Why is it that neutrino oscillations are allowed to happen in terms of energy?

[jeebs]

If I'm not mistaken, the 3 flavours of neutrino are supposed to have different masses, right? Why then, if you had, say, an electron neutrino traveling along with a certain value of (kinetic + mass) energy, and then it oscillates into a muon neutrino with a different mass, could that be allowed?

I can't imagine that it would somehow be able to slow itself down so that its kinetic energy loss balances out its mass energy gain. So, what's going on there?

Or is an oscillation only allowed to last for short times within the confines of the energy-time uncertainty principle?

 

[phyzguy]

The point is that the states of given mass (the mass eigenstates) and the states of given flavor (the flavor eigenstates) are not the same. So an electron neutrino does not have a definite mass - it is a mixture of three states of different masses. And a state of definite mass does not have a given flavor - it is a mixture of three different flavors. Since a state of fixed mass is what propagates (as you say, it can't change in mid-flight), it has a certain probability of being any of the three flavors.

 

[jeebs]

ahhh right, thanks.

one other thing though, in my reading I've came across talk of "mass states" and "interaction states". When people talk about these interaction states, is that term interchangeable with the flavour states you mentioned?

 

[phyzguy]

ahhh right, thanks.

one other thing though, in my reading I've came across talk of "mass states" and "interaction states". When people talk about these interaction states, is that term interchangeable with the flavour states you mentioned?

As I understand it, yes. An interaction will result in a state of definite flavor, but since this state of definite flavor is a mixture of states of different energy (mass), each of which evolves according to the Schrodinger equation with different frequencies, you get oscillations.

 

[jeebs]

nice one, thanks.

 

[kloptok]

This is because the (weak) interactions between leptons appear to couple to the flavour eigenstates, and not the mass eigenstates or mixtures of the flavour eigenstates. This is interesting as it is not true for quarks, where the weak coupling is between mixtures of the quark flavours.