Oscillations among three neutrino types andCPviolation

If ${\nu }_e$ ${\nu }_{\mu }$ and ${\nu }_{\tau }$ are treated symmetrically in a $\mathrm{CP}$-invariant theory, it is impossible to have vacuum neutrino oscillations in which on the average each of the three neutrino types becomes an equal mixture of all three. It is shown how this becomes possible for a $\mathrm{CP}$-noninvariant theory.