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Theories surrounding wormhole based time travel are annoying me tonight... So the way time works is relative, right? The closer you are to the frame of reference, the faster time moves. So, if we use our sun as our frame of reference, then time moves slightly faster on Mercury than it does here on Earth. Let's say a wormhole opens up in your living room, connecting you to a habitable planet in the Andromeda galaxy. You step through, and successfully travel backwards in time, because technically you are much, much further away from the sun now. Oh, and shock factor, the wormhole slams shut.

A few years pass, and a new wormhole opens up in your front yard connecting you to your parent's house back on Earth. You step through looking like Robin Williams fresh after his decades long stay in Jumanji, and to your surprise, your parents are home, thrilled with the fact that you've graced them with your presence after a very long silence on your end.

Now for the plot twist... Your trip to the Andromeda galaxy was planned, and you did it to try and trigger the grandfather paradox, because he was a hateful human being and you never got your chance to say your ardent goodbye and send him off like the true Viking king he never was. Unfortunately, things didn't go as planned. Everything is still the same. It's the year 2030, and people are pretty upset that you just disappeared for a decade without even a word.

Why did it happen this way?

Well, my thought here after such a colorful story, is that since time was measured relative to our sun, you weren't technically traveling back in time. You were traveling to the present time in the Andromeda galaxy, which means you were never going to get back to Earth in time to take the hit out on your Pappy. Is this the correct way to think? Am I missing something?

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  • $\begingroup$ Any question featuring both the words "wormhole" and "really" seems suspect. $\endgroup$
    – TimRias
    Nov 30, 2020 at 12:40

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There is no global time in general relativity. Your resolution to an apparent paradox seems contingent on finding a global time variable and making an appeal to it. General relativity, in the most general case, makes this impossible.

In the absence of a global time variable, when one says "travel back in time", in the context of general relativity, one is always talking about "closed timelike curves", which means that a space time that admits time travel has some circle whose tangent is everywhere timelike, so that the future eventually becomes the past.

A very large class of wormhole solutions enable exactly this sort of solution, where you can have timelike histories that connect with their causal past. This enables things exactly like the grandfather paradox. In general, spacetimes like this are generally considered "bad" because they do not admit solutions that respect the initial value boundary problem, which says that the present (and a time derivative of the present) is all you need to predict the future.

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  • $\begingroup$ Re "which says that the present (and a time derivative of the present) is all you need to predict the future." Does this imply second order equations connect the future and the past? $\endgroup$
    – user45664
    Dec 1, 2020 at 17:34
  • $\begingroup$ Hi! I wonder why in en.wikipedia.org/wiki/Wormhole#Time_travel travel example has moving entrance? I recall just going forth and back with FTL ship somewhere allows to break causality. Is it that going there and back via hole is somehow not? If so, why? TIA P.S. If hole is one way, just make two near each other. Would it work that way to have loop? $\endgroup$ Jul 29, 2022 at 13:27
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While there is no absolute global time variable in GR, there is a cosmological time (the time parameter in the Friedmann-Lemaitre-Robertson-Walker metric) which can be understood similarly to a global time (with several caveats). However, I think that the wormhole solutions are all (in some sense) in local coordinates (they are in a local coordinate patch separate from the FLRW metric's time parameter) so that to answer your question might require the projection of a wormhole metric upon the FLRW solution. (Projecting any one solution of GR upon another is no easy task...)

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