Violation of the Greisen-Zatsepin-Kuzmin (GZK) Cut-off @ 6x1019 eV.
Problem: We should not see cosmic rays above 6x1019 eV. At above this energy, it becomes possible to interact with photons in the Cosmic Microwave Background (CMB).
Cosmic rays above this GZK cut-off can travel at most ~100-150 million light-years before losing energy in such interactions.