[coldtea]

>Light travels slower in water than in air, by your assertion that light is the limit of causality

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.

[withinboredom]

I fail to see how a vacuum permits violations of casualty. Care to explain?

[coldtea]

Who said anything about a vacuum permitting violations of casualty?

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.

[MattPalmer1086]

The vacuum has nothing to do with causality.

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).

[andsoitis]

> Causality violation can happen in general relativity

The only theoretical case I’m aware of are closed timelike curves (CTC) which are paths in spacetime that loop back on themselves, allowing an object to return to its own past. A famous example is the Gödel metric, a solution to Einstein’a field equations.

It should be noted, however, that these solutions are generally regarded as unphysical because they require conditions that don’t seem to exist in our universe (such as a globally rotating universe).