Explanation of The GZK Limit Based on the WSM Model of SRT

It has been calculated by Greisen, Zatsepin and Kuz’min that the interaction between cosmic rays and CMBR photons would result in pion production through the ∆-resonance at cosmic ray energies above 5 x 10 19 eV [1][2]. Thus, the maximum cosmic ray energy that we should measure for relativistic cosmic ray protons that reach Earth is 5 x 10 19 eV, but some cosmic ray observatories have measured 10 20 eV, including the measured energy of 3 x 10 20 eV for the OMG particle by the Fly’s Eye at Dugway Proving Grounds in 1991 [3][4]. One explanation for the violation of the GZK limit is that the relativistic effects at the center of mass collision are different than what is predicted by the standard SRT model. A version of SRT has been developed based on the wave structure of matter (WSM) that, unknown to the authors at the time of development (2007), yields results that explain the GZK-limit violation while still keeping the energy threshold for pion-production of proton-photon collisions at the standard model level of 5 x 10 19 eV [5]. The WSM hypothesizes that a particle is a combination of an in-wave and out-wave and that the superposition of these waves at r = 0 (wave center of the particle) produces the measured effects of the particle [6]. The in-wave, which has a fixed frequency based on a standing wave model [7] and travels at the speed of light, appears Doppler-shifted and higher in frequency by the particle moving relative to the in-wave’s stationary reference frame: ωCin = ωin (1 + v /c) 1 Where ωin = the frequency of the in-wave as seen by a stationary observer and ωCin is the Doppler shifted frequency of the in-wave as seen by the moving particle at its wave center. A blue-shifted photon in the WSM is modeled as a geometric resonance between ωin and ωCin: ωFin = (ωin ωCin