# I Neutrino mass

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1. May 12, 2018

### Kiley

Why is there an assumption that if neutrinos didn't have mass they would move at the speed of light? and how does the fact they oscillate prove they have mass?

2. May 12, 2018

### ChrisVer

Because of the $E^2 -p^2 = m^2$
When the mass is 0, then the particle moves at the speed of light and there is no reference frame where it appears at rest.

Because the oscillation pattern appears with the mass-squared difference between the neutrinos... if they are massless (or even mass-degenerate) there wouldn't be any oscillation visible.

3. May 12, 2018

### Orodruin

Staff Emeritus
It is not just neutrinos. Anything massless in relativity moves at the speed of light, this follows directly from special relativity.

The oscillation phase in neutrino oscillations is directly proportional to the difference between the squares of the masses of the different neutrino mass eigenstates. This means that at most one out of three neutrino masses can be zero.

4. May 12, 2018

### Janus

Staff Emeritus
Any massless particle is required to travel at c in a vacuum. Massless neutrinos would travel at c for the same reason massless photons do.

The oscillations occur because the the wave length of three mass states (electron, muon, and tau) are different, and thus shift in phase with respect to each other. This phase shift is what creates the oscillation. But for the wavelengths to be different, the mass of the three types of neutrinos have to be different, which in turn means they must be finite and non-zero.

5. May 12, 2018

### Kiley

Thank you all for your replies. Could you recommend any literature of the subject?

6. May 12, 2018

### Staff: Mentor

A suitable introduction to neutrino oscillations depends on how much quantum mechanics you know. Most of the stuff I find with a Google search for "neutrino mass and oscillations" seems to be reviews for physicists who already know something about particle physics and are comfortable with Dirac-bracket notation, superposition of states, etc. Maybe try this on for size, starting with section 4 on page 3:

http://web.mit.edu/shawest/Public/8.06/termPaperDraft.pdf

7. May 12, 2018

### Kiley

Thank you so much Jtbell, this is very helpful! :)

8. May 17, 2018 at 7:47 AM

### Orodruin

Staff Emeritus
Some small bit of nit-picking. The electron muon and tau states are not the neutrino mass states. In fact, it is crucial for oscillations that not only the masses of the mass eigenstates are different, but also that the flavour states, i.e., the electron muon and tau neutrino states, are not equivalent to the mass states but instead are linear combinations of the mass states.