If a message was sent from a space ship travelling at relativistic speeds (going away from the target) would it arrive at it’s intended destination; faster, slower or at the same time as it otherwise would have compared to a ship that is ‘stationary’?
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Assuming that the message is conveyed by some light-speed medium, like a radio wave, it would arrive at the same time as it would have for a stationary transmission, though with lower energy (that is, it would be redshifted by its movement away from the receiver). The speed of light is constant for every observer, regardless of the speed of the object emitting it.
[Disclaimer; it’s late and I haven’t done the maths.]
We have to be very careful with Special Relativity as concepts like “at the same time as” no longer have any fixed meaning; they depend on perspective.
From the Earth’s perspective, the ship travels away at some relativistic speed, and the Earth sends a message at the speed of light towards it (assuming using radio waves or something). The light has to travel extra distance, though, because the ship will move while the light is travelling.
From the ship’s perspective, though, the ship is stationary and the *Earth* is moving away at a relativistic speed. Meaning the Earth sends the message while moving, and so the signal only has to travel the distance between the Earth and the ship at the instant when the Earth sends it.
Except time isn’t universal; so the time it takes the light to get from the Earth to the ship can be different for the different observers.
My instincts are that it would take the same time whether the ship is stationary or moving, because the speed of light is constant. From the ship’s point of view the signal would have been sent “later” but have to travel less distance, whereas from the Earth’s point of view the signal would have to travel further but be sent “earlier.” But again, I haven’t done the maths.
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