Simple quantum mechanics explains GSI Darmstadt oscillations Even with undetected neutrino; Momentum conservation requires Same interference producing oscillations in initial and final states

GSI experiment studying oscillations in K-capture decay of radioactive ion investigates neutrino masses and mixing without detecting neutrino. Even when neutrino is not detected quantum mechanics relates initial and final states. The basic physics is very simple. Neutrinos emitted in beta decay are coherent linear combinations of states with different masses, different momenta and same energy. Since the weak interaction producing the neutrino conserves momentum, the initial state before the transition must also contain a coherent linear combination of states with the same momentum difference and a well defined relative magnitude and phase. A one-particle state with a definite momentum difference also has an easily calculated energy difference. In the time interval between creation of the ion and its decay a linear combination of two states with different energies oscillates in time. Measuring the oscillation period gives a value for the difference between squared neutrino masses of the two neutrino mass eigenstates. The value obtained from a crude approximation with no free parameters for this "two-slit" or "which path" experiment in momentum space differs by less than 10% from the result observed in the KAMLAND experiment. Observing only ion disappearance without detecting neutrino avoids signal suppression by low neutrino absorption cross section