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The phenomena of neutrino oscillations (as I understand it) is based on the idea that neutrino mass eigenstates are not the same as the flavor eigenstates and being in a definite mass eigenstate means the paticle has no definite flavor and vice versa. But this doesn't make sense to me, because the quantum state of a particle is the combination of its state in several Hilbert spaces, the Hilbert space of complex functions over spatial coordinates, the flavor Hilbert space, etc. As long as the interactions in the Hamiltonian don't couple flavor with spatial coordinates, these Hilbert spaces are completely independent and have nothing to do with each other. So I don't understand this effect that arises from the supposed inter-dependency of these two independent Hilbert spaces. Can anyone make things clear?
Thanks
Thanks