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special relativity should reduce to familiar everyday results when speeds are much less than c.

Time dilation is not an artifact of the light clock that we have depicted in Fig. 7.4. It applies to all clocks. For example, it applies to the decay of unstable elementary particles. Particles moving close to the speed of light should appear to live longer than the same particles at rest. This is tested almost daily in particle accelerators around the world. A dramatic example is in cosmic rays, which contain unstable particles which can decay as they pass through the Earth's atmosphere. If we measure the flux of cosmic rays at high altitude and near the ground, we find that many more survive this trip than we would expect, unless we account for the effect of time dilation.

Example 7.1 How fast must a particle be traveling to live ten times as long as the same particle at rest?

SOLUTION We simply set

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