Tensors and Relativity: Chapter 1

The twin paradox

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To continue our discussion of the Lorentz transformations and relativistic effects, we consider the famous ``twin paradox'' of Peter and Paul. When they are old enough to drive a spaceship, Paul flies away from earth at very high speed. Because Peter who is left on the ground, sees Paul going so fast, all of Pauls' clocks appear to go slower , from Peter's point of view. Of course, Paul notices nothing unusual. After a while he returns and finds that he is younger that Peter! Now some people might say ``heh, heh, heh, from the point of view of Paul, can't we say that Peter was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that they are both the same age when they meet''. But in order for them to come back together and make a comparison, Paul must turn around which involves decelerating and accelerating, and during that period he is not in an inertial frame. This breaks the apparent symmetry and so resolves the paradox.