Quantum gravity shall be the bridge linking the largest and the smallest objects in the universe, explained by General Relativity and Quantum Field Theory, respectively. One of the physical consequences of a quantized gravitational field are departures from classical spacetime symmetries, specifically the Lorentz symmetry.
Such symmetry breaking would be translated into modified dispersion relations for particles, producing energy-dependent group velocities. This effect can be studied with the MAGIC telescopes, by looking for energy-dependent delays on very-high-energy gamma rays coming from distant sources, using the Time-of-Flight technique.
The talk presents results from Time-of-Flight studies using an outstanding flare of the Mrk 421 blazar, detected by the MAGIC telescopes in 2014, the most energetic candidate used for Time-of-Flight studies up to date. No significant delay is detected, however, the results are later used to set among the best constraints on the effective energy scale for Quantum Gravity.