Condensed matter approach to ν oscillations

Abstract

Neutrino scillations cannot arise from an initial isolated one particle state if four‐momentum is conserved. The transition matrix element is generally squared and summed over all final states with no interference between orthogonal final states. Lorentz covariant descriptions based on relativistic quantum field theory cannot describe interference between orthogonal states with different ν masses producing neutrino oscillations. Simplified model presents rigorous derivation of hand‐waving argument about “energy‐time uncertainty.” Standard time‐dependent perturbation theory for decays shows how energy spectrum of final state is much broader than natural line width at times much shorter than decay lifetime. Initial state containing two components with different energies decay into two orthogonal states with different ν masses completely separated at long times with no interference. At short times the broadened energy spectra of the two amplitudes overlap and interfere. “Darmstadt oscillation” experiment attempts to measure the momentum difference between the two contributing coherent initial states and obtain information about ν masses without detecting the ν. Simple interpretation gives value for the squared ν mass difference differing by less than a factor of three from values calculated from the KAMLAND experiment. Treatment holds only in laboratory frame with values of energy, time and momentum determined by experimental environment at rest in the laboratory.