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This outcome is predicted by Einstein's special theory of relativity. It is an experimentally verified phenomenon called time dilation. One example is with muons produced in the upper atmosphere being detectable on the ground. Without time dilation, the muons would decay long before reaching the ground. Another experiment confirmed time dilation by comparing the effects of speed on two atomic clocks, one based on earth the other aboard a supersonic plane. They were out of sync afterwards, with the one on the plane being slightly behind.

The apparent paradox arises if one takes the position of the traveling twin: from his perspective, his brother on Earth is moving away quickly, and eventually comes close again. So the traveler can regard his brother on Earth to be a "moving clock" which should experience time dilation. Special relativity says that all observers are equivalent, and no particular frame of reference is privileged. Hence, the traveling twin, upon return to Earth, would expect to find his brother to be younger than himself, contrary to that brother's expectations. Which twin is correct?

It turns out that the traveling twin's expectation is mistaken: special relativity does not say that all observers are equivalent, only that all observers in inertial frames are equivalent. But the traveling twin jumps frames when he does a U-turn. The twin on Earth rests in the same inertial frame for the whole duration of the flight (no accelerating or decelerating forces apply to him) and he is therefore able to distinguish himself from the traveling twin.

There are not two but three relevant inertial frames: the one in which the stay-at-home twin remains at rest, the one in which the traveling twin is at rest on his outward trip, and the one in which he is at rest on his way home. It is during the acceleration and deceleration of the departure and arrival to Earth and similar accelerations at the U-turn when the traveling twin switches frames. That's when he must adjust the calculated age of the twin at rest. This is a purely artificial effect caused by the change in the definition of simultaneity when changing frames. Here's why.

In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer. The notion of simultaneity depends on the frame of reference, so switching between frames requires an adjustment in the definition of the present. If one imagines a present as a (three-dimensional) simultaneity plane in Minkowski space, then switching frames results in changing the inclination of the plane.

In the spacetime diagram on the right, the first twin's lifeline coincides with the vertical axis (his position is constant in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. During the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps a large segment of the lifeline of the resting twin. Suddenly the resting twin "ages" very fast in the reckoning of the traveling twin.

It is sometimes claimed that the twin paradox cannot be resolved without the use of general relativity. Indeed, one of the twins must undergo acceleration during the U-turn, and only general relativity can properly describe accellerating observers. Strictly speaking this is true. Special relativity, however, is an excellent approximation to general relativity, except for very strong gravitational fields and large accellerations. If we can make the inertial legs of the trip long enough and the accelleration at the U-turn small enough, the effects of general relativity in the above analysis would amount to very small corrections.