If nothing can travel faster then the speed of light, how does one explain Cerenkov Radiation?
For the sake of other readers of this answer who might not have any idea what
Cerenkov (pronounced more like Cherenkov) radiation is, let me try to explain in
simple terms what it is.
Whenever an object moves in a medium faster than the waves in that medium can
travel, it radiates energy in the form of a 'shock wave'. This is observed in
airplanes traveling faster than the speed of sound, for example, and it is called
the 'sonic boom'. The shockwave has a conic shape, and the faster the airplane, the
narrower is the opening angle of the cone. The reason for the formation of the
shockwave is that the sound waves emitted by the airplane interfere constructively
on the surface of this cone. A simple consideration of the airplane and sound
speeds in a drawing should make the matter clear.
Another example, perhaps more familiar, happens in water. If something (a duck, a
ship, etc...) moves faster than the speed of water waves, they will cause that
familiar v-shaped wake. That is another example of a shockwave (and radiation of
energy) but this time in water. Note that a ship moving slower than the speed of
waves will _not_ create any wake, and will not radiate much energy.
Cerenkov radiation is exactly that -- but for light. If a particle moves faster
than the speed of light, it must create a shockwave, and radiate energy. Now we can
return to the actual question -- if relativity states that the speed of light can
not be exceeded, how can there be Cerenkov radiation?
The problem here is that relativity states that the ultimate speed limit is the
speed of light _in_vacuum_. It follows that Cerenkow radiation never occurs in
vacuum. But, propagation of light can be slowed down considerably in materials due
to interactions between light (photons) and particles of the material. Thus, it
becomes possible for a particle moving at relativistic speeds to actually exceed
the speed of light _in_that_medium_. When that happens, the particle emits
radiation in the form of a 'shock wave', widely known as Cerenkov radiation.
In fact this principle is used for detecting and differentiating particles in
physics experiments. Two particles having the same energy may be difficult to
differentiate by measuring the total energy -- but the particle with the smaller
mass (like an electron)will have a greater speed, and will emit Cerenkov radiation,
while the particle with greater mass will be relatively slow, and will not generate
any Cerenkov radiation.
So, to wrap everything up, let me restate:
Nothing can travel faster than the speed of light in vacuum.
It is possible to travel faster than light in a material, and if you do, you will
emit Cerenkov radiation.