In theories explaining neutrino oscillations (with 3 neutrinos to make it simple), it is explained that a neutrino flavor eigenstate that is produced with an electroweak process is actually a superposition of various neutrinos mass eigenstates.
During their flight, each mass eigenstate evolves in a different way, thus, at an arbitrary non trivial distant, the flavor of the neutrino is a mixture of all flavors together. Do you agree with my sentence ? (Books typically don't state that the neutrino at a given distance is a flavor superposition... they typically only say that a given flavor neutrino is a superposition of mass eigenstates, which is not enough to fully understand.)
Thus my question is : let's consider a given flavor neutrino produced, that flight to a long distant that is known with an extremely good precision. Let's suppose that in the detector, it will interact (I know that cross-section is low) and transform to a charged lepton.
Will the flavor of the neutrino at the detector always be the same ? That is exactly reproducible result.
-> Or is it the same spirit of the quantum mechanism : when interacting with the detector, there will be projection of the system on one of the flavor, with a given probability : that is non reproducible result : the result is reproducible only on an average/statistics base.
Do the laws explain in average the mechanism, but don't explain why each measurement will be a specific given flavor instead of another one ?
Thank you for your help