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

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Discussion Overview

The discussion revolves around the phenomenon of neutrino oscillations, specifically exploring the relationship between neutrino flavors and their masses, and how these oscillations can occur in terms of energy. The scope includes theoretical aspects of particle physics and the implications of the energy-time uncertainty principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how neutrino oscillations can occur if different flavors correspond to different masses, suggesting a potential conflict with energy conservation.
  • Another participant explains that flavor eigenstates and mass eigenstates are distinct, indicating that an electron neutrino is a mixture of states with different masses, which allows for oscillation without violating energy conservation.
  • A participant seeks clarification on the terms "mass states" and "interaction states," asking if they are interchangeable with flavor states.
  • It is suggested that interaction states correspond to flavor states, as interactions yield states of definite flavor that evolve according to different frequencies due to their mass differences, leading to oscillations.
  • One participant notes that weak interactions couple to flavor eigenstates for leptons, contrasting this with quarks, where the coupling involves mixtures of flavors.

Areas of Agreement / Disagreement

Participants generally agree on the distinction between flavor and mass eigenstates, but there is ongoing exploration regarding the implications of this distinction and the nature of interactions involved in neutrino oscillations. The discussion remains unresolved regarding the full implications of energy conservation in the context of oscillations.

Contextual Notes

Participants express uncertainty about the relationship between energy conservation and neutrino oscillations, particularly in the context of the energy-time uncertainty principle. There are also unresolved questions about the terminology used to describe different states of neutrinos.

jeebs
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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?
 
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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.
 
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?
 
jeebs said:
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 Schrödinger equation with different frequencies, you get oscillations.
 
nice one, thanks.
 
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.
 

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