  Gamma ray burst (GRB) fireballs provide one of very few astrophysical
environments where one can contemplate the acceleration of cosmic rays to
energies that exceed 10^20 eV. The assumption that GRBs are the sources of the
observed cosmic rays generates a calculable flux of neutrinos produced when the
protons interact with fireball photons. With data taken during construction
IceCube has already reached a sensitivity to observe neutrinos produced in
temporal coincidence with individual GRBs provided that they are the sources of
the observed extragalactic cosmic rays. We here point out that the GRB origin
of cosmic rays is also challenged by the IceCube upper limit on a possible
diffuse flux of cosmic neutrinos which should not be exceeded by the flux
produced by all GRB over Hubble time. Our alternative approach has the
advantage of directly relating the diffuse flux produced by all GRBs to
measurements of the cosmic ray flux. It also generates both the neutrino flux
produced by the sources and the associated cosmogenic neutrino flux in a
synergetic way.
