John Carlos Baez on Nostr: - No, if E is the expected energy of a neutrino then E = |α₁|² E₁ + |α₂|² ...

- No, if E is the expected energy of a neutrino then

E = |α₁|² E₁ + |α₂|² E₂ + |α₃|² E₃

where αᵢ is the amplitude for the neutrino to be in the ith mass eigenstate, and Eᵢ is the energy, which equals the mass, of that mass eigenstate. The numbers Eᵢ are the eigenvalues of the neutrino mass operator, which is diagonal in the mass eigenstate basis (by definition) but not in the flavor eigenstate basis.

The unitary matrix relating mass eigenstates to flavor eigenstates is the Cabibbo-Kobayashi-Maskawa matrix, and I was explaining the absolute value squared of its matrix entries when I wrote this:

• the ν₁ is 68% electron neutrino, 10% mu neutrino and 22% tau neutrino. These are the probabilities that if you let a ν₁ interact with matter that it will interact in three different ways.

• the ν₂ is 30% electron, 36% mu and 34% tau. This is the most "democratic" of the mass eigenstates.

• the ν₃ is 2% electron, 48% mu and 50% tau.