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.
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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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Claims the paper makes
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- Findingown data§ Nonstandard optics from quantum spacetime · p. 1
Quantum gravity corrections to Maxwell's equations produce non-vanishing corrections that depend on the helicity of propagating waves under certain circumstances.
“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.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The birefringence effect is of the order of a shift of one Planck length per wavelength.
“The group velocity has two branches, and the effect is of the order of a shift of one Planck length per wavelength.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The corrected Maxwell equations gain a correction proportional to the Laplacian Δ^2 of the fields.
“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.”
Quote in the paperSubstantial claim - Findingnone given§ Nonstandard optics from quantum spacetime · p. 3
The additional term in the Maxwell Hamiltonian is rotationally invariant.
“It should be noticed that the additional term we found is rotationally invariant, i.e., it respects the original spirit of the weave construction.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 4
In the model considered, parity invariance is violated.
“in the model considered it is violated.”
Quote in the paperSubstantial claim
- Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The next-order terms in the Δ/λ expansion average to zero in first approximation because the sum is over an isotropic set of vertices.
“This quantity averages out to zero in a first approximation, since one is summing over an isotropic set of vertices.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The correction is symmetrical in both fields.
“the correction is symmetrical in both fields, but is not Lorentz covariant.”
Quote in the paperNot a substantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 4
In the example considered, Poincaré invariance is broken simultaneously with parity invariance.
“In the example considered we see that this invariance is broken simultaneously with parity invariance.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The discrete nature of the weave construction produces a correction to the Maxwell Hamiltonian.
“We have therefore found a correction to the Maxwell Hamiltonian arising from the discrete nature of the weave construction.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
Assuming a non-parity invariant weave, the equations of motion from the corrected Hamiltonian can be viewed as corrections to Maxwell's equations.
“Assuming a non-parity invariant weave, the resulting equations of motion from the above Hamiltonian can be viewed as corrections to the Maxwell equations,”
Quote in the paperSubstantial claim- The authors state this as an assumption: The weave is non-parity invariant.
- Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The additional term in the Maxwell Hamiltonian is parity violating.
“It is, however, parity violating.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
The correction is not Lorentz covariant.
“the correction is symmetrical in both fields, but is not Lorentz covariant.”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
For a gamma-ray burst at cosmological distances (about 10^10 light years) and frequencies of order 200 keV, the delay between the two group velocities of both polarizations composing a plane wave is 10^-5 s.
“if one considers a gamma-ray-burster at cosmological distances (about 10 10 light years) and frequencies of the order of 200 keV (like the channels of the BATSE detector), this implies a delay between the two group velocities of both polarizations that compose a plane wave of 10 -5 s .”
Quote in the paperSubstantial claim - Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3
With such observations, one is two orders of magnitude away from observing these effects.
“We therefore see that with such observations one is two orders of magnitude away of observing these effects.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
The effects can be used to constrain the type of semi-classical states considered to represent realistic cosmologies, rather than being viewed only as predictions of the theory.
“In a sense, one can turn the argument around and suggest that rather than viewing these effects as a prediction of the theory, they can be used to constrain the type of semi-classical states one considers to represent realistic cosmologies.”
Quote in the paperSubstantial claim - Interpretationnone given§ Nonstandard optics from quantum spacetime · p. 1
The nature of the effects predicted by loop quantum gravity depends on the type of semi-classical state considered.
“We will see however, that the nature of the effects predicted by loop quantum gravity depend on the type of semi-classical state that one considers.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
These effects could lead to observable cosmological predictions of the discrete nature of quantum spacetime.
“These effects could lead to observable cosmological predictions of the discrete nature of quantum spacetime.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
In a semi-classical spacetime with a polymer-like structure at microscales, departures from the perfect non-dispersiveness of ordinary vacuum are natural to expect.
“In such picture, where space-time exhibits a polymerlike structure at microscales, it is natural to expect departures from the perfect non-dispersiveness of ordinary vacuum.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
The simultaneity of time structures in gamma-ray burst light implies stringent limits on any dispersive effects that light might suffer in travel towards Earth.
“This implies stringent limits on any dispersive effects that light might suffer in travel towards the Earth.”
Quote in the paperSubstantial claim - Premisecitation§ Nonstandard optics from quantum spacetime · p. 1
Gamma-ray bursts present detailed time structures, with features smaller than 1 ms, received simultaneously through a broad band of frequencies ranging from 20 keV to 300 keV, as reported by BATSE.
“In particular, the bursts present detailed time structures, with features smaller than 1 ms , that are received simultaneously through a broad band of frequencies, ranging from 20 keV to 300 keV , as reported by the BATSE detector of the Compton Gamma Ray observatory [2].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [2] C. Bhat et al, Nature, 359 , 217 (1992); J. Scargle, J. Norris, J. Bonnell, astro-ph/9712016. source
Not checked in the free run.
- Interpretationnone given§ Nonstandard optics from quantum spacetime · p. 1
Loop quantum gravity might imply a unique signature of the discrete nature of spacetime tantamount to an intrinsic birefringence of quantum spacetime.
“An attractive feature of this approach is that it might imply a unique signature of the discrete nature of space time tantamount to an 'intrinsic birefringence' of quantum space-time.”
Quote in the paperNot a substantial claim - Premisecitation§ Nonstandard optics from quantum spacetime · p. 2
Thiemann [7] has a concrete proposal for realizing in the loop representation the operator corresponding to the metric divided by the determinant.
“Thiemann [7] has a concrete proposal for realizing in the loop representation the operator corresponding to the metric divided by the determinant.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7] T. Thiemann, Class. Quan. Grav. 15 , 1281 (1998). source
Not checked in the free run.
- Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
Recent observations of non-dispersiveness in gamma-ray burst spectra at various energies could be used to constrain the type of semi-classical state that describes the universe.
“In particular, recent observations of non-dispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semi-classical state that describes the universe.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 1
The birefringence effect would imply a distinctive doubling of patterns observed in time series analysis of gamma-ray bursts.
“This effect would imply a distinctive 'doubling' of patterns observed in the time series analysis of the bursts, making it attractive from the observational point of view.”
Quote in the paperSubstantial claim - Premisecitation§ Nonstandard optics from quantum spacetime · p. 3
Birefringence was also considered in the context of modifications of electromagnetism and nonsymmetric gravity [9], but in those cases the effect was not frequency dependent.
“Birefringence was also considered in the context of modifications of electromagnetism and also in nonsymmetric gravity [9]. In those cases the effect was not frequency dependent.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [9] S. Solanki, M. Haugan Phys. Rev. D53 , 997 (1996). source
Not checked in the free run.
- Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 4
A fundamental, Planck-level violation of parity in the weave approach can occur without detriment to the ability of the weave to approximate a given metric.
“That is, one can envisage a fundamental, Planck-level violation of parity in the weave approach, without detriment to the ability of the weave to approximate a given metric.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 3
The lack of Lorentz covariance is not surprising because the weave selects a preferred foliation of spacetime.
“The lack of covariance is not surprising, since the weave selects a preferred foliation of spacetime.”
Quote in the paperSubstantial claim - Interpretationnone given§ Nonstandard optics from quantum spacetime · p. 4
Without further input from the dynamics of the theory, a weave structure would be expected to lead to the loss of Poincaré invariance of the Maxwell equations.
“In general, without further input from the dynamics of the theory, one would expect that a weave structure would lead to the loss of Poincar´ e invariance of the Maxwell equations.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 4
If the weave is parity preserving, Poincaré invariance is preserved as well.
“It is interesting to notice that if the weave is parity preserving Poincar´ e invariance is preserved as well.”
Quote in the paperSubstantial claim
- May combine two claims. 9
- Classified as probably not a substantial claim. 7
- The quote only partly states this claim. 2
May combine two claims.
Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3The resulting effect is a birefringence effect associated with quantum gravity corrections, with two group-velocity branches.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Findingreasoning§ Nonstandard optics from quantum spacetime · p. 3The leading contribution to the next-order term is proportional to l_P/Δ and is a rotational invariant tensor of three indices given by χ ε_abc l_P/Δ, with χ a proportionality constant of order one.
“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).”
Quote in the paperSubstantial claimMay combine two claims.
Findingreasoning§ Nonstandard optics from quantum spacetime · p. 2In the weave approximation, the sum over vertices of the metric operator yields the classical metric, and the usual Maxwell Hamiltonian in flat space is recovered.
“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.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 1In reference [1] it was shown that the simultaneity of time structures in gamma-ray burst light patterns are possible candidates to set limits on string quantum gravity models.
“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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Not checked in the free run.
Classified as probably not a substantial claim.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 1Various models of string quantum gravity imply dispersive frequency-wavelength relations for light propagation.
“Various models of string quantum gravity imply dispersive frequency wavelength relations for light propagation”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Not checked in the free run.
Classified as probably not a substantial claim.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 1In loop quantum gravity, the kinematic framework has led to physical predictions associated with a polymer-like structure of quantum spacetime.
“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].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [4] A. Ashtekar, J. Lewandowski, Class.Quant.Grav. 14 , A55 (1997); Adv. Theor. Math. Phys. 1 , 388 (1998). source
Not checked in the free run.
May combine two claims.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 1Light from gamma-ray bursts travels very large distances before detection on Earth and is therefore quite sensitive to departures from orthodox theories.
“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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Not checked in the free run.
The quote only partly states this claim.
Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 3Combining the corrected equations to study wave propagation suggests modifications to the usual dispersion relation for light propagation.
“This already suggests that there will be modifications to the usual dispersion relation for light propagation.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 3If the weaves are parity-invariant, the additional term would vanish.
“If one were to assume that the weaves are parity-invariant, the term would vanish.”
Quote in the paperSubstantial claimMay combine two claims.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 3The observed width of gamma-ray bursts appears to be of order 0.1 s, with features like a rising edge as small as 1 ms.
“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 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [2] C. Bhat et al, Nature, 359 , 217 (1992); J. Scargle, J. Norris, J. Bonnell, astro-ph/9712016. source
Not checked in the free run.
May combine two claims.
Interpretationcitation§ Nonstandard optics from quantum spacetime · p. 3The birefringence effect is distinct from the effects considered by Amelino-Camelia et al. [1], who find only a change in the dispersion relation, whereas this effect is additionally helicity-dependent.
“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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Nonstandard optics from quantum spacetime · p. 3This is in line with the observation of ref. [1] that quantum gravity effects will increase with frequency, the opposite being expected for other more standard sources of cosmological dispersion or birefringence.
“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.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [1] G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. Nanopoulos, S. Sarkar, Nature 393 763 (1998). source
Not checked in the free run.
May combine two claims.
Interpretationnone given§ Nonstandard optics from quantum spacetime · p. 3The effect is absent for scalar fields, whereas other quantum gravity corrections are all-encompassing (they can be viewed as corrections to quantum mechanics itself).
“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).”
Quote in the paperSubstantial claimMay combine two claims. The quote only partly states this claim.
Interpretationreasoning§ Nonstandard optics from quantum spacetime · p. 3The corrective terms introduced in Maxwell theory are linear in the fields but higher order in derivatives, which explains why the effect is frequency dependent.
“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.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone given§ Nonstandard optics from quantum spacetime · p. 3The additional term would also vanish on average if different regions of size Δ have random orientations in their parity violation.
“The term would also vanish -on average- if one assumes that the different regions of size ∆ have 'random orientations' in their parity violation.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
Premisecitation§ Nonstandard optics from quantum spacetime · p. 2The operators w_a acting on spin network states are finite and only give contributions at intersections.
“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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [7] T. Thiemann, Class. Quan. Grav. 15 , 1281 (1998). source
Not checked in the free run.
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,”
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Early model calculations suggest that Lorentz-invariance-violation effects may arise from a quantum-gravity granularity of spacetime measured at rest by a preferred frame.
“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]
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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 479 · see citing works
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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
“[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 337 · see citing works
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 · see citing works
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 301 · see citing works
Carlo Rovelli, C. (2006) · The frontiers collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 347 · see citing works
DOUBLY-SPECIAL RELATIVITY: FIRST RESULTS AND KEY OPEN PROBLEMS
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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 · see citing works
“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 270 · see citing works
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 · 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
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 · see citing works
Lectures on Loop Quantum GravityPreprint
Thiemann, T. (2003) · Cited by 286 · see citing works
Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
Giovanni Amelino-camelia, A. (2010) · Symmetry · doi:10.3390/sym2010230 · Cited by 257 · see citing works
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 259 · 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
“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 · see citing works
Jacobson, T., Liberati, S., & Mattingly, D. (2003) · Physical Review D · doi:10.1103/physrevd.67.124011 · Cited by 240 · see citing works
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 · see citing works
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 · see citing works
“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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · 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
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 233 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 192 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
New varying speed of light theoriesPreprint
Magueijo, J. (2003) · Cited by 174 · 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
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 · see citing works
“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 · see citing works
“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 · see citing works
Astrophysical limits on quantum gravity motivated birefringence
Gleiser, R., & Kozameh, C. (2001) · Physical Review D · doi:10.1103/physrevd.64.083007 · Cited by 156 · see citing works
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 · see citing works
“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 · see citing works
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 · see citing works
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 148 · see citing works
Gauge Field Theory Coherent States (GCS): I. General Properties
Thiemann, T. (2000) · Cited by 147 · see citing works
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 · see citing works
“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 · see citing works
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 144 · see citing works
Quantization ambiguities in isotropic quantum geometry
Martin Bojowald, A. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/20/306 · Cited by 142 · see citing works
“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 155 · see citing works
Loop Quantum Gravity: An Inside View
Thiemann, T. (2007) · Lecture notes in physics · doi:10.1007/978-3-540-71117-9_10 · Cited by 137 · see citing works
“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 · see citing works
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
“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 126 · see citing works
“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 · see citing works
“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 · see citing works
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 · see citing works
Quantum gravity with a positive cosmological constantPreprint
Smolin, L. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0209079 · Cited by 125 · see citing works
“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 · see citing works
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 · see citing works
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 · see citing works
Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product ExtensionPreprint
Sahlmann, H., Thiemann, T., & Winkler, O. (2001) · Cited by 120 · see citing works
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 · see citing works
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 · 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
“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 · see citing works
Vacuum solutions of a gravity model with vector-induced spontaneous Lorentz symmetry breaking
Bertolami, O., & 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 96 · see citing works
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 114 · see citing works
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 · see citing works
The Search for Quantum Gravity Signals
Giovanni Amelino-camelia, A. (2005) · AIP conference proceedings · doi:10.1063/1.1900507 · Cited by 115 · see citing works
“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 · see citing works
“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 · see citing works
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 · see citing works
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 109 · see citing works
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 106 · see citing works
Hendi, S. H., Panah, B. E., & Panahiyan, S. (2017) · Physics Letters B · doi:10.1016/j.physletb.2017.03.051 · Cited by 105 · see citing works
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 109 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
“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 · see citing works
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 104 · see citing works
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 · see citing works
- 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 › 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 › 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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Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-06.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-06.
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 ›
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