Neutrino Oscillation: Explaining the Solar Neutrino Problem

[nhmllr]

I've been reading about the solar neutrino problem.
I heard that if the neutrinos had mass, then they could "oscillate" between all three types. Whatever. I'll buy it.

But here are two things I don't get:

Why do they need mass to oscillate (is it because having different masses is the only distinguishing features of the three flavors)?

Why don't electrons, muons, and tauons also oscillate between each other? They have different masses and have the same charge.

Thanks

 

[bm0p700f]

I think the answer is very mathematical. I don't understand the maths so I cannot help and from your post I don't think you will either so this is one of the thing we have to acept rather than uinderstand. Which is why at some point I want to study physics to a much higher level than I can currently explain.

 

[alemsalem]

the reason they need a mass difference is close to this:
if you have an initial state that is a sum of three states that have equal energies, then each of these states evolves with a factor of exp[-iEt] meaning it only changes by a phase,, if they had different energies the state changes over time and in the case of neutrinos we get a non-zero probability of finding a type other than the one we started with.
that's my primitive understanding.

this might be relevant: https://www.physicsforums.com/showthread.php?p=3457913#post3457913

 

[Accidently]

I've been reading about the solar neutrino problem.
I heard that if the neutrinos had mass, then they could "oscillate" between all three types. Whatever. I'll buy it.

But here are two things I don't get:

Why do they need mass to oscillate (is it because having different masses is the only distinguishing features of the three flavors)?

Why don't electrons, muons, and tauons also oscillate between each other? They have different masses and have the same charge.

Thanks

neutrino mass difference (and mixing) will lead to oscillation. But there were several other models explain neutrino oscillation without neutrino masses. Unfortunately, they were ruled out by some experiments. Neutrino mass is the only one survived.

Electron, muon, tauon and quarks cannot oscillate because they are much heavier. Their large masses (wrt neutrinos) make them lost their coherence in an extremely short time/distance. Thus, they cannot oscillate after that.

 

[belliott4488]

To understand how neutrinos oscillate, you have to understand the concept of mixed states, which is why "neutrino mixing" is sometimes suggested as a better term than "neutrino oscillations". As you might know from Quantum Mechanics, particles are described as existing in quantum states (technically, "eigenstates" of some observable quantity), some of which are stable, others of which are not. As it happens, a neutrino can exist in a mass eigenstate, where its mass is well-defined, or in a Weak eigenstate, where its identity as electron-, mu-, or tau-neutrinos is well-defined.

These states are not the same, and moreover, each kind is a mixture of the other. That is to say, a neutrino in a mass eigenstate is in a mix of all three Weak eigenstates, and conversely, a neutrino on a Weak eigenstate (such as an electron neutrino) is in a mix of mass eigenstates.

Being in a mixed state means that if the observable quantity whose states are mixed is measured, any one of the values corresponding to those state can be observed. The relative probabilities of those different values evolve with time, hence oscillations.

The point of all this is that if the neutrinos masses are all zero, then this mixing goes away and you don't get the oscillation.

 

[DrBenStill]

If you would like to know a the general idea of neutrino oscillations then check out this blog post on the Neutrino Science blog.

Identity Crisis

For more in-depth information follow this ongoing series of posts

Coming At It From All Angles: Part 1
Coming At It From All Angles: Part 2
http://neutrinoscience.blogspot.com/2011/06/coming-at-it-from-all-angles-part-3.html

Please do ask questions in the comments or I will check back here when I can.

 

[Bill_K]

The answer is a lot simpler than the responses above. Oscillation requires an off diagonal term in the Hamiltonian, and when the Hamiltonian is diagonalized this necessarily leads to a mass difference.