= Cosmic-ray muon time-dilation experiment
Atmospheric <cosmic rays> generate <muons> whose <mean lifetime> at rest is about $2.2\,\mathrm{\mu s}$. For a selected speed $v$ and production-to-detection distance $h$ in the terrestrial frame, <special relativity> predicts survival fraction $e^{-h/(\gamma v\tau_0)}$, where $\gamma$ is the <Lorentz factor>. Without <time dilation>, the exponent would instead be $-h/(v\tau_0)$. Comparing altitude-dependent counts at controlled energies, allowing for acceptance and energy loss, tests these alternatives. In the <muon> <rest frame> the terrestrial distance is shortened to $h/\gamma$ by <length contraction>, so the proper flight time and survival fraction agree with the terrestrial calculation. This frame comparison does not turn the same decay measurement into two independent tests.
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