Well, the speed that the photons travel between the water atoms is still c.
An underwater explosion travels slower in water than it does in a vacuum. That's not just to do with the coefficient of friction of the water. The light from the explosion will take longer to reach you than it would if you and the explosion were in a vacuum.
Which leads me to another thought - does that mean that the matter of water is basically just another form of spacetime, in which the speed of Causality is different from the speed of Causality in spacetime in a vacuum?
The speed of light is slower in water, yes, which is why Cherenkov radiation exists -- that's basically the photon equivalent of a supersonic shockwave. The speed of causality doesn't change, and it's easy to demonstrate that by throwing particles through it at superluminal speeds; nuclear reactors do it all day long.
Cherenkov radiation is still light/electromagnetic energy, and it still must obey the speed of light (Causality) through the water, which means it will still be slower to arrive from source to observer at a slower speed than it would have had it been travelling through a vacuum.
You're not supposed to measure the speed of the Cherenkov radiation. You're supposed to measure the particles that are causing Cherenkov radiation.
If you measure those fast particles, you'll see that they will cross a tank of water just as fast as they will cross a tank of vacuum. They can cross faster than a beam of light will.
I am confused, what particles could reach superluminal speeds?
A.k.a. hydrogen oxide.