When we see a star from the earth that is 5 light years away, we are essentially looking at light emitted from the star 5 years ago. What if you were to instantly reach near the star, either by teleportation or Alcubierre drive, are you traveling back in time 5 years?
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4$\begingroup$ In relativity there is no single way to decide if two events separated in space take place at the same time, or not, which means your question doesn't really have an answer. "Instantly teleporting" (or building an Alcubierre drive) would require some new physics that would presumably provide an answer, but what the answer is depends on what the new physics is. $\endgroup$– Steve LintonMar 23, 2018 at 8:26
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4$\begingroup$ Asking "what if we break physics" is unfortunately impossible to answer in the framework of physics. $\endgroup$– AtmosphericPrisonEscapeMar 23, 2018 at 12:43
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3$\begingroup$ I'm voting to close this question as off-topic because violation of the laws of physics belongs on WorldBuilding.SE $\endgroup$– Carl WitthoftMar 23, 2018 at 12:49
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$\begingroup$ I'm voting to close this question as off-topic because asking what happens if we break the laws of physics is unanswerable within that framework, which is what we use here. $\endgroup$– StephenG - Help UkraineMar 23, 2018 at 14:45
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$\begingroup$ @CarlWitthoft Wolrdbuilding SE doesn't automatically close these "impossible physics" questions, but if you ask them with the science, hard-science or reality-check tags (which the OP probably would want to) they'd likely to voted off-topic. $\endgroup$– StephenG - Help UkraineMar 23, 2018 at 14:47
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Well not sure teleporting requires an answer. There is not such a physics. However assuming the impossible I do not think we really need relativity SR in a technical sense. If I teleport instantaneously myself I would appear on the star as it will be seen from earth in 5 years. As such, in the earth calendar, I disappear for 5 y and "in a way" I move in the earth future as for an earth observer it will take 5 y to see me again. But he/she will see me as I was during my absence, ie his past. As far the star is concerned, I simply materialize there. The point is that from there, I will see my last 5 y on earth as a recorded movie. The same is for a star resident watching the movie with me. He see me before leaving so I wasn't able to give to him any sensible information. Even a pre alert of my arrival wouldn't alter anything on the succession of events. This does not qualify as moving or moving information through time, especially not backwards. At the end, the fictional teleporting seems to lead to less mind blowing results than a technological difficult but in principle possible travel at a relativistic speed. There is even no room for time dilation and it seems to me that the famous twins can use teleporting and re-meet with no even (apparent) paradox.
Edit. Please note that the scenario can be made fully realistic (well almost, but because of merely technological limits) by replacing
earth and star by widely separated islands;
sound as the only way to communicate, such as big detonation while being away and whispering while sitting on the same rock;
a really supersonic vehicle for moving between the two islands, so that the time of the person travel can be taken to be negligible as compared to the time at sound speed.
Nothing can alter a cause effect succession of events even considering a third observer passing by or through the islands even on board a similar vehicle.
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1$\begingroup$ A moving observer will see you as arriving before you left in their reference frame, although not long enough before to create any paradox like sending yourself a message that would arrive before you left. However, if the same moving observer had a teleporter of their own and if it worked instantaneously in their (and its) frame of reference then you could create a paradox. $\endgroup$ Mar 23, 2018 at 10:47
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$\begingroup$ Good point about the third party observation. How would a paradox be create? I would add it to the answer. @Steve Linton $\endgroup$ Mar 23, 2018 at 11:29
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$\begingroup$ Suppose you send an instantaneous message to a star 5 ly away. In your frame of reference it arrives now. At the moment it arrives a spaceship is passing that star moving towards you at half the speed of light. The pilot of the spaceship immediately uses its own teleporter to reply and that message arrives instantaneously in the spaceships frame of reference. Then the second message arrives 2.5 years before the first one is sent (and might, for example say "don't send the message") $\endgroup$ Mar 23, 2018 at 12:44
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$\begingroup$ @SteveLinton except, of course, that the "teleport" operation can cheerfully violate frame-of-reference rules however it pleases. $\endgroup$ Mar 23, 2018 at 12:48
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$\begingroup$ @Steve Linton. Shall not I get his answer over imposed to my sending rather than before? I am afraid is the fictional character of teleporting that run one of us into troubles at this specific point. Or you are just putting a number 2.5 meaning that pilot see a shorter distance between star and me? But teleporting does not let us implement distances at all. Not a polemic. It is just me surely get more confused by SR than by fiction :) $\endgroup$ Mar 23, 2018 at 12:57