- A SKEPTIC's GUIDE - A SKEPTIC's GUIDE 
Like most "paradoxes," this one isn't. But it sure looks like one at first glance. Suppose two identical twins part company at age twenty; the first twin hops aboard a spaceship of very advanced design and heads out for the distant stars, eventually travelling at velocities very close to c, while the second twin stays home at rest. They give each other going-away presents of identical watches guaranteed to keep perfect time under all conditions. At the midpoint of the voyage, while coasting (and therefore in an inertial reference frame), the first twin looks back at Earth with a very powerful telescope and observes the second twin's wristwatch. After correcting for some truly illusory effects, he concludes that the first twin's watch is running slower than his and that his twin on Earth must be aging more slowly as well. Meanwhile, the second twin, on Earth, is looking through his telescope at the first twin's watch (aboard the spaceship) and concludes that the first twin is suffering the effects of time dilation and is consequently aging more slowly than him! Who is right? Both, at that moment.
Aha! But now we can bring the first twin home after his relativistic journey and compare ages. Certainly they can't both be younger; this truly would create a logical paradox that goes beyond the mere violation of common sense!
What happens? The first twin, who went travelling, is in fact younger now than the twin who stayed home. The paradox is resolved by a meticulous use of the LORENTZ TRANSFORMATIONS, especially if we make use of the graphical gimmick of the LIGHT CONE, to be discussed later.