  It is shown that a variety of characteristic features of the high-energy
hadronic cosmic ray spectra, in particular the abrupt changes in the spectral
index that occur around 3 PeV and 300 PeV, as well as the corresponding changes
in elemental composition that are evident from kinks in the $<X_{\max}>$
distribution, can be explained in great detail from interactions with relic Big
Bang antineutrinos, provided that the latter have a rest mass of $\sim 0.5$
eV/$c^2$.
