Physics text books like to make a big deal out of muon decay, since so far only relativity can explain why muons reach the earth's surface. With a half-life of about 2.2 microseconds, classical physics says they should all decay after having travelled a mere 700 meters. But muons travel at close to the speed of light; and a fair number make it to our detectors on the ground.
Relativity explains why. Looked at from the frame of reference of the earth, the muon's internal time slows down relative to an outside observer, including its rate of radioactive decay. The muon itself does not notice any time dilation; however, because it is traveling so fast with respect to the earth it seems as if the distance to the surface has contracted considerably, well within the 700 meters the muon can travel before it decays.
Maintained by Elisabeth Adams. Feel free to send me questions, comments, or corrections; though I might not have the answer, at least this way we can be befuddled about the universe together.