# 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? – wonderich Jan 17 '14 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 '14 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 '14 at 20:05
• – user10851 Jan 17 '14 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. – kd88 Jan 17 '14 at 21:18

The answer is yes. Neutrinos 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 neutrinos interacts only very weakly (only through the weak nuclear force) with the medium, neutrinos 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 a neutrino is enough to consider it as going to nearly the vacuum 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 '14 at 21:30
• What about media with $n<1$? – ybeltukov Jan 19 '14 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 '14 at 16:07
• given the refractive index of air is "very close" to 1 and the speed of a neutrino is typically "very close" to $c$ can you give some typical values. What you say sound intuitively right but some numbers would make me feel better. – By Symmetry Oct 11 '14 at 23:53
• @VanillaSpinIce Just a quibble. It is the signal transmission velocity which stays below $c$. The group velocity is only an approximation to this (albeit an excellent one in most cases). What matters is that the medium's transfer function should be causal, i.e. no output before a time $t/c$ when the wavefront first reached the input of the medium and $t$ is the distance through it and such criteria can be reduced to things like the Paley-Wiener integral criterion: see discussion here – WetSavannaAnimal Oct 12 '14 at 3:02

It looks so, as neutrino speed was measured to coincide with the light speed, and neutrino interacts very weakly with matter. However, as neutrino probably has mass, the answer to your question is positive only for neutrinos of sufficient energy.

• "However, as neutrino probably has mass (en.wikipedia.org/wiki/Neutrino#Mass ), the answer to your question is positive only for neutrinos of sufficient energy" --> Neutrinos are known to have mass "the answer to your question is positive only for neutrinos of sufficient energy" --> Neutrino masses are however (currently) immeasurably small... which means even with the current best upper limits on neutrino masses you would only need a neutrino with energy > 10 eV to be categorised as ultra-relatavistic. – kd88 Jan 17 '14 at 20:59
• @jk88: "Neutrinos are known to have mass"--> As far as I know, "some neutrinos are known to have mass" - only differences of masses are known to be non-zero. – akhmeteli Jan 17 '14 at 21:43
• @jk88: I agree that neutrinos need to have very small energy to be ultrarelativistic, but they do need to have some energy for that. – akhmeteli Jan 17 '14 at 22:05
• "If a neutrino flavor is a mix of a massless and a massive state, it does not mean the flavor is necessarily massive" --> yes it does! – kd88 Jan 19 '14 at 0:31
• @jk88: I gave my argument, you have not offered yours. – akhmeteli Jan 19 '14 at 0:42