A misnamed thought experiment called a "paradox" by people in an attempt to demonstrate the inconsistency of special relativity, in which role it, of course, fails.

In this thought experiment, there are two identical twins. One leaves Earth in a spaceship, travelling away at a relativistic speed. Eventually the spacefaring twin turns around and returns to the Earth.

Upon arriving home, he/she finds that much more time has passed on the Earth than was experienced subjectively on the spaceship. In some versions, the stay-at-home twin is elderly while the spacefaring twin is much younger; in others, the stay-at-home twin has died centuries before. The time interval, of course, depends only upon the speed the spacefaring twin attained and how long he/she went at that speed.

People wonder where the extra time comes from (or goes to, depending upon your point of view). The answer is that it is swallowed up by the spacefaring twin's changes of speed, in effect fixing the time dilation or length contraction caused by the relativistic speed.

But be careful. Just because changes of speed cause time to be lost or gained does not mean that acceleration is responsible. The Three Planets thought experiment demonstrates this. The difference in age between the two twins, all of it, happens at the moment the first twin turns around to go home.

The twin paradox is this. You have two twins A and B. A decides to go on a long space journey to a distant star and back while B stays at home. From the point of view of B time passes slower for A(by time dilation) so when A returns A is younger than B.

The paradox comes about when you consider the same situation from the point of view of A. From A's point of view B is travelling away and back. Thus time passes slower for B according to A. Thus when they meet it should be B who is younger. So who is younger when they meet - A or B?

The resolution to this paradox is that while all inertial reference frames are equivalent everything is not relative. In particular A had to accelerate while moving away from the Earth and had to deccelerate when he(she) reached the distant star. Acceleration is not relative thus it is A who actually moved and it is A who will be younger.