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

Abstract

Neutrino oscillations occur only if it is impossible to determine $\nu$ mass by using conservation laws on measurements of nucleon-lepton system absorbing $\nu$. No oscillations if $\nu$ 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 $\nu$ mass. Condensed matter physics needed to describe the $\nu$ detector, show it is not a mass spectrometer and identify which properties of the incident $\nu$ are unobservable. Relativistic quantum field theory can only describe $\nu$ wave function entering detector but not large uncertain momentum transfers to detector nor associated energy-momentum asymmetry. Absorption of incident $\nu$'s with different momenta but same energy leaves no trace of initial $\nu$ momentum difference in finite-size $\nu$ 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 $\nu$'s with different momenta produce same nucleon-charged-lepton final state. Oscillations in time described in textbooks as interference between $\nu$ states with different energies not observable in realistic experiments. Different energy $\nu$'s not coherent because energy can be determined by measurements on initial and final states. Experiments detecting $\nu$ produced by $\pi to \mu \nu$ decay observe no electrons even though $\nu$ mass eigenstates produce electrons. Electron amplitude canceled by interference between amplitudes from different $\nu$ mass eigenstates with same energy and different momenta entering massive detector.