Lorentz symmetry violations might produce anomalies in the propagation of particles travelling through the Universe. The IceCube Collaboration performed the most precise search for such an effect with neutrinos, finding no sign of anomalous behaviour.
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Gubitosi, G. Lorentz invariance beyond the Planck scale. Nat. Phys. 18, 1264–1265 (2022). https://doi.org/10.1038/s41567-022-01806-6
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DOI: https://doi.org/10.1038/s41567-022-01806-6