The Achilles Twins Paradox: Proof of a Preferred Frame?

The Achilles Twins Paradox: Proof of a Preferred Frame?

Paradox Abstract: Both Achilles and Bob spend the exact same amount of time accelerating and decelerating at the same rates. Both Achilles and Bob spend the exact same amount of time in inertial frames moving at the exact same constant velocities relative to one-another. The only asymmetry is that they spend different amounts of times in different inertial frames. Hence the cause of their difference in age is due to the difference of inertial frames, and hence there is a preferred frame.

The Achilles Twins Paradox: Proof of a Preferred Frame

Consider two twins Achilles and Bob standing together on a spaceship. Achilles and Bob both accelerate to .99c in one minute as they travel side-by-side away from their spaceship. After one year of traveling at .99c together, Achilles spends a minute decelerating to rejoin the rest frame of the spaceship, while Bob continues to travel away from the spaceship at .99c. Achilles then accelerates to .99c in one minute in the direction of the spaceship, and when he returns to the spaceship, he spends a minute decelerating to rejoin the rest frame of the spaceship.

Meanwhile, Bob continues to spend the next ten years traveling at .99c away from the spaceship. After ten years have passed, Bob spends a minute decelerating to rejoin the rest frame of the spaceship. Bob then accelerates to .99c in one minute in the direction of the spaceship, and when he returns to the spaceship, he spends a minute decelerating to rejoin the rest frame of the spaceship, where he is reunited with Achilles.

Both Achilles and Bob spent the exact same amount of time accelerating and decelerating at the same rates. Both Achilles and Bob spent the exact same amount of time in inertial frames moving at the exact same constant velocities relative to one-another.

Who will be younger?

And more importantly, who will be younger and why?

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