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.