Time is a dimension, but not like space

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!

How could an effect precede a cause if there were no speed limit to causality?

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.

> How could an effect precede a cause if there were no speed limit to causality?

> 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.

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.

Yes. You can pretty easily think of an experiment where a waterborne person throws a switch that changes some distant object, only to see that object change "before" they threw the switch because the experiment actually communicated the switch change via an airborne method unavailable to the waterborne observer.

I don’t think that actually works. In this case you’re talking about a round trip, with the switch’s outbound signal traveling fast (airborne/vacuum light speed) and the return signal of the object visually changing traveling slower (water light speed). The total round-trip where you see the effect of flipping the switch would take longer if either leg involved water, but it wouldn’t cause the perception of it to happen ahead of the act of flipping the switch.

Observer A and observer B are mermaids. A throws a switch that turns on a light on a light house. Relative to each observer, the can see the cause and effect. B invents a periscope that allows them to see faster than light. Now B will be able to see the light turn on before the switch is flipped.

Replace periscope with “wormhole” and you get a more traditional experiment. The question of can we use this to violate casualty is non-sensical, because we can’t violate casualty (even with faster than light travel). In the traditional experiment, if I see the light turn on, the cause has already happened; sending a message “back in time” won’t change that.

However, this is only because all frames of reference stay the same. If you could actually travel back in time, who knows what would happen. That’s largely why this whole conversation makes no sense. You can’t violate casualty with FTL, only with time machines and FTL isn’t a Time Machine.

In general relativity, FTL can be used as a time machine.

Then you should be able violate casualty with simple water, otherwise FTL cannot be a Time Machine because it is quite simple to go FTL.

Faster than light in a vacuum. Not faster than light in other mediums. See the many other explanations on this thread.

It's literally the same thing. The medium doesn't matter, see Einstein's equations. It all boils down to "relative to what". Light moves slower around a black hole, and that is in a vacuum. None of the arguments make any actual sense.