Dual Phase Cosmic Rays
  A calculation based on flat spacetime symmetries shows how there can be two quantum phases. For one, extreme phase change determines a conventional classical trajectory and four-momentum, i.e. mass times four-velocity. The other phase occurs in an effective particle state, with the effective energy and momentum being the rate of change of the phase with respect to time and distance. A cosmic ray proton moves along a classical trajectory, but exists in an effective particle state with an effective energy that depends on the local gravitational potential. Assumptions are made so that a cosmic ray proton in an ultra-high energy state detected near the Earth was in a much less energetic state in interstellar space. A 300 EeV proton incident on the Earth was a 2 PeV proton in interstellar space. The model predicts such protons are in states with even more energy near the Sun than when near the Earth. 
Richard Shurtleff