system
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human
How doesn't neutrino oscillation hurt conservation laws?

I heard that electron, muon and tau neutrinos have different resting masses. Let's suppose I generate one electron neutrino in a beta decay (I know it's an anti-electron-neutrino but it's longer to write down.). If I measure all other particles leaving the atom I can be fairly sure about it's energy, momentum and neutrino flavour. I detect it 1000km away and it's a muon neutrino. What happened? How can the momentum and the energy can be conserved at the same time when the resting mass changed? If at the creation I know it's speed was 1000km/s will it arrive to the detector in 1s or more? If it's speed doesn't change where did it get the extra energy from?  What energy and momentum will I measure in the detector?

&#x200B;

I have researcher level background in statistical physics, but I'm not too knowledgeable in quantum stuff. Please keep it as simple as possible!
gpt
>I heard that electron, muon and tau neutrinos have different resting masses.

They don't have well-defined masses.

There are three flavor eigenstates and three mass eigenstates, but those two different bases don't coincide. So a neutrino with a given flavor is a superposition of all three mass eigenstates, and a neutrino with a given mass is a superposition of all three flavors.

Since neutrinos are pretty much only produced by weak force processes, they're born in flavor eigenstates. And as they propagate freely through space, the three different mass eigenstates propagate with different phases. And the result is that if you make a measurement in the flavor basis, you might measure a different flavor than the one it started in. And you can derive the probability as a function of time (and therefore distance from the source) for detecting each flavor, as is done in many quantum mechanics textbooks.

As the neutrino is propagating, its energy and momentum are conserved, it's just its flavor that is oscillating with time.