Section 14. 3 describes how the number of muons reaching Farth's surface is greater than the number expected based on the muon half-life of \(1.5 \times 10^{-6} \mathrm{~s}\). How fast, relative to Earth, must muons be moving in order for onc of every million muons to pass through a distance equal to Earth's diameter without decaying?

Data from Section 14. 3

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The fact that simultancity is relative rather than abso- lute makes us rethink the whole concept of time. If simultaneity depends on the motion of observers rela- tive to each other, shouldn't the rate at which a clock is observed to tick depend on the motion of the observer relative to the clock? The answer is yes, and here is the easiest way to see that. Consider the device shown in Figure 14.14, called a light clock. At the bottom is a source that emits a very short light signal; at the top is a mirror that reflects the signal back down. At the instant the reflected signal reaches the bottom, the source is triggered to emit a new light signal. The up- and-down motion of the signals determines the period of this clock. If the mirror is a distance h away from the source, it takes each light signal a time interval b/c to travel from the source up to the mirror and the same time interval to travel back down to the source. The period of this clock is thus 2h/co. Just as the tick- ing of a mechanical clock defines the unit of time for the clock, this period defines the unit of time for the light clock.