Then it doesn't violate any fundamental laws of existence, does it? We're just talking about receiving delayed images of events. The ship isn't engaging in backwards time travel by contacting Earth after seeing its call being received, because Earth knows it already placed the call. No information from the future is being conveyed to Earth, and the third party isn't actually able to affect the "cause" after seeing the "effect", because the cause is over and done with.

No, you misunderstand me. Earth hasn't placed the call yet; the ship can use FTL and its knowledge of the effect to send a message to Earth that Earth receives before it places the call. The scenario you're describing is described as such in the link above:

"""

Now, you might say "wait, light takes a finite amount of time to travel. You've just shown what times the spaceship will assign to various events, but they can't see it immediately. That'll save us!" Sadly no. Here's when the ship actually gets the light from the events. [complicated figure, but it shows there's enough time in the light-cone chart for the ship to receive the 'Proxima received the phone call' event and then travel to Earth slower than speed of light and tap Earth on the shoulder before the phone call was sent]

As you can see, the light from the phone call reception arrives well before the light from the placing of the phone call. Again: causality is violated.

"""

In fact, that message can be "Place the call," which means the call is placed because Earth was told to by the third party because the third party knew the call had to be placed because they observed the effect because the call was placed... FTL allows for closed-causal loops.

I'm still not getting it. What mechanism allows for knowledge of the effect before the cause objectively happens? For the third party to observe the effect, the cause had to have happened from Earth's perspective. The fact that the light hasn't reached the third party yet seems immaterial. I'm not trying to play gotcha, seriously don't get it.

"As you can see, the light from the phone call reception arrives well before the light from the placing of the phone call. Again: causality is violated."

It's still only speaking about the perspective of the ship, and it seeing effect before cause.

> What mechanism allows for knowledge of the effect before the cause objectively happens?

Yeah, it's tough. I don't think I can explain it without bootstrapping a college semester of relativistic physics, and I'm afraid I'm not that good. :(

To start your search, "Objectively happens" is the intuition that doesn't hold water in relativity. There is no objective frame of reference (i.e. nothing in the universe is moving at 'speed zero', or more precisely, everything moves at 'speed zero' relative to itself). So everything is relative; there's no place anyone can stand and observe things objectively. Relativity changes the rules upon which reality operates so they hinge, loosely, on two fundamentals:

1) The speed of light, in a vacuum, must be observed to be the same by all observers

2) Observers do not agree on the times that they measure for when events occurred (for example, the "moving train" thought experiment shows that simultaneity is violated by relativity), but they can agree that the events align to each other subject to the Lorentz transformation when relative velocities are accounted for.

Under these rules, causality is maintained; I don't have the whole proof at my fingertips, but it can be shown that regardless of how you apply Lorentz transforms to sublight-velocity observers, they'll agree that events that caused one another have the same ordering (this is a subtlely different statement than "Two things happened at the same time," and it's partially a property of the events that are effects being within the 'light cones' of the effects that are causal). FTL travel allows one to exceed the "light-cone limit" and as a result, the causality constraint that 'effects are in the light cones of causes' is violated. The frame of reference where one event caused the other exists (i.e. there are velocities one could have where the light cones will line up that way), but there are also now velocities one can have where the light cones do not line up that way. It's only impossible for any observer to see effects happen before their causes if nothing can exceed light-speed.

For your specific question ("What mechanism allows for knowledge of the effect before the cause objectively happens?"), I think I can offer a short hypothetical thought experiment that might illuminate things. Imagine there were a door from Earth to Mars allowing instantaneous transit (so infinite velocity, in excess of speed of light). One day, the sun blinks out of existence. Earth will see this occur three light-minutes before Mars does. Someone steps through the door and yells "People of Mars! I come with a warning! In three minutes, the sun will go out! Evacuate now!"

From the Martian point of view, that person is a time traveler from the future, and the intuition relativity brings to us is that the Martian point of view is as "objective" as any other point of view. This (Lorentz-transform-violating) visitor has knowledge of an event that will definitely occur in three minutes before the cause of that knowledge has occurred.