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25.3 Bc Arising MH brief communications arising Cosmology Lorentz-invariant dispersion relation, avoid- ing other constraints5,6. Synchrotron radiation and quantum gravity The strong bound of Jacobson et al.1 on Arising from: Jacobson, T., Liberati, S. & Mattingly, D. Nature 424, 1019–1021 (2003) the electron underlines the interest in probing directly the dispersion relation of uantum gravity may cause the vacuum leaving measurements on time profiles of very the photon. The study of the arrival times of to act as a non-trivial medium remote g-ray bursts2,7 as the best approach for photons from g-ray bursts2 still appears to be Q(space–time foam), which alters the probing quantum-gravity effects. the best experimental probe of any possible standard Lorentz relation between the The basic reason for this violation of the refractive index for photons, and should be energy and momentum of matter particles, equivalence principle in the quantum-gravity pursued further. It has already established a 3 16 thereby modifying their dispersion model is its description of space–time foam lower limit on MQG close to 10 GeV (ref. 7), relations. Jacobson, Liberati and Mattingly1 by using quantum defects in space–time with and current (HETE,INTEGRAL) and future argue that synchrotron radiation from the vacuum quantum numbers, as in one inter- (GLAST, AMS) high-energy space missions Crab nebula imposes a stringent constraint pretation of Liouville string theory8. These have the potential to reach the Planck scale on any modification of the dispersion rela- can be excited only by particles that are neutral for any linear quantum-gravity modifica- tion of the electron that might be induced by under the gauge group of the standard model, tion of the photon’s dispersion relation. quantum gravity, but their analysis does not such as photons, and such interactions give John Ellis*, N. E. Mavromatos†‡, constrain any modification of the dispersion the vacuum a non-trivial refractive index for D. V.Nanopoulos§||¶, A. S. Sakharov*# relation of the photon2,3. Such quantum- light of different frequencies (energies)2. *Department of Physics, CERN Theory Division, gravity effects need not obey the equivalence Charged particles, such as electrons, cannot 1211 Geneva 23, Switzerland principle4 in the sense of being universal for form such excitations, so do not ‘see’ the e-mail: [email protected] all matter particles, as exemplified by space–time foam at all, and hence obey the †Department of Physics, King’s College London, quantum-gravity models in which photons usual Lorentz kinematics. As a result of the University of London, London WC2R 2LS, UK are the only standard-model particles able to excitation of the vacuum by an energetic ‡Departamento de Fisica Teorica, Universidad de ‘see’special quantum-gravity configurations photon, space–time is distorted and the Valencia, 46100, Burjassot, Valencia, Spain that modify their dispersion relations. This photon travels with a velocity smaller than the §George P. and Cynthia W. Mitchell Institute for implies that photons may be the only (supposedly universal) speed of light in vacuo, Fundamental Physics, Texas A&M University, sensitive probe of quantum-gravity effects c, as postulated in the special and general College Station, Texas 77843, USA on particle dispersion relations, and the theories of relativity. ||Astroparticle Physics Group, Houston Advanced results of Jacobson et al. do not exclude all As the electron has no interaction with Research Center, Mitchell Campus, Woodlands, possible modifications of dispersion rela- the quantum-gravitational vacuum medium Texas 77381, USA tions, even if they are suppressed by only a in this approach, it emits no Cˇerenkov ¶Academy of Athens, Division of Natural Sciences, single power of the Planck mass (the radiation, despite travelling faster than pho- Athens 10679, Greece characteristic quantum-gravity scale) — tons, thus avoiding the vacuum Cˇerenkov #Swiss Institute of Technology, ETH–Zürich, 8093 contrary to some subsequent interpretations radiation constraint9, as well as the Crab Zürich, Switzerland of their results. nebula constraint derived by Jacobson et al.1 doi:10.1038/nature02481 4 As pointed out previously , there are The model in ref. 3 also avoids the strong 1. Jacobson, T., Liberati, S. & Mattingly, D. Nature 424, 1019–1021 theoretical models in which quantum gravity constraints described in ref. 10, as well as (2003). produces Lorentz invariance-violating effects many other constraints on quantum-gravity 2. Amelino-Camelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, 11 D. V. & Sarkar, S. Nature 393, 763–765 (1998). for neutral particles, such as the photon, but effects . Claims that modified dispersion 3. Ellis, J., Mavromatos, N. E. & Nanopoulos, D. V. Phys.Rev.D62, not charged particles, such as the electron. relations for photons would result in phase 084019(1–10) (2000). One model of space–time foam3 suggests a incoherence of light, and thereby destroy 4. Ellis, J., Mavromatos, N. E. & Sakharov, A. S. Astropart. Phys. 20, linear modification of the dispersion relation diffraction patterns in images of extragalactic 669–682 arXiv:astro-ph/0308403 (2004). 4 1 2 12 13 5. Carroll, S. Nature 424, 1007–1008 (2003). for the photon: pg Eg (Eg /MQG), where pg sources , have been criticized by Ng ,who 6. Myers, R. C. & Pospelov, M. Phys.Rev.Lett.90, 211601(1–4) (Eg) is the photon’s momentum (energy) and pointed out that the induced incoherent (2003). 12 MQG is some characteristic scale associated effects had been overestimated by a large 7. Ellis, J., Mavromatos, N. E., Nanopoulos, D. V. & Sakharov, A. S. with quantum gravity, which may be of the factor. In the specific model of ref. 3, the Astron. Astrophys. 402, 409–424 (2003). LJ 19 8. Ellis, J., Mavromatos, N. E. & Nanopoulos, D. V. J. Chaos Solit. same order as the Planck mass MP 10 GeV. re-emission of the photon by a space–time Fract. 10, 345–362 (1999). 3 However, this model predicts that there is no defect is accompanied by a random phase in 9. Liberati, S., Jacobson, T. & Mattingly, D. Phys.Rev.D67, such modification of the dispersion relation its wave function, destroying any cumulative 124011(1–26) (2003). for the electron4,and hence is compatible with phase incoherence. Finally, we note that, as 10.Alfaro, J. & Palma, G. Phys.Rev.D67, 083003(1–18) (2003). the constraint1 from the Crab nebula. In such the nucleon is a bound state, it is more com- 11.Ellis, J., Mavromatos, N. E. & Nanopoulos, D. V. Phys.Rev.D65, 064007(1–7) (2002). models, constraints on the electron and plex to analyse,but we also do not expect it to 12.Lieu, R. & Hillman, L.W. Astrophys. J. 585, L77–L80 (2003). 1,5,6 nucleon dispersion relations are irrelevant, exhibit a linear modification of the normal 13.Ng, Y. J. Mod. Phys. Lett. A 18, 1073–1097 (2003). NATURE | www.nature.com/nature © 2004 Nature Publishing Group.
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