  Cosmic rays in the regime of 10^19-10^20 eV should not exist, according to
the GZK bound. Conflicts between data and the bound have led to suggestions
that laws of physics must be modified. We find that physical processes
neglected in the early history terminate the LPM effect, important in
calibrating the energy of electromagnetic and hadronic showers in the GZK
energy regime. The processes neglected are the direct losses of electrons and
positrons, overlooked by LPM and greatly augmented by ultra-high energy
circumstances. We present an exact formula for direct energy losses of e^+e^-
pairs in electromagnetic showers. Numerical integration in current hadronic
models shows that actual energy losses are always substantially larger than LPM
estimates, but the energy at which crossover occurs depends on models.
