The Twin Paradox

Sunday, October 28, 2018

The Twin Paradox

Stationary Sam and Rocket Rob are identical twins and so have been the same age their whole lives. Rob then builds a high-speed rocket, goes out into space and then returns. The question is: who is older?

We know that time dilation occurs for moving observers. From Sam's frame of reference, he is stationary while Rob is moving at a constant velocity. This means from his POV, time moves slowly for Rob.

Another equally valid claim is the one made by Rob.

Rob moves at a constant velocity (is in an inertial reference frame and feels no forces on himself) and so can also claim to be at rest while Sam moves away from him at a constant velocity. This means time moves slowly for Sam.

Both claim the other aged slower so when Rob returns; who actually aged slower?

Usually the answer to these kind of questions is that they are both right and we reconcile these perspectives using our understand of special relativity like in the pole in the barn paradox. This will not work in this case however.

At the end of the journey Rob and Sam are together. They can stand next to each other and go into the same frame of reference. In this case there can be no disagreement in who has aged and who has not.

The answer is that Rocket Rob is the one who is younger. This is because his frame of reference turns out to be non inertial. In order to get back to Earth; Rob has to slow down and fire his boosters the other way (or make a U turn) and so experience acceleration and therefore forces. He therefore can't claim that he is at rest and that Sam is the one moving.

The only valid claim is the one of Sam. This means that when Rob and Sam come together, Rob's clocks have moved slowly and so he is younger than Sam.

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