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The blue glow characteristic of Cherenkov radiation is visible emanating from underwater reactors.

Is it also visible through ice, at the IceCube neutrino experiment (not that anyone is physically standing there looking)?

Would the radiation be around for such a short time, produced discontinuously, that it wouldn't be visible?

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The flash of Cerenkov light from a single neutrino interaction is probably not sufficient for the human eye to detect; this is why an array of PMTs is used to pick up the signal. It's not a question of light being transmitted, but whether the intensity is sufficient to be "visible". In a reactor there are very large numbers of particles traveling at greater than the speed of light, and interacting strongly with the surrounding medium. That's why there is a blue "glow". Neutrinos have a lot of energy, but not a high probability of interacting. According to the icecube wiki page, they expect one neutrino event every 20 minutes. Blink and you would miss it. And while there may be a lot of photons produced in one flash, very few (if any) of these would reach your eye unless you were very close - the light spreads over an area $4\pi r^2$ and of that, your extended pupil (say 8 mm diameter) only occupies $\pi \cdot \mathrm{0.004^2 m^2}$. So at 1 m distance only 4 in $\mathrm{10^6}$ photons would reach your eye - and if you were 20 m away, that number would drop to 1 in $\mathrm{10^8}$ - ignoring any scatter in the ice, etc.

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