# Do neutrinos travel faster than light in air?

I read in wiki that the speed of light is 88km/s slower in air than it is in a vacuum.

Do neutrinos travel faster than light in air?

-
Even if so, it is not that interesting: because neutrino cannot decay to photons, so perhaps there is no cherenkov radiation? –  Idear Jan 17 at 19:42
It could be interesting if scientists forget to account for air when comparing speeds from various experiments. Do scientists account for air in all speed of light experiments and observations? –  Jitter Jan 17 at 19:55
Ps. Is the 88km/s just refering to the phase velocity? Does the group velocity still travel at c? –  Jitter Jan 17 at 20:05
–  Chris White Jan 17 at 20:19
If you're worrying about whether the scientists at CERN were accounting for air when measuring the neutrino speed, you needn't worry. They measured the speed of neutrinos travelling through the ground (see neontommy.com/sites/default/files/users/user718/…). Anyway they weren't comparing the speed of neutrinos to the speed the light travels at in the same medium, they were comparing the speed of neutrinos to the speed of light in a vaccuum. –  jk88 Jan 17 at 21:18

The answer is yes. Neutrino will travel faster than light in a medium with a refractive index ($n$) greater than one (which is the case of air). Indeed the speed of light in that medium will be $v_{\text{medium}}=c/n$ where $c=2.998\times10^8$ m/s and $n>1$.

Then, because neutrino interacts only very weakly (only through the weak nuclear force) with the medium, it will barely be slowed compared to how much light is slowed and thus will go faster than light. Remember that neutrinos are almost massless and thus already travel to nearly the speed of light.

--- New Edit --- Indeed, the neutrino speed will depend on it's energy (as pointed out in comments). But I think that in most process in which neutrinos are produced (take for instance a beta-decay), the energy of the neutrino is enough to consider it as going to nearly the speed of light. So strictly speaking, the answer is that it depends on the neutrino energy and what type of medium you are in.

-
Note that the speed of a neutrino depends on it's mass and energy. The absolute masses are not currently known, though they are believed to be much less than 1 eV. –  dmckee Jan 17 at 21:30
What about media with $n<1$? –  ybeltukov Jan 19 at 6:41
Well this depends on the specific type of media. In media with $n<1$ (which in general is frequency dependent), the phase velocity of light is indeed faster than $c=2.98\times10^8$ m/s. However the group velocity (which I guess is implicitly what the question is about) will always be equal or smaller than $c$. –  VanillaSpinIce Jan 19 at 16:07