Question 26.AP.1: Faster Clocks in a “Mile-High City” Atomic clocks are extrem...
Faster Clocks in a “Mile-High City”
Atomic clocks are extremely accurate; in fact, an error of 1 s in 3 million years is typical. This error can be described as about one part in 10^{14}. On the other hand, the atomic clock in Boulder, Colorado, is often 15 ns faster than the atomic clock in Washington, D.C., after only one day. This error is about one part in 6 × 10^{12}, which is about 17 times larger than the typical error. If atomic clocks are so accurate, why does a clock in Boulder not remain synchronous with one in Washington, D.C.?
According to the general theory of relativity, the passage of time depends on gravity: clocks run more slowly in strong gravitational fields. Washington, D.C., is at an elevation very close to sea level, whereas Boulder is about a mile higher in altitude, so the gravitational field at Boulder is weaker than at Washington, D.C. As a result, an atomic clock runs more rapidly in Boulder than in Washington, D.C. (This effect has been verified by experiment.)