The Twin Paradox

The previous subsection illustrates a curious feature of Special Relativity that, at first glance seems paradoxical. We argued that astronauts could travel to a star four light years from Earth and only age two months if they traveled at 0.999c. Meanwhile the people back on Earth age the full eight years. This seems to contradict one of the basic postulates of Special Relativity, namely the relativity of uniform motion. After all, time dilation should be symmetrical, so how is it that the astronauts age less during the journey instead of the people on Earth. In fact the prediction that the astronauts age less is the correct one. It has been experimentally verified, on a smaller scale, but putting very accurate atomic clocks in orbit around the Earth, and comparing them to their Earthbound counterparts after the journey. The clocks that went into orbit were slower in accordance with the predictions of Special Relativity.

This dilemma highlights a limitation of the Special Theory of Relativity that we have already alluded to. It only applies to observers in uniform motion, and not to accelerated frames. In order for astronauts to go to a distance star, and return to compare clocks with Earthbound observers, the astronauts' spaceship must accelerate to near light speeds, decelerate once the reach the star, and the repeat the process in the other direction. While they are accelerating, the rules of Special Relativity don't apply, and the symmetry between the astronauts and the Earthbound observers breaks down. (This applies to the atomic clocks in orbit as well.) A detailed examination of the problem therefore requires us to go beyond Special Relativity (to General Relativity), with the result that time actually slows down in accelerated frames of reference. However, it turns out that the calculation we did in the previous sub-section is approximately correct. We get nearly the right answer for the difference in aging of the astronauts by ignoring the acceleration and just taking into account time dilation on the forward and return journeys. Thus, there is no ``paradox'' associated with this effect. As with most paradoxes, it merely points to a limitation of the theory under consideration.