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I have heard that if faster than light travel were ever made possible, such as by an Alcubierre drive, the user would be taken backwards in time, violating causality.

This is odd to me, as it already seems explained by the twin paradox. The astronaut twin sees Earth as moving at relativistic speeds, and aging slower, but when the astronaut turns back around, time on Earth seems to accelerate, until he arrives in the "present" from Earth's perspective, where he is the one younger than his twin on Earth.

If an Alcubierre drive were ever made, the astronaut would see Earth going "back in time" as he leaves it, seeing light from further and further before he left. On the return, we are to believe he would still see Earth in the past. But why wouldn't time reconcile as in the twin paradox? Shouldn't the astronaut still see the Earth rapidly age until he arrives in the "present" from Earth's perspective?

Put another way, if we were to take an Alcubierre drive from Earth to Proxima Centauri, we would see Earth suddenly appear 4.246 years younger, as we would be seeing light that left it 4.246 years ago. But Proxima Centauri should appear to suddenly age 4.246 years, as we would now be seeing light that just left it. So, when turning back around, why should we arrive at the younger Earth we see from Proxima Centauri, as oppose to the Earth appearing to suddenly age 4.246 years, and thus arriving in the present?

Ben Warner
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    Your first error is in paragraph 1: The existence of an Alcubierre drive does not imply backward time travel. Your second is in paragraph 2: An astronaut traveling relative to earth sees clocks on earth running slow on the inbound trip, just as much as on the outbound trip. Your 14 or so additional errors are in some (but not all) cases consequences of the first two. – WillO May 31 '22 at 21:20
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    @willo I wish I could upvote your comment. – Marco Ocram May 31 '22 at 21:23
  • @WillO I have seen multiple sources claim Alcubierre drives can never be because they would break causality. Are they all wrong? – Ben Warner May 31 '22 at 21:34
  • @MarcoOcram : Why can't you? – WillO May 31 '22 at 21:37
  • @BenWarner: I do not know if they are wrong. It's possible you've misquoted them. – WillO May 31 '22 at 21:37
  • @BenWarner I think those sources are often wrong; a process breaking our ideas of causality does not mean that it cannot be logically possible. The real problem with superluminal travel is with logical consistency, which we should maintain; but this does not necessarily require that cause and effect are absolute. I.e. what is cause in one view can be effect in another. – Ján Lalinský May 31 '22 at 22:49

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If you allow for superluminal travel, it is relatively easy to construct curves where you can go to earlier points on your own timeline, or send signals back to a younger version of yourself, or whatever. You can do this without even invoking acceleration arguments like the ones needed for the "reconciliation" in the twin paradox.

Zo the Relativist
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  • It is a long time since I looked at Alcubierre's paper, but unless I am remembering it very wrong, he shows that in the absence of further assumptions, the existence of an Alcubierre drive does not imply the existence of closed timelike curves. – WillO Jun 01 '22 at 02:33
  • @WillO: his solution involved a warp bubble that did not turn around, and was the only one in the universe. It also heavily leveraged 3+1 decompositions of the einstein equation, and relied on that to get the final result. – Zo the Relativist Jun 01 '22 at 02:39
  • So yes, if you have only one superluminal traveller who travels only once, in one direction, no contradictions arise. – Zo the Relativist Jun 01 '22 at 02:40
  • Yes, this exactly matches my memory. Thanks. – WillO Jun 01 '22 at 02:41