How much does a moving clock slow down?

Suppose you are reading The Handy Physics Answer Book while sitting on a moving bus? To another bus passenger your velocity would be zero, but to a person watching you while standing on a sidewalk your velocity would be equal to that of the bus. If you were walking forward on the bus, then the standing observer could show that your velocity was the sum of that of the bus plus your walking speed. Similarly, if you were walking toward the back of the bus, your velocity would be the velocity of the bus less your walking velocity.

Earth itself is in motion. It is rotating on its axis, revolving around the sun, and moving with the entire solar system around the center of the Milky Way galaxy. If is therefore important that the frame of reference for motion be specified. Usually Earth’s surface is used as the frame of reference, which means that its velocity is zero.

A clock on a jet plane (v = 550 mph) would lose 0.9 milliseconds per year, while one in the space shuttle (v = 17,500 mph) would lose 0.9 s/yr. In 1971 atomic clocks were placed on planes, one of which flew around the world eastbound, the other westbound. The changes in time were measured and agreed with relativity theory. Clocks on GPS satellites must be adjusted for the loss of time. More conclusive tests have been done with very fast moving (0.995c) muons. Muons, when at rest, decay in 2.2 μs (microseconds). The number of muons, produced high in Earth’s atmosphere by cosmic rays, were measured at the peak and base of a high mountain. The ratio of numbers at the two heights showed that the muons lived 22 μs, which agreed with their measured speed of 0.995c. From the viewpoint of the muons, they decayed in 2.2 μs, but the height of the mountain was 10 times shorter than that measured by observers on Earth. Thus the predictions of slower clocks and shorter distances have been tested and agree with Einstein’s predictions.

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