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.
It's just that light (if there is nothing in its way, so in a vacuum) will travel at the max speed of causality.
Causality violation can happen in general relativity when something moves faster than the max speed of causality (which is the same speed as light in a vacuum).