Perovskite manganites of the form R(1-x)A(x)MnO(3) (R=rare earth, A=Ca, Sr, Ba, Pb) remain a topic of great interest not just because of the colossal magnetoresistance they can exhibit - up to several orders of magnitude change in resistivity in a few Tesla - but because of the fundamental physics of the metal-insulator transition. The underlying physics involves competition between different complex ground states, e.g. charge- and orbitally-ordered, ferromagnetic metal, ferromagnetic insulator, etc. For the half-doped (x=0.5) compounds the balance seems to be especially delicate, and this has led to controversy surrounding the nature of the ground state. The debate has focused on whether the CE model where the Mn ions separate into Mn3+ and Mn4+ on adjacent sites and order ferromagnetically in zig-zag chains, or the Zener polaron model in which pairs of spins become rigidly coupled and form a herringbone pattern, provides an appropriate description. Distinguishing between these models with neutron diffraction is difficult, which partly accounts for the controversy. I will show that inelastic neutron scattering (INS) provides an unambiguous discriminant provided a large enough energy scale is probed, and will present such INS data, taken using the time-of-flight technique, that strongly favour the CE ground state.