I have heard this mentioned several times with this exact wording, that faster than light travel would break/violate causality and I do not exactly understand why and how it would do that. Could someone more well-versed in physics explain to me why that would be the case? Or is it not the case? (Yes, I am fully aware, that faster than light speeds are impossible in real life, but I am more curios about how it would hypothetically affect physics, were it possible). I am somewhat familiar with physics and more so with mathematics (engineering student), if that helps anyone to explain it at an appropriate level.
According to special relativity, all non-accelerating frames of reference are equally valid, so the observations are symmetric: both Earth and the ship see the other moving away at 0.5c, so they both see the other slow down.
Now it’s true that if the ship turned around and returned to earth at 0.5c, it would be the ship’s clock that was behind earth’s, and not the other way around—but that’s because, when the ship turns around, it accelerates, and while it does so the whole non-accelerating frame of reference thing goes out the window. After it finishes turning around, the point in earth’s timeline the ship judges to be simultaneous with its own will have jumped forward in time—so that even though it observes earth-time moving slower than its own during both the outbound and return trips, the time jump as it turns around will more than compensate.
(Or equivalently, you could say that after turning around, the ship observes its own past history on the outbound trip to have been slowed down even more than earth’s.)
Okay. Thank you! This explanation made it click for me (now I think I get the original example too). Here the real cause of the violation is the instant communication, isn’t it? If the communication was done via radiowaves (which as far as I know also travel at the speed of light) it would not be violated, because of the time it takes for the information to arrive from the Earth to the spaceship and back, is that correct? Is this why (as I have read/heard on several occasions) the upper bound for the speed of information is also the speed of light?
Exactly.
When I say the parties observe each other slowing down, or observe the simultaneous point in the other’s timeline jumping around, they don’t observe this in real time unless they’re using faster-than-light communication. Using conventional means, it’s only after receiving the signals and compensating for the redshift or blueshift that they can reconstruct the other’s past timeline relative to their own.