Quantum Theory of Neutrino Oscillations for Pedestrians - Simple Answers to Confusing Questions

Abstract

Why are different mass states coherent? What is the correct formula for the oscillation phase? How can textbook formulas for oscillations in time describe experiments which never measure time? How can we treat the different velocities and different transit times of different mass eigenstates and avoid incorrect factors of two? How can textbook forumulas which describe coherence between energy states be justified when Stodolsky's theorem states there is no coherence between different energies? Is covariant relativistic quantum field theory necessary to describe neutrino oscillations? How important is the detector, which is at rest in the laboratory and cannot be Lorentz tranformed to other frames? These questions are answered by a simple rigorous calculation which includes the quantum fluctuations in the position of the detector and in the transit time between source and detector. The commonly used standard formula for neutrino oscillation phases is confirmed. An "ideal" detector which measures precisely the energy and momentum of the neutrino destroys all phases in the initial wave packet and cannot observe oscillations. A realistic detector preserves the phase differences between neutrinos having the same energy and different momenta and confirms the standard formula. Whether phase differences between neutrinos with different energies are observable or destroyed by the detector is irrelevant.