  Low energy supersymmetry with bilinear breaking of R-parity leads to a
weak-scale seesaw mechanism for the atmospheric neutrino scale and a radiative
mechanism for the solar neutrino scale. The model has striking implications for
collider searches of supersymmetric particles. Assuming that the lightest SUSY
particle is the lightest neutralino we demonstrate that (i) The neutralino
decays inside the detector even for tiny neutrino masses. (ii) Measurements of
the neutrino mixing angles lead to predictions for the ratios of various
neutralino branching ratios implying an independent test of neutrino physics at
future colliders, such as the Large Hadron Collider or a Linear Collider.
