14
Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
Carmona, J. M., Cortés, J. L., Pereira, L., & Relancio, J. J. (2020) · Symmetry · doi:10.3390/sym12081298 · Cited by 13
“In particular, quantum gravity models generically predict [1–15] deformations of the kinematics of special relativity in processes involving particles of sufficiently high energy, where this energy has to be compared with the high-energy scale Λ that controls this deformation (disappearing in the limit Λ→ ∞), which is…”
BackgroundLorentz Invariance Violation from Gamma-Ray Bursts
Song, H. C., & Ma, B.-Q. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/adb8d4 · Cited by 13
Hermitian realizations of κ-Minkowski space–time
Kovačević, D., Meljanac, S., Samsarov, A., & Škoda, Z. (2015) · International Journal of Modern Physics A · doi:10.1142/s0217751x15500190 · Cited by 13
Electromagnetism with dimension-five operators
Campanelli, L. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.105014 · Cited by 13
A small mission featuring an imaging x-ray polarimeter with high sensitivity
Weisskopf, M. C., Baldini, L., Bellazini, R., Brez, A., Costa, E., Dissly, R., Elsner, R. F., Fabiani, S., Matt, G., Minuti, M., et al. (2013) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2024473 · Cited by 13
“5% on Crab) Gas mixture 1-cm, 1-bar He-DME (20-80) Energy range 2–6 keV Crab rate 486 ct/s (3 mirror modules & GPDs) Background (point sources) 3.”
BackgroundTesting relativity with neutrinos
Altschul, B. (2009) · Journal of Physics Conference Series · doi:10.1088/1742-6596/173/1/012003 · Cited by 13
Carle, A., Chanon, N., & Perriès, S. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-7715-2 · Cited by 13
Novel features of Schwarzschild-like black hole of Lorentz violating bumblebee gravity
Izmailov, R. N., & Nandi, K. K. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac8fda · Cited by 12
“LV was first envisaged in the context of string theory [2–5], non-commutativefield theories [6] or loop quantum gravity [7, 8].”
An application of Lorentz-invariance violation in black hole thermodynamics
Li, G.-P., Pu, J., Jiang, Q.-Q., & Zu, X.-T. (2017) · The European Physical Journal C · doi:10.1140/epjc/s10052-017-5220-z · Cited by 12
Cañate, P., Ramírez, E., & Sudarsky, D. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/08/043 · Cited by 12
Particle processes in a discrete spacetime and GW170814 event
Roushan, M., & Nozari, K. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-6714-7 · Cited by 13
Dimensional reduction of the electromagnetic sector of the nonminimal standard model extension
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Impact of relativity on particle localizability and ground state entanglement
Papageorgiou, M., & Pye, J. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab3593 · Cited by 14
“Here we consider the non-relativistic dispersion relation as an approximation to the relativistic one, but many of the conclusions would qualitatively hold for quantum field theories with more general dispersion relations, as occur with condensed matter systems, sonic analogues [20,21], and quantum gravity inspired ef…”
Addazi, A., & Marcianò, A. (2020) · International Journal of Modern Physics A · doi:10.1142/s0217751x20420038 · Cited by 13
Gamma-Ray Bursts as Probes for Quantum Gravity
Piran, T. (2005) · Springer eBooks · doi:10.1007/11377306_10 · Cited by 13
Chiral bosonization for non-commutative fields
Das, A., Gamboa, J., ndez, F. M., & n, J. L. P.-S. (2004) · Journal of High Energy Physics · doi:10.1088/1126-6708/2004/05/022 · Cited by 13
CERENKOV'S EFFECT AND NEUTRINO OSCILLATIONS IN LOOP QUANTUM GRAVITY
Lambiase, G. (2003) · Modern Physics Letters A · doi:10.1142/s0217732303009538 · Cited by 13
Emergent spacetimesPreprint
Weinfurtner, S. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0711.4416 · Cited by 25
“There are many different quantum gravity models that suggest the violation of Lorentz symmetry at ultraviolet scales, for example string theory [119, 69], wraped brane worlds [37], and loop quantum gravity [78].”
BackgroundOPERA SUPERLUMINAL NEUTRINOS AND KINEMATICS IN FINSLER SPACETIME
Chang, Z., LI, X., & WANG, S. (2012) · Modern Physics Letters A · doi:10.1142/s0217732312500587 · Cited by 12
Spontaneous Lorentz violation and asymptotic flatness
Bonder, Y., & Peterson, C. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.104016 · Cited by 12
Search for Lorentz-invariance violation with the first KATRIN data
Aker, M., Batzler, D., Beglarian, A., Behrens, J., Berlëv, A. I., Besserer, U., Bieringer, B., Block, F., Bobien, S., Bornschein, B., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.082005 · Cited by 15
Lorentz Breaking Effective Field Theory and Observational Tests
Liberati, S. (2013) · Lecture notes in physics · doi:10.1007/978-3-319-00266-8_13 · Cited by 12
HIGH ENERGY NEUTRINO OSCILLATION AT THE PRESENCE OF THE LORENTZ INVARIANCE VIOLATION
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Decay b→sγ in the presence of a constant antisymmetric tensor field
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Implications of Lorentz violation on Higgs-mediated lepton flavor violation
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Renormalization in a Lorentz-violating model and higher-order operators
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Why Cerenkov Radiation May Not Occur, Even When It Is Allowed by Lorentz-Violating Kinematics
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The thermodynamics and phase transition of a rainbow black hole
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Loop Quantum Gravity and planck Scale Phenomenology
Smolin, L. (2005) · Springer eBooks · doi:10.1007/11377306_11 · Cited by 11
“There are in the literature a number of proposals for candidates for the ground state, for both vanishing and small positive or negative Λ [31, 32, 33, 34, 35].”
BackgroundEikonal equation of the Lorentz-violating Maxwell theory
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Global defects in theories with Lorentz symmetry violation
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Gravitation as deduced from submicroscopic quantum mechanicsPreprint
Krasnoholovets, V. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0205196 · Cited by 12
“Semi-classical space-time is emerged in canonical quantum gravity in the loop presentation as a polymer-like structure at microscales, which allows a possible correction to the Maxwell equations caused by quantum gravity [ 30 ].”
BackgroundFundamental Physics in Space: A guide to present projects
Lämmerzahl, C., & Dittus, H. (2002) · Annalen der Physik · doi:10.1002/1521-3889(200202)11:2 · Cited by 13
XPOL: a photoelectric polarimeter onboard XEUSPreprint
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Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime
Giovanni Amelino-camelia, A., Frattulillo, D., Gubitosi, G., Rosati, G., & Bedić, S. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/01/070 · Cited by 11
“In some scenarios (LIV) relativistic invariance is broken [4–6], giving rise to a preferred frame, while in other scenarios (DSR) relativistic invariance is merely deformed [7–9], preserving the equivalence of reference frames but requiring a deformation of relativistic laws of transformation among…”
Super-entropy bumblebee AdS black holes
Panah, B. E. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139273 · Cited by 11
Lorentz invariance violation and simultaneous emission of electromagnetic and gravitational waves
Passos, E., Anacleto, M. A., Brito, F. A., Holanda, O., Souza, G. B., & Zarro, C. A. D. (2017) · Physics Letters B · doi:10.1016/j.physletb.2017.07.064 · Cited by 11
Black holes, Planckian granularity, and the changing cosmological ‘constant’
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Skewon modification of the light cone structure
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Planck-scale traces from the interference pattern of two Bose-Einstein condensates
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Review of the Multimessenger Working Group at UHECR-2012
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Causal sets and conservation laws in tests of Lorentz symmetry
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PERSPECTIVES ON QUANTUM GRAVITY PHENOMENOLOGY
Sudarsky, D. (2005) · International Journal of Modern Physics D · doi:10.1142/s0218271805008145 · Cited by 11
Lorentz violation naturalness revisited
Belenchia, A., Gambassi, A., & Liberati, S. (2016) · Journal of High Energy Physics · doi:10.1007/jhep06(2016)049 · Cited by 11
One-loop structure of the photon propagator in the standard model extension
Hernández-Juárez, A. I., Montaño, J., Novales-Sánchez, H., Salinas, M., Toscano, J. J., & Vázquez-Hernández, O. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.013002 · Cited by 11
“Explicit or spontaneous LV has been studied in the context of string theory [2], noncommutative geometry [3], loop quantum gravity [4], cosmologically varying scalar [5], random-dynamics models [6], Horava-Lifshitz theories [7], and brane-world scenarios [8].”
BackgroundRay, S., Panda, A., Majumder, B., Islam, M. R., & Manna, G. (2022) · Chinese Physics C · doi:10.1088/1674-1137/ac8868 · Cited by 11
A review of one-way and two-way experiments to test the isotropy of the speed of light
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One-loop renormalization of Lorentz and CPT -violating scalar field theory in curved spacetime
Netto, T. D. P. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.055048 · Cited by 12
“As examples, we can cite quantum effects in string theory [1] and loop quantum gravity [2], geometrical effects as noncommutativity [3], torsion [4], and nonmetricity [5]; and so on [6].”
MethodConstraints on Lorentz Invariance Violation from Optical Polarimetry of Astrophysical Objects
Kislat, F. (2018) · Symmetry · doi:10.3390/sym10110596 · Cited by 11
Reis, J. A. A. S., & Schreck, M. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.095029 · Cited by 13
Bernardini, A. E. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.097901 · Cited by 11
Noncommutative electrodynamics and ultra-high-energy gamma rays
Castorina, P., & Zappalà, D. (2003) · Europhysics Letters (EPL) · doi:10.1209/epl/i2003-00276-4 · Cited by 11
Trimble, V., & Aschwanden, M. J. (2001) · Publications of the Astronomical Society of the Pacific · doi:10.1086/322844 · Cited by 11
Corrections to scattering processes due to minimal measurable length
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Bumblebee gravity: Spherically symmetric solutions away from the potential minimum
Bailey, Q. G., Murray, H. S., & Walter-Cardona, D. T. (2025) · Physical review. D/Physical review. D. · doi:10.1103/nkbj-vbjf · Cited by 11
“Since the 1990s, there has been substantial work on experimental and observational searches for hypothetical spacetime-symmetry breaking [19, 20], motivated by theoretical scenarios in which it could arise [21– 25].”
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Bluhm, R., & Yu, Z. (2023) · Symmetry · doi:10.3390/sym16010025 · Cited by 14
Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetry
Escobar, C. A., & Potting, R. (2020) · International Journal of Modern Physics A · doi:10.1142/s0217751x20501742 · Cited by 10
Dong, Y., Wang, Z., & Shao, L. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.084024 · Cited by 10
Bouncing universe with modified dispersion relation
Pan, W.-J., & Huang, Y.-C. (2016) · General Relativity and Gravitation · doi:10.1007/s10714-016-2138-y · Cited by 11
Do high-energy neutrinos travel faster than photons in a discrete space–time?
Xue, S.-S. (2011) · Physics Letters B · doi:10.1016/j.physletb.2011.11.001 · Cited by 12
Projective interpretation of some doubly special relativity theories
Jafari, N., & Shariati, A. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.065038 · Cited by 10
“For example, in some approaches to quantum gravity the spacetime has a polymer-like structure [1], in some the spacetime is non-commutative [2], and in some the spacetime has extra dimensions [3], though there are experimental and observational limits on such violations [4].”
BackgroundTime delay of light signals in an energy-dependent spacetime metric
Grillo, A. F., Luzio, E., & Méndez, F. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.104033 · Cited by 10
The deformation-stability fundamental length and deviations from c
Mendes, R. V. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.04.038 · Cited by 10
Cosmic-ray fermion decay through tau-antitau emission with Lorentz violation
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Photon emission and decay from generic Lorentz invariance violation
Martínez-Huerta, H., & Pérez-Lorenzana, A. (2017) · Journal of Physics Conference Series · doi:10.1088/1742-6596/866/1/012006 · Cited by 10
Decays Z → γγ and Z → gg in the Standard Model Extension
Castro-Medina, J., Novales-Sánchez, H., Toscano, J. J., & Tututi, E. S. (2015) · International Journal of Modern Physics A · doi:10.1142/s0217751x15502164 · Cited by 10
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
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