Abstract
Models of quantum gravity suggest that the vacuum should be regarded as a medium with quantum structure that may have non-trivial effects on photon propagation, including the violation of Lorentz invariance. Fermi Large Area Telescope (LAT) observations of gamma-ray bursts (GRBs) are sensitive probes of Lorentz invariance, via studies of energy-dependent timing shifts in their rapidly-varying photon emissions. In this paper we analyze the Fermi-LAT measurements of high-energy gamma rays from GRBs with known redshifts, allowing for the possibility of energy-dependent variations in emission times at the sources as well as a possible non-trivial refractive index in vacuo for photons. We use statistical estimators based on the irregularity, kurtosis and skewness of bursts that are relatively bright in the 100 MeV to multi-GeV energy band to constrain possible dispersion effects during propagation. We find that the energy scale characterizing a linear energy dependence of the refractive index should exceed a few $\times 10^{17}$ GeV, and we estimate the sensitivity attainable with additional future sources to be detected by Fermi-LAT.
Highlights
AND SUMMARYThe idea that the space-time vacuum should be regarded as a nontrivial medium—baptized “space-time foam” by Wheeler and Ford [1]—is based on very general intuition
Without additional inputs on the physics of the processes responsible for high-energy emission of gamma-ray bursts (GRBs) [42], one can only assume that there are some source-dependent contributions to the spectral evolution of individual sources that could be responsible for the mistuning we find in the K-reduced distributions of the compensation parameters obtained for different sources
We have developed in this paper three distinct statistical nonparametric measures of GRB emissions, which we have used in an analysis of Fermi-Large Area Telescope (LAT) data to search for the possible effect of quantum gravity on the propagation of high-energy gamma rays from GRBs
Summary
AND SUMMARYThe idea that the space-time vacuum should be regarded as a nontrivial medium—baptized “space-time foam” by Wheeler and Ford [1]—is based on very general intuition. Wheeler and Ford [1] argued that on timescales Δt ∼ 1p=MffiffiffiPffiffiffi,ffiffiffiwffiffiffihffiffi ere MP ∼ 1019 GeV is the Planck mass: MP 1⁄4 ħc=GN and GN is the Newton constant of classical gravity; there would appear quantum-gravitational fluctuations in the space-time continuum with ΔE ∼ MP, resulting in a “foamy” structure on short timescales Δt ∼ ħ=MP This observation led Wheeler to argue that space-time would no longer appear smooth at distance scales Δx ∼ ħ=MP, and that it might exhibit both nontopological irregularities and topological fluctuations. This intuitive picture suggests the appearance of a refractive index η for particles such as photons propagating through “empty” space, corresponding to a phase velocity vph 1⁄4 p=E 1⁄4 c=η [2]. One would expect that the refractive index should increase with energy, because gravitational interactions are proportional to some negative power of MP, in general, and should increase as some
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