Time is a dimension, but not like space

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.

>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.

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.

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

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.

Causality does not depend on the speed of light. Rather, light travelling in a vacuum happens to travel at the maximum speed of causality.

If light is slower in other mediums, that has no effect on how quickly causation can happen.

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).

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

Light moves with `c` speed regardless of medium. Whenever we say light moves slower in a medium, we simply mean it is measured to be slower, it is macroscopically slower, it's as if having a hypothetical vehicle that, when it moves, it always moves with a constant speed, but you measure it by taking the time of departure in place A, time of arrival in place B, measure the distance |AB| on a map, and from that calculate the speed of the vehicle. Your measurement will be affected by exact path shape (which isn't a straight line), as well as the number of times the driver decided to take a break to sleep in a motel, eat something, go to a toilet on a gas station etc.

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.

FTL is shorthand for "Faster than Light" but here it really means "Faster than Light in a Vacuum".

Light actually has nothing to do with it; it just happens to travel at the max speed allowed by the universe when there's nothing that impedes it's motion (i.e. in a vacuum).

So the acronym should really be "FTLIAV"!

This example seems… bad to me. Are you simply saying that light moves slower from A to B through a medium like water because it takes a path that is less direct to navigate the medium?

I agree, that answer is misleading. The way I've always understood it: light is an EM wave, and it interacts with medium that it travels through. When traveling through a vacuum, the "beam" source is the origin, but when traveling through a medium the "beam" is a propagation of emissions from the matter absorbing, oscillating, and re-emitting a photon. These interactions take (an extremely small, but nonzero) amount of time, but the light being absorbed and emitted always travels at c.

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

There are many things that can go faster than light, most of which we don't know about yet. But one thing is for sure, quantum entanglement can be undone faster-than-light. It's just that nobody has yet figured out how to send information through that medium, and it may even be impossible. But clearly, causality isn't being violated here and it goes faster than light in a vacuum.

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.

There is a maximum speed, "c" that anything can move relative to something else in this universe.

If light happens to move slower than c under some conditions, that is irrelevant. It isn't the speed of light we care about, it is c.

Essentially, when we say FTL, it means "faster than c", not "faster than light".

No. It actually goes slower. https://youtu.be/uo3ds0FVpXs?si=b7sDxNuQkTuwAkcP gives a pretty good overview.

Edit: wrong one https://youtu.be/yP1kKN3ghOU?si=hsBj0RpzOb3JZWdS the one above is the "why."

Maybe we should have started with c. Could have avoided this whole discussion.

No. It propagates slower.

https://youtu.be/KTzGBJPuJwM?si=Pab2F0EFsB4oGhUo

> But one thing is for sure, quantum entanglement can be undone faster-than-light. It's just that nobody has yet figured out how to send information through that medium, and it may even be impossible. But clearly, causality isn't being violated here and it goes faster than light in a vacuum.

In quantum entanglement, two particles can be entangled in such a way that measuring one particle instantly determines the state of the other, even if they are light-years apart. This "instantaneous" connection seems faster than light, but it cannot be used to transmit usable information in a meaningful way.

The phenomenon does not violate relativity because no classical information can travel between the particles faster than light. Entanglement is a correlation, not a means of communication and hence NOT a means of causation.

The absorptions are the "breaks" in the analogy.

> 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).

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.

I trust the quantum physicist more than a pop-sci YouTuber.

Both videos come to the same conclusion so your comment betrays the fact you didn't even watch the one I linked.

That or you misunderstood the physicist. You need to watch both videos to understand what's happening here.

The speed of light is not "slower in water". Light propagates more slowly through water. The subtle difference is not just pedantic semantics. It's the key to understanding how we don't have a paradox on our hands.