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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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1 Answers1

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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.

Professor Sushing
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