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I'm learning Special Relativity at the moment and I'm confused by time dilation.

Let the Earth be the frame of reference and have some spacecraft leave the planet at 0.5c for instance. If the spacecraft travels for 15 years (as seen from earth), time dilation means that it seems like only 13 years has passed on the spacecraft. So now 15 years on Earth will seem like 13 years to those in the spacecraft.

If you now take the spacecraft as the frame of reference and 13 years has passed, the above would mean that 15 years would have passed on Earth wouldn't it? However, this isn't so, since from that frame of reference, you see the Earth move away and thus that undergoes time dilation - so time would appear slower on Earth. I was just wondering if you could explain it to me, since it seems like a contradiction. Some people said that it involves the twin paradox but that involves an accelerating frame of reference, yet this does not.

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# Time Dilation Confusion

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