Cherenkov Radiation

They didn't word that very well.

Would have been clearer if they said "However, in other mediums (like water), particles can potentially move faster than light does in that same medium."

How can something travel faster than light?

Answer: Light slows down when going through water or air or gas. It's only in a vacuum that light travels at 'c' (from Einstein's equation). And it's that speed c that is a limit due to relativity.

But the exciting thing is that when you're not in a vacuum particles can be traveling faster than the local speed of light (maybe 75% c). And that process of a particle zipping along gives off Cherenkov radiation.

I think of it as the light equivalent of a supersonic shockwave and sonic boom. Faster than sound gives noise. Faster than light gives light (or other electro magnetic radiation)

(People with more knowledge might say the sonic boom analogy is very inaccurate but not sure)

It took me a long time to develop an intuition for light and electromagnetic wave propagation, and I’m still working on it.

Fundamentally, changes in the EM field propagate always with the speed of light in a vacuum, i.e., c (also known as the speed of causality). Single EM waves propagate with exactly this speed and they do not magically slow down in a medium... they propagate happily at speed c! (FYI EM waves are more complicated like this and involve electric and magnetic fields evolving together).

But since EM radiation interacts with matter and this interaction itself changes the EM field again it results in more EM waves that propagate also at c. Hence, they propagate together and the net result be constructive or deconstructive as well as anything in between. If they have different frequencies, they can also create "interference" patterns or pulse envelopes that seem to propagate slower and even faster than c.

No doubt that the causes and effects are not easy to understand but always thinking in terms of changes in the EM field ALWAYS propagating at c helped me.

To be precise, what we call the “speed of light” is the limiting speed at which information and causal effects can propagate through spacetime. In vacuum, it coincides with the propagation speed of photons, i.e. of light. In other media or under certain conditions, however, light can propagate at a speed lower than , without changing the fundamental limit imposed by relativity. So "speed of light" used to denote is a bit misleading

In a medium, this can create a "phase kickback" which creates a combined wave that appears to travel slower than the original one. The kickback is just the result of multiple EM changes propagating, i.e. the photons interact with the material, re-emitting photons.

3Blue1Brown has a beautiful animation for this phase kickback here: https://youtube.com/shorts/XIW-2ykgVPI?si=PJWiAC2BO7_xP0S6