Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
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No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.
> No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
If everything happens instantaneously then there is no real cause and effect, and the universe would be over before it really got started.
The limit of causality is the light speed limit in vacuum, not "whatever happens to be the max speed of light in some medium".
Light (as in visible light) is also irrelevant to this, it's just an example of something moving at that speed.
You wrote: "I'm having trouble with this assertion. Light travels slower in water than in air, by your assertion that light is the limit of causality; then surely we can create a paradox with ftl right in a pool."
I answered that the "speed of casuality" is not "how fast light travels in a given medium": it's the maxiumum speed of light, which is the speed of light in a vacuum.
So that the light travels slower in a pool doesn't mean we can violate casuality - the overall casuality "speed limit" remains regardless (it's a maximum limit in the universe, not a regional one).
Btw, light doesn't really slow down in a medium like water. Photons always travel at the speed of light. The aggregate light appears to slow down in the water, as invidividual photons are converted to energy when interacting with the water particles and then the energy is emitted again as new photons.
The photons while they exist (i.e. before and after the conversion to/from energy) always run at the speed of light, even inside a medium like water or whatever else. Some of them will be converted to heat though, warming up the water - but in that case they're not light anymore.