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Imagine identical triplets on Earth: Ana, Barb, and Evelyn. Ana launches in a spaceship traveling .85c. She knows time on Earth is elapsing 1.9 times faster.

A few months later, Barb launches in a faster spaceship that travels at .99 to catch Ana. When Barb catches Ana, she slows down to match her speed. They lunch together. Barb looks younger to Ana, but that’s not important to this story.

After lunch, Barb returns to her spaceship and flies back to Earth at .99c. Ana knows time moves more slowly for Bev on her ship. In time, Bev slows down to match the speed of Earth, lands, and lunches with her sister Evelyn who looks quite old.

Here’s the paradox for Ana. Initially, time moved faster on Earth, but after Bev returned, time moved more slowly.

So, is time moving faster or slower on Earth relative to Ana? They can’t both be right or can they?

BobA
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  • https://en.wikipedia.org/wiki/Twin_paradox – Pato Galmarini Dec 13 '23 at 21:33
  • Plot them all on a spacetime diagram. You can work out all of their clocks by applying the spacetime interval along each path. – m4r35n357 Dec 13 '23 at 22:01
  • Your numbers are all over the place. If .99 is correct, and you want the kind of relationships, then the planet goes at .8676 and it takes about 8.17 years. The time dilation is then about 2 seconds per one second. If .85 is correct, then .9869, and it takes about 6.2 years. I'm not sure where you even got 70% slower anywhere. – naturallyInconsistent Dec 14 '23 at 02:16
  • I have resolved your critiques. It’s now a single reference point and the math is straightforward. Thank you. – BobA Dec 15 '23 at 17:03
  • This comment should not be closed because of the existence of the linked question. That question deals purely with special relativity. Due to the three accelerations, this question also deals with general relativity. Maybe there is another question that already deals with GR and accelerating spaceships.

    BobA: you are a bit confused as others have pointed out. But, if cleaned up, your question would probably be the Twin "Paradox".

     – Dr. Nate Dec 15 '23 at 18:49
  • "So, is time moving faster or slower on Earth relative to Ana?". Every clock ticks faster in its own frame than in any other. That is all you need to know to resolve all your questions. – WillO Dec 16 '23 at 02:00
  • When Ana leaves Earth, she knows her clock is ticking slower, not faster than one on Earth. If she returned to Earth this would be the typical twin paradox. Something isn’t working by using Ana as the reference point. – BobA Dec 16 '23 at 21:21

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Time dilation is symmetric, so if the distant planet is 70% time dilated in the frame of the Earth, then Earth is 70% time dilated in the frame of the distant planet. You need to be careful in how you interpret time dilation- it doesn't mean that clocks on one planet tick more slowly than clocks on the other. What it means is that time in the frame of the Earth is out of synch with time in the frame of the distant planet.

Marco Ocram
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