Why do neutrinos with different masses interfere and oscillate? Why are states with different masses but same energy coherent? Overcoming barrier between particle & condensed matter physics
Neutrino oscillations occur only if it is impossible to determine $ν$ mass by using conservation laws on measurements of nucleon-lepton system absorbing $ν$. No oscillations if $ν$ detector is mass spectrometer. Beam is split into components with different masses entering different counters. For each event only one counter will click and determine $ν$ mass. Condensed matter physics needed to describe the $ν$ detector, show it is not a mass spectrometer and identify which properties of the incident $ν$ are unobservable. Relativistic quantum field theory can only describe $ν$ wave function entering detector but not large uncertain momentum transfers to detector nor associated energy-momentum asymmetry. Absorption of incident $ν$'s with different momenta but same energy leaves no trace of initial $ν$ momentum difference in finite-size $ν$ detector with effectively infinite mass at rest in laboratory. Undetectable recoil-free momentum is transferred to the detector with negligible energy transfer. The Debye-Waller factor common in X-ray diffraction by crystals gives probability that absorbing $ν$'s with different momenta produce same nucleon-charged-lepton final state. Oscillations in time described in textbooks as interference between $ν$ states with different energies not observable in realistic experiments. Different energy $ν$'s not coherent because energy can be determined by measurements on initial and final states. Experiments detecting $ν$ produced by $πto μν$ decay observe no electrons even though $ν$ mass eigenstates produce electrons. Electron amplitude canceled by interference between amplitudes from different $ν$ mass eigenstates with same energy and different momenta entering massive detector.