First thing first: the twin paradox is not a paradox! Now, what is it?
Before we go to the twin paradox, we must know the concept of relativity of simultaneity. It is a central concept in the special theory of relativity and happens because the speed of light is constant. A famous thought experiment is when a light flashes at the centre point of a train, running at constant velocity. To the observer inside the train, the light will reach the engine and the tail simultaneously (the same distance from the light source). But for a standing observer on the platform, the light will hit the back of the train first, as it is catching up, and strike the engine last, as it is going away from the light source. And both are right. Or the distant simultaneity depends on the reference point.
Put differently, A and B are two objects. And A moves towards the static B at a constant velocity. But from A’s vantage point, it feels stationary, and B is moving towards A. Both A and B are correct.
Over the twin paradox: Anne and Becky are twins. Becky goes away in a spaceship to a distant planet and comes back. From the stay-at-home Anne’s perspective, Becky’s clock is running slow due to the special theory of relativity. So, when she comes back, Becky will be younger than Anne. But Becky, while heading back, looks at Anne and says it was Anne who was moving towards her (in her perspective), so Anne is younger. How can both be happening? So, it’s a paradox.
Interestingly, this time, we can’t say both are right. Anne is right; Becky is the younger of the two when she returns. The only time one can claim to be at rest and the rest of the world is moving is when the moving person is moving with constant velocity. Sadly, Becky cannot claim it; she changed her direction to return and created acceleration. Remember: velocity comprises speed as well as direction. On the other hand, Anne’s version is valid as she had no acceleration but was standing at constant (zero) velocity.
WSU: Space, Time, and Einstein with Brian Greene
