Does faster than light travel violate causality? Why/Why not? How?

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.

AbouBenAdhem ,

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.

surepancakes OP ,

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

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?

AbouBenAdhem , (edited )

Why is time on earth slowed down from the ship’s perspective? Shouldn’t it be faster?

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.)

surepancakes OP ,

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?

AbouBenAdhem ,

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.

perviouslyiner , (edited )

Has anyone actually proven no violation of causality? Wikipedia seemed to suggest that it’s not physically impossible to have a wormhole, take one of the ends on a round trip so that it doesn’t age as much, and you’d be left with a situation where you can go in one end and come out in the past.

ExchangeInteraction ,

This argument, as far as I know, relies on the nature of time dilation. You see as your velocity increases closer and closer to the speed of light, time itself begins to slow down. This is not an analogy or some fancy math trick, this is a real thing you can measure in the lab. As you get closer and closer to the speed of light time slows more and more. Such that as you reach the speed of light (again this is physically impossible at least for anything with mass) you can think of time as stopping. So for light or anything that moves at the speed of light they’re kind of isn’t such a thing as time, but I digress.

So (again even though it’s actually impossible), what happens as you start to go faster than light? Does this trend continue? If it does that would mean that time starts to reverse. And once you see that faster than light travel might imply time reversal, it should be easier to understand how this would violate causality. Because how do you get event A caused by event B when event B was before even A?

surepancakes OP ,

Thank you for your answer. When viewed from this perspective it makes more sense.

WantsToPetYourKitty ,

iirc the only method of faster than light travel that doesn’t violate laws of physics involves warping spacetime. We can now detect ripples in spacetime, and scientists postulate that in the far future it might be possible to manipulate spacetime by warping it with technology not currently in existence.

Of course you could argue this method isn’t really faster than light travel, since you’re actually bending the distance between you and the destination.

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