http://en.wikipedia.org/wiki/Cherenkov_radiation
The electrons are travelling faster than light.
http://en.wikipedia.org/wiki/Faster-than-l..._speed_of_light
Last line, first paragraph: Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here.
For an object to be classified faster than the speed of light, it must not act according to special relativity or casuality, Cherenkov radiation does.
General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However,
it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer.
It gets complicated here, because now we are dealing with space-time continiums, worm holes blah blah blah blah
But there is no solid proof of a particle breaking the speed of light as observed from 2 reference frames, lots of debate on this issue nowadays.
I think they are talking about exceeding the light barrier in the specific medium not the speed of light itself. So, as the example gives the speed of light in water is .75c then when a particle exceeds that speed in that specific medium, which still means it'll never be able to go as fast as light itself.