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Here’s a concrete example:
Say a ship leaves Earth traveling half the speed of light, but it carries a communication device that can communicate with Earth “instantaneously” (i.e., faster than light). From Earth’s frame of reference, time on board the ship is slowed down by a factor of 0.866, while from the ship’s frame of reference, time on Earth is slowed down by the same factor. (This isn’t some trick of perception—the geometry of spacetime distorts in such a way as to make both these observations true simultaneously.)
Now suppose a year has passed on Earth, and we use the device to communicate with the ship ”instantaneously”. From Earth’s frame of reference, the ship has currently experienced only 316 days of elapsed time, so that’s when they receive the signal according to their clock. But from their frame of reference, Earth at that point has only experienced 274 days of elapsed time—so when they send their “instantaneous” reply, it arrives on Earth three months before the original signal was sent.
Why is time on earth slowed down from the ship's perspective? Shouldn't it be faster? Like if earth perceives that the time on the ship is passing slower shouldn't the people on the ship perceive the time on earth as passing faster to compensate?
Also, I have quite a hard time understanding how time exactly slows down. Is it sort of as though we adjusted the time step duration (tickrate, more precisely) of a physics simulation in an area (making everything happen slower/faster there in relation with the rest, where the original timestep is kept)? (Without losing precision and all those problems that occur in a simulation normally) Or is this analogy flawed and that is why I'm not getting it?
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?