# If Neutrinos have mass.

1. Oct 18, 2015

### Ishanmu

The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald "for the discovery of neutrino oscillations, which shows that neutrinos have mass" So I was wondering if they have mass how fast are they traveling?

2. Oct 18, 2015

### Orodruin

Staff Emeritus
As for anything with mass, this depends on their kinetic energy. In most cases, the neutrino mass is very small compared to the energy, which makes them ultra relativistic, i.e., they travel at speeds very close to the speed of light.

3. Oct 19, 2015

### Staff: Mentor

If I remember correctly, the neutrinos detected at OPERA (after ~700km of flight) are expected to be less than the diameter of a proton (10-15m) behind light in vacuum.

4. Oct 19, 2015

### Orodruin

Staff Emeritus
Easy to check. The average neutrino energy in OPERA is roughly 17 GeV, we also have that
$$1-v = 1- \frac pE \simeq \frac{m^2}{2E^2}.$$
With an upper mass bound of order 1 eV, this would mean a lag of roughly 700 km * (1.7 * 10-21), which evaluates to something surprisingly close to 10-15 m ...

5. Oct 19, 2015

### Staff: Mentor

For a solar p-p neutrino with E = 400 keV and mc2 = 1 eV, and a flight distance of 93 million miles (sun to earth), I get a lag of about 0.5 m.

6. Oct 19, 2015

### snorkack

How much is the lag from neutrinos emitted by gamma ray bursts?