John Carlos Baez on Nostr: - oh, okay - a more reasonable usage of 𝐸ᵢ is the ith eigenvalue of the ...

- oh, okay - a more reasonable usage of 𝐸ᵢ is the ith eigenvalue of the mass/energy matrix: that's how I'm using it.

"Does every electron neutrino start with the same mixture, or is it determined by the kinematics?"

Every electron neutrino has the same values of αᵢ up to an overall phase; these numbers are 3 entries of a famous matrix that says how flavor eigenstates are linear combinations of mass eigenstates.

It's called the PMNS matrix, or Pontecorvo–Maki–Nakagawa–Sakata matrix.

In my post, I was using the inverse matrix to express mass eigenstates in terms of flavor eigenstates! Like this:

• the ν₁ is 68% electron neutrino, 10% mu neutrino and 22% tau neutrino.

• the ν₂ is 30% electron, 36% mu and 34% tau.

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

But these numbers are absolute values squared of the matrix elements, so we get probabilities.

https://en.wikipedia.org/wiki/Pontecorvo%E2%80%93Maki%E2%80%93Nakagawa%E2%80%93Sakata_matrix