MuonautMuon Time Dilation / Length ContractionSticker

Muonaut is born about 15 km up, in the spray of particles a cosmic ray knocks out of the upper air, and she is not built to last.

A muon at rest lives on average 2.197 microseconds before it decays. That is the mean life; the half-life is shorter, 1.52 μs. Even at almost the speed of light, one mean life carries her only about 659 m, the last line on this page. Without relativity, very few muons born that high would survive the 15 km to the ground. Plenty do.

The ground’s account is time dilation. She is moving fast, so by the station’s clocks her lifetime stretches by the Lorentz factor γ, the first lines. At γ = 23 her 2.2 μs becomes about 50 μs, just what the 15 km trip takes at nearly light speed.

Her own account is different and just as right. In her frame she is at rest and her clock runs normally. It is the atmosphere that rushes past, contracted by the same factor: 15 km squashed to about 0.65 km, roughly one mean life’s flight. Same arrival, two consistent stories.

Bruno Rossi and David Hall tested it in 1941, comparing muon decay at different altitudes in Colorado, and found that faster muons lived longer, as relativity requires. In 1963 David Frisch and James Smith did it cleanly: they counted muons on Mount Washington in New Hampshire and again near sea level, about 1900 m lower, and far more survived the descent than their resting lifetime allowed.

Muonaut doesn’t argue with the station clock. She just points out of the window.

In my frame, the sky is short.