A possible violation of Lorentz Invariance (LIV) appeared in the late 90s as a striking prediction of some models developed with the goal to provide a full theory of Quantum Gravity (QG). Since then, several ways to probe quantum spacetime at the Planck scale from high-energy gamma-ray observations of distant sources have been followed and provided stringent limits on the energy scale of QG.
In this talk, the latest results obtained from observations of Gamma-Ray Bursts (GRBs), flaring Active Galactic Nuclei (AGNs) and pulsars (PSRs) will be briefly reviewed. Then, focusing on the search for energy-dependent time-delays with flaring AGNs, the main problem encountered in this kind of analysis will be emphasized. Then, efforts on-going to solve this issue will be discussed and put in context with the beginning of the Cherenkov Telescope Array (CTA) operations in the next few years.
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