We present elastic and inelastic neutron-scattering results on highly oxygen-ordered
YBa2Cu3O6.5 ortho-II. We find no evidence of the presence of long-ranged ordered magnetic moments to a sensitivity of ∼0.003μB, an order of magnitude smaller than has been suggested in theories of orbital or d-density-wave (DDW) currents. The absence of sharp elastic peaks rules out the existence of well-correlated static DDW currents in our crystal. We cannot exclude the possibility that a broad peak may exist with extremely short-range DDW correlations. For less ordered or more doped crystals it is possible that disorder may lead to static magnetism. We have also searched for the large normal-state spin gap that is predicted to exist in an ordered DDW phase. Instead of a gap we find that the Q-correlated spin susceptibility persists to the lowest energies studied, ∼6meV. Our results are only compatible with the coexistence of superconductivity and orbital currents if the latter are dynamic and do not participate in a sharp phase transition to a highly ordered DDW state.