Can an object move faster than the speed of light in a medium? In water the speed of light changes to $2.25 \cdot 10^8m/s$.   Can a electron travel faster/travel at the same speed   in water. I don't see any violation of SR. So   shouldn't it  be possible for an electron to travel at say $2.5 \cdot 10^8m/s $. Water is just an example.In other mediums like hydrogen electrons in excited states should travel at higher speeds than that of light in the same medium.
 A: Yes, it can, the limit is 299792458 m/s.
For example  in water the speed of light is reduced by the refraction index, and therefore a particle exceeding (c/n) does not violate the SR.
Read more here: https://en.m.wikipedia.org/wiki/Cherenkov_radiation
A: Yes it is possible, for instance electrons regularly win the race against photons in water.
And they emit radiation known as Cherenkov Radiation. It's properties are similar to those of the shockwaves produced when an object crosses the sound barrier: a classical conical shockwave, just with light in this case.
A: The maximum speed of light is defined as the velocity of electromagnetic waves in a vacuum. Light is a range of electromagnetic wavelengths that can be detected by our eyes. Electromagnetic waves traveling through a non-vacuum region can be "slowed down" by interactions with matter/energy present in the non-vacuum region. As another commentator stated, other non-electromagnetic-wave mass/energy entities (atoms,sub-atomic particles),can pass through identical regions at a higher velocity than light (electromagnetic waves), Neutrinos are a primary example of matter particles that may achieve this higher velocity in a non-vacuum. No neutrino, or anything else that has rest-mass, can ever attain the velocity of light in vacuum.
