If I’m not mistaken neutrino oscillation is a function of the difference between the squares of the neutrino masses, so a massless neutrino can oscillate with a massive one.
A neutrino with a definite mass (be it zero or finite) does not oscillate. Only superpositions of mass eigenstates oscillate.
I meant it doesn’t affect your larger point that one is free to pick a different metric for a quantity of interest and thereby change the apparent fractional uncertainty.
I offered the more run-of-the-mill mapping in the hopes that it was more intuitive pedagogically to the OP than one constructed specifically to yield infinite errors. (Also, a proper statistical treatment of a quantity that may or may not be infinite is non-trivial.)
You are not mistaken.
Ah, right, even if nu_1 is massless, nu_e (which appears to be a mixture of roughly equal parts nu_1 and nu_2) will have a nonzero expectation value for its mass. It still doesn’t sit right with me, but I’ll have to give it some more thought.