Hot electrons injected into antiferromagnetic Mn layers from the tip of a low temperature scanning tunneling microscope have been used to determine the energies, lifetimes, and momenta of antiferromagnetic spin waves on the nanometer scale. The spin waves show a linear dispersion with a velocity of 160±10 meV Å and lifetimes that scale linearly with energy in agreement with neutron scattering and theory. It is shown that the method is sensitive enough to detect the influence of surface anisotropies on the spin wave dispersion.