  A la Pontecorvo when one defines electroweak flavour states of neutrinos as a
linear superposition of mass eigenstates one ignores the associated spin. If,
however, there is a significant rotation between the neutrino source, and the
detector, a negative helicity state emitted by the former acquires a non-zero
probability amplitude to be perceived as a positive helicity state by the
latter. Both of these states are still in the left-Weyl sector of the Lorentz
group. The electroweak interaction cross sections for such helicity-flipped
states are suppressed by a factor of $(m_\nu/E_\nu)^2$, where $m_\nu$ is the
expectation value of the neutrino mass, and $E_\nu$ is the associated energy.
Thus, if the detecting process is based on electroweak interactions, and the
neutrino source is a highly rotating object, the rotation-induced helicity flip
becomes very significant in interpreting the data. The effect immediately
generalizes to anti-neutrinos. Motivated by these observations we present a
generalization of the Pontecorvo formalism and discuss its relevance in the
context of recent data obtained by the IceCube neutrino telescope.
