# Time and the Twin Paradox [Preview]

Does time tick by at the same rate for everyone?

### In Brief

• We take for granted that time ticks by at the same rate for everyone. But Einstein's special theory of relativity shows that this assumption is not strictly true.
• The classic case of time disparity involves twins--one of whom leaves Earth and travels round-trip to a star at nearly the speed of light, arriving back much younger than his brother. This aging difference is noticeable only when long distances are traveled at speeds approximating the speed of light.

AS MAXIMS GO, “TIME IS RELATIVE” MAY NOT BE QUITE AS famous as “time is money.” But the notion that time speeds up or slows down depending on how fast one object is traveling relative to another surely ranks as one of Albert Einstein's most inspired insights.

The term “time dilation” was coined to describe the slowing of time caused by motion. To illustrate the effect of time dilation, Einstein proposed an example—the twin paradox—that is arguably the most famous thought experiment in relativity theory. In this supposed paradox, one of two twins travels at near the speed of light to a distant star and returns to Earth. Relativity dictates that when he comes back, he is younger than his identical twin [see “How to Build a Time Machine,” by Paul Davies, on page 24].

The paradox lies in the question “Why is the traveling brother younger?” Special relativity tells us that an observed clock, traveling at high speed past an observer, appears to run more slowly—that is, it experiences time dilation. (Many of us solved this traveling-clock problem in sophomore physics to demonstrate one effect of the absolute nature of the speed of light.) Because special relativity says that there is no absolute motion, wouldn't the brother traveling to the star also see his brother's clock on Earth move more slowly? If this were the case, wouldn't they both be the same age?

This paradox is discussed in many books but solved in very few. It is typically explained by saying that the one who feels the acceleration is the one who is younger at the end of the trip; hence, the brother who travels to the star is younger. Although the result is correct, the explanation is misleading. Some people may falsely assume that the acceleration causes the age difference and that Einstein's general theory of relativity, which deals with noninertial or accelerating reference frames, is required to explain the paradox. But the acceleration incurred by the traveler is incidental, and the paradox can be unraveled by special relativity alone.