  We present a relationship, E_\nu^{max} = m_{\nu} M_{Planck}/M_{weak}, among
the highest observed neutrino energy (~PeV) and the neutrino mass, the weak
scale, and the Planck energy. We then discuss some tests of this relationship,
and present some theoretical constructs which motivate the relationship. It is
possible that all massive particles are subject to maximum energies given by
similar relationships, although only the neutrino seems able to offer
interesting phenomenology. We discuss implications which include no neutrino
detections at energies greater than PeV, and changes in expectations for the
highest energy cosmic rays. A virtue of this hypothesis is that it is easily
invalidated should neutrinos be observed with energies much great than the PeV
scale. An almost inescapable implication is that Lorentz Invariance is a low
energy principle, yet it appears that violation may be only observable in
high-energy astrophysical neutrinos.
