How do muons and airliner clocks show that time stretches?

Time dilation sounds like pure thought experiment, but two famous tests make it real: particles falling from the sky, and clocks flown around the world.

The particles are muons. Cosmic rays smash into the upper atmosphere and make muons about 10 kilometres up. A muon has a mean lifetime of just 2.2 microseconds, so they should be undetectable on the ground. Yet roughly 10 percent of them are detected at the surface. The explanation is time dilation: a muon moving at 98 percent of the speed of light lives about five times longer, in agreement with observations. In 1941 Rossi and Hall compared the number of muons at the top of a mountain with the number at sea level, the classic atmospheric test. In particle accelerators, too, fast particles live longer.

The clocks are the story of two physicists with a plane ticket problem. In 1971 Joseph Hafele, working on lecture notes, did a back-of-the-envelope calculation showing that an atomic clock on a commercial airliner should be precise enough to detect relativistic effects. After a year of failing to find funding, he teamed up with Richard Keating, an astronomer at the U.S. Naval Observatory. They got $8,000, spent $7,600 of it on round-the-world tickets, including two seats on each flight for "Mr. Clock", and flew four caesium clocks twice around the world, eastward then westward.

Two effects acted on the clocks. Altitude, in weaker gravity, made them tick faster. Speed has to be judged from the Earth's centre, where the ground clocks move too, carried east by the spin: flying east added to that speed and slowed the clocks, while flying west subtracted from it. Compared with the observatory's clocks, the flying clocks lost 59 nanoseconds eastward and gained 273 nanoseconds westward, in line with the predictions. A 1996 repetition measured a gain of 39 nanoseconds against a prediction of 39.8.

Today the test never stops: GPS can be considered a continuously operating experiment in relativity.