I discuss an upper bound on the boost and the energy of elementary particles. The limit is derived utilizing the core principle of relativistic quantum mechanics stating that there is a lower bound for localization of an elementary quantum system and the assumption that when the localization scale reaches the Planck length, elementary particles are removed from the S-matrix observables. The limits for the boost and energy, MPlanck/m and MPlanck C 2 ≈ 8.6 · 1027 eV,are defined in terms of fundamental constants and the mass of elementary particle and does not involve any dynamic scale. These bounds imply that the cosmic ray flux of any flavor may stretch up to energies of order 1028 GeV and will cut off around this value.
Japaridze, George, "Maximal attainable boost and energy of elementary particles as a manifestation of the limit of localizability of elementary quantum systems" (2016). Clark Atlanta University Faculty Publications. 17.
arXiv.org (April 9, 2015). arXiv:1504.02176v2 [hep-ph] Accessed March 17, 2017.