We discuss possible signatures of quantum gravity for the propagation of
light, including an energy-dependent velocity (refractive index), dispersion in
velocity at a given energy, and birefringence. We also compare the
sensitivities of different astrophysical observations, including BATSE data on
GRB 920229, BeppoSAX data on GRB 980425, the possible HEGRA observation of GRB
920925c, and Whipple observations of the active galaxy Mrk 421. Finally, we
discuss the prospective sensitivities of AMS and GLAST.Comment: LaTex, 3 page

Amelino-Camelia, G.

Ellis, John

Mavromatos, N. E.

Nanopoulos, D. V.

Sarkar, Subir

English

arXiv

We discuss possible signatures of quantum gravity for the propagation of light, including an energy-dependent velocity (refractive index), dispersion in velocity at a given energy, and birefringence. We also compare the sensitivities of different astrophysical observations, including BATSE data on GRB 920229, BeppoSAX data on GRB 980425, the possible HEGRA observation of GRB 920925c, and Whipple observations of the active galaxy Mrk 421. Finally, we discuss the prospective sensitivities of AMS and GLAST

Amelino-Camelia, G

Ellis, J

Mavromatos, NE

Nanopoulos, DV

Oxford University Research Archive

Sensitivity of Astrophysical Observations to Gravity-Induced Wave
  Dispersion in Vacuo

We discuss possible signatures of quantum gravity for the propagation of
light, including an energy-dependent velocity (refractive index), dispersion in
velocity at a given energy, and birefringence. We also compare the
sensitivities of different astrophysical observations, including BATSE data on
GRB 920229, BeppoSAX data on GRB 980425, the possible HEGRA observation of GRB
920925c, and Whipple observations of the active galaxy Mrk 421. Finally, we
discuss the prospective sensitivities of AMS and GLAST

Sarkar, S

Oxford University Research Archive (ORA)

We discuss possible signatures of quantum gravity for the propagation of light, including an energy-dependent velocity (refractive index), dispersion in velocity at a given energy, and birefringence. We also compare the sensitivities of different astrophysical observations, including BATSE data on GRB 920229, BeppoSAX data on GRB 980425, the possible HEGRA observation of GRB 920925c, and Whipple observations of the active galaxy Mrk 421. Finally, we discuss the prospective sensitivities of AMS and GLAST.We discuss possible signatures of quantum gravity for the propagation of light, including an energy-dependent velocity (refractive index), dispersion in velocity at a given energy, and birefringence. We also compare the sensitivities of different astrophysical observations, including BATSE data on GRB 920229, BeppoSAX data on GRB 980425, the possible HEGRA observation of GRB 920925c, and Whipple observations of the active galaxy Mrk 421. Finally, we discuss the prospective sensitivities of AMS and GLAST

Ellis, John R.

Mavromatos, N.E.

Nanopoulos, Dimitri V.

CERN Document Server

ACT-10/98CTP-TAMU-40/98NEIP-98-014astro-ph/9810483Sensitivity of Astrophysical Observations to Gravity-InducedWave Dispersion in VacuoG. Amelino-Cameliaa, John Ellisb, N.E. Mavromatosc,D.V. Nanopoulosd and Subir Sarkarca Institut de Physique, Universite de Neucha^tel, CH-2000 Neucha^tel, Switzerlandb Theory Division, CERN, CH-1211, Geneva, Switzerland,c Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UKd Dept. of Physics, Texas A & M University, College Station, TX 77843-4242, andHARC, The Mitchell Campus, Woodlands, TX 77381, USA;Academy of Athens, 28 Panepistimiou Avenue, Athens 10679, Greece.AbstractWe discuss possible signatures of quantum gravity for the propagation of light,including an energy-dependent velocity (refractive index), dispersion in velocityat a given energy, and birefringence. We also compare the sensitivities of differentastrophysical observations, including BATSE data on GRB 920229, BeppoSAXdata on GRB 980425, the possible HEGRA observation of GRB 920925c, andWhipple observations of the active galaxy Mrk 421. Finally, we discuss theprospective sensitivities of AMS and GLAST.We pointed out recently [1] that observations of γ-ray bursters (GRBs) can be usedto test models of quantum gravity in which the velocity of light depends on the photonenergy E. This is because GRBs combine large distances, z  1, with ne time structure, t  O(10−3) s. Assuming a linear dependence of the velocity, v = c(1  (E=EQG), wesuggested that eective quantum gravity scales EQG up to the Planck scale, MP  1019 GeV,can in principle be probed using GRBs, and argued that extant data already has a sensitivityto EQG  1016 GeV. Subsequently there have been several interesting developments whichwe comment on here.The energy-dependent dispersion eect [1] can be interpreted as a refractive index invacuo induced by quantum gravity. Another possibility is a statistical velocity spread amongphotons of the same energy E; higher-order quantum-gravity eects may induce  v (E) / Ewhich can be probed in a similar manner. Arguments have also been given in the context ofa loop representation of canonical quantum gravity [2] for the possibility of energy-dependentbirefringence: v = c(1  E=EQG) for  photon helicity states, as well as a linear energydependence of the refractive index in vacuo. We note that birefringence eects are, in general,characteristic of theories with (spontaneous) violation of Lorentz invariance [3]; probing sucheects might be possible with polarization measurements of GRBs. In each case, the gureof merit for comparing the sensitivities of dierent sources (at distance D) is the parameter  (DE=cMP )= t, which we now compare for various observations.We had previously discussed GRB 920229, which exhibited micro-structure in its burstat energies up to  200 keV. We estimated conservatively that a detailed time-series analysismight reveal coincidences in dierent BATSE energy bands on a time-scale  10−2 s, which1would yield   10−3 i.e. sensitivity to EQG  1016 GeV, assuming that GRB 920229 hasan (apparently) typical redshift of O(1), corresponding to a distance of  3000 Mpc. Asimilar sensitivity might be obtainable with GRB 980425, given its likely identication withthe unusual supernova 1998bw [5]. This is known to have taken place at a redshift z = 0:0083corresponding to a distance D  40 Mpc (for a Hubble constant of 65 km sec−1Mpc−1)which is rather smaller than a typical GRB distance. However GRB 980425 was observed byBeppoSAX at energies up to 1:8 MeV, which gains back an order of magnitude in the overallgure of merit. If a time-series analysis were to reveal structure at the  t  10−3 s level,which is typical of many GRBs [6], it would yield the same sensitivity as GRB 920229, withthe advantage that its redshift is known rather than estimated.A more speculative possibility is oered by GRB 920925c, observed by WATCH [7] andpossibly in high-energy γ rays by the HEGRA/AIROBICC array above 20 TeV [8]. Severalcaveats are in order: taking into account the appropriate trial factor, the condence level forthe signal seen by HEGRA to be related to GRB 920925c is only 99:7% ( 2:7), the reporteddirections dier by 90, and the redshift of the source is unknown. Nevertheless, the potentialsensitivity is impressive. The events reported by HEGRA range up to E  200 TeV, and thecorrelation with GRB 920925c is within  t  200 s. Making the reasonably conservativeassumption that GRB 920925c occurred no closer than GRB 980425, viz.  40 Mpc, wend a minimum gure of merit   1, corresponding to a possible sensitivity to EQG 1019 GeV, modulo the caveats listed above. Even more spectacularly, several of the HEGRAGRB 920925c candidate events occurred within  t  1 s, providing a potential sensitivityeven two orders of magnitude higher.Other astrophysical objects may also provide sensitive experimental probes of the quantum-gravity eects discussed earlier [1]. In particular, a strong limit has been extracted [4] usingdata from the Whipple telescope on a TeV γ-ray flare associated with the active galaxyMrk 421. This object has a redshift of 0.03 corresponding to a distance of  100 Mpc. Fourevents with γ-ray energies above 2 TeV have been observed within a period of 280 s. Theseprovide a gure of merit somewhat larger than we had previously suggested for GRB 920229,and with the capital advantage that the redshift of the source is known. Thus a denite limitEQG > 4 1016 GeV was derived [4].What of the future? A new generation of orbiting spectrometers, e.g., AMS [9] andGLAST [10], are being developed, whose potential sensitivities are very impressive. Forexample, assuming a E−2 energy spectrum, GLAST would expect to observe about 25 GRBsper year at photon energies exceeding 100 GeV, with time resolution of microseconds. AMSwould observe a similar number at E > 10 GeV with time resolution below 100 nanoseconds.For a nominal redshift of z  0:1 corresponding to a distance of D  300 Mpc, the expectedtime-delay at 10-100 GeV would be  t  30− 300 ms for EQG  1019 GeV, which should besimple to detect. We conclude that these missions would be adequate to exclude or establishthe existence of quantum-gravity eects such as a refractive index, statistical dispersion orbirefringence, if they appear with a linear dependence scaled by E=MP. We believe this addssignicantly to the scientic case for these experiments since they should be able to constrainsignicantly interesting theories of fundamental physics.AcknowledgementsWe thank Steven Biller, Elliot Bloom, Hans Hofer, Luis Padilla and Sergei Sazonov foruseful communications. This work was supported in part by a grant from the Swiss NationalScience Foundation (G.A.-C.), a P.P.A.R.C. advanced fellowship (N.E.M.), and D.O.E. GrantDE-FG03-95-ER-40917 (D.V.N.).2References[1] G. Amelino-Camelia, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos and S. Sarkar, Nature393, 763-765 (1998).[2] R. Gambini and G. Pullin, eprint gr-qc/9809038.[3] D. Colladay and V. A. Kostelecky , eprint hep-ph/9809521.[4] S.D. Biller et al., eprint gr-qc/9810044.[5] S.R. Kulkarni et al, Nature 395, 663-669 (1998);T.J. Galama et al, Nature 395, 670-672(1998).[6] K.C. Walker, B.E. Schaefer and E.E. Fenimore, eprint astro-ph/9810271.[7] S.Y Sazonov et al, Astron. Astrophys. Suppl. 129, 1-8 (1998).[8] L. Padilla et al, Astron. Astrophys. 337, 43-50 (1998).[9] AMS Collaboration, S. Ahlen et al, Nucl. Instrum. Meth. A350, 351-367 (1994).[10] GLAST Team, E.D. Bloom et al, Proc. Intern. Heidelberg Workshop on TeV Gamma-rayAstrophysics, eds. H.J. Volk and F.A. Aharonian (Kluwer, 1996) pp.109{125.3

Sensitivity of Astrophysical Observations to Gravity-Induced Wave Dispersion in Vacuo

Sensitivity of Astrophysical Observations to Gravity-Induced Wave Dispersion in Vacuo

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