Wheeler's 'spacetime-foam'picture of quantum gravity (QG) suggests spacetime fuzziness (fluctuations leading to non-deterministic effects) at distances comparable to the Planck length, L Pl â ‰ 1.62 × 10 â '33 cm, the inverse (in natural units) of the Planck energy, E Pl â ‰ 1.22 × 10 19 GeV. The resulting non-deterministic motion of photons on the Planck scale is expected to produce energy-dependent stochastic fluctuations in their speed. Such a stochastic deviation from the well-measured speed of light at low photon energies, c, should be contrasted with the possibility of an energy-dependent systematic, deterministic deviation. Such a systematic deviation, on which observations by the Fermi satellite set Planck-scale limits for linear energy dependence, is more easily searched for than stochastic deviations. Here, for the first time, we place Planck-scale limits on the more generic spacetime-foam prediction of energy-dependent fuzziness in the speed of photons. Using high-energy observations from the Fermi Large Area Telescope (LAT) of gamma-ray burst GRB090510, we test a model in which photon speeds are distributed normally around c with a standard deviation proportional to the photon energy. We constrain the model's characteristic energy scale beyond the Planck scale at >2.8E Pl (>1.6E Pl), at 95% (99%) confidence. Our results set a benchmark constraint to be reckoned with by any QG model that features spacetime quantization.
Bibliographical noteFunding Information:
The Fermi-LAT Collaboration acknowledges support for LAT development, operation and data analysis from NASA and DOE (United States), CEA/Irfu and IN2P3/CNRS (France), ASI and INFN (Italy), MEXT, KEK and JAXA (Japan), and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board (Sweden). Science analysis support in the operations phase from INAF (Italy) and CNES (France) is also gratefully acknowledged. This research was supported by an ERC advanced grant (GRBs), by the I-CORE (grant No 1829/12), by the joint ISF-NSFC program (T.P.) and by the Templeton Foundation (G.A-C.).
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