During years a considerable evidence has accumulated suggesting that this upper bound is not respected by the real world physics (Centauros and Geminions). For instance, Japan's Akeno Giant Air Shower Array (AGASA) experiment announced in 2004 that, after 15 years of running, it had detected 11 cosmic rays with energies greater than the GZK cut-off (see the popular article in New Scientist).
One can make two questions.
- What these particles are: ordinary protons or something more exotic? I have considered a possible identification of the ultrahigh energy cosmic ray event in terms of hadrons of a scaled up copy of ordinary hadron physics corresponding to Mersenne prime M107 characterized by Mersenne prime M31 (see this). The p-adic mass scale of this hadron physics would be by a factor 2(107-31)/2= 238≈ 2.8×1011 larger than that of hadron physics. The recent progress in understanding of hadron masses (see this) supports the view that hadron masses obey rather precise scaling. This would mean that the masses of pion and proton of M31 physics would be 3.9×1010 GeV and 2.6&;1011 GeV to be compared with GZK bound 5×1010 GeV.
- How these particles end up here? The super-heavy particles could also propagate along dark space-time sheets, where Planck constant is very large. Since the dissipation rates are expected to scale down as 1/hbar, cosmic rays should propagate over much longer distances.