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I've heard many-an-explanation of wormholes. From as a kid with the hole punch through paper, to the sci-fi something something magic, to popular YouTube science channels talking about how it could be used for time travel.

I don't buy the time travel bit. It seems as though the two places that are connected by a wormhole would just be causally linked. Is this not the case? Why?

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Suppose in the year 3000 the planet Splot passes the Solar System at a speed of $c/\sqrt{2}$ (I chose this value because it makes the time dilation a factor of 2). The Splotians like our calendar so they decide to reset their calendar to also be the year 3000 as they pass, which means we all agree on the dates. At the moment Splot passes the Earth we create a wormhole between the two planets.

In the year 3100 you decide you'd quite like to visit Splot so you jump into the wormhole and arrive on Splot. But remember that time dilation I mentioned above. During the 100 years on Earth only 50 years have passed on Splot so when you get to Splot you find it's only the year 3050.

It turns out that Splot is a bit of a dump, so you very quickly get bored and want to come home. But here's the problem. In Splot's rest frame it was the Earth that zoomed past at $c/\sqrt{2}$ so it's the time on Earth that is running slowly. That means when the year is 3050 on Splot it is only the year 3025 on Earth. So you jump into the wormhole and get back to Earth in 3025, which is 75 years before you left. This is when you decide you always really hated your grandfather :-)

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  • $\begingroup$ So relitivity allows for wormholes that exist in two different reference frames? $\endgroup$ – Michael Smith Aug 4 '18 at 7:41
  • $\begingroup$ @MichaelSmith yes, though you could achieve the same end result with wormholes whose ends were stationary if you have two of them - one stationary relative to Earth and the other stationary relative to Splot. The key feature of time travel using FTL transport is that it involves two different reference frames. Just jumping around with wormholes doesn't cause time travel without also changing reference frames. $\endgroup$ – John Rennie Aug 4 '18 at 8:30

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