  Ultra-high energy cosmic rays and neutrinos probe energies far above the weak
scale. Their usefulness might appear to be limited by astrophysical
uncertainties; however, by simultaneously considering up- and down-going
events, one may disentangle particle physics from astrophysics. We show that
present data from the AMANDA experiment in the South Pole ice already imply an
upper bound on neutrino cross sections at energy scales that will likely never
be probed at man-made accelerators. The existing data also place an upper limit
on the neutrino flux valid for any neutrino cross section. In the future,
similar analyses of IceCube data will constrain neutrino properties and fluxes
at the O(10%) level.
