Maximal boost and energy of elementary particles as a manifestation of the limit of localizability of elementary quantum systems

TL;DR

This paper proposes fundamental upper bounds on the boost and energy of elementary particles based on the principle of minimal localization, suggesting a universal energy cutoff relevant for cosmic rays.

Contribution

It introduces a new limit on particle energy and boost derived from localization bounds and the Planck scale, independent of dynamic scales.

Findings

Upper energy limit for elementary particles is approximately 8.6 x 10^{27} eV.

Cosmic ray flux may extend up to 10^{18} GeV before cutoff.

Limits are derived from fundamental constants and localization principles.

Abstract

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, M_{Planck}/m and M_{Planck}c^{2}\approx\,8.6 * 10^{27} 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 10^{18} GeV and will cut off around this value.