Two muons, one at 30,000 meters and the other at 29,999 meters (in our
frame of reference, and therefore one meter apart) are both travelling
toward the ground at near light speed. The tip of a ray of light is
also at 30,000 meters, and is alongside the higher muon at the moment
this thought experiment begins. Due to time dilation and length
contraction, both muons reach ground level, on behind the other. The
light ray tip also reaches the ground, having travelled 30,000 meters
in our frame of reference and one meter in the frame of reference of
the muon pair. It then reflects and travels toward to trailing muon,
which is one meter above ground level and also stationary at 30,000
meters where it meet the reflected light ray, for it takes the same
time for light to travel from the ground to 30,000 meters as it does to
travel from 30,000 meters to the ground. In the frame of reference of
the muon pair, it travels 1 meter in each direction. Muons are evidence
of Special Relativity. Since we have a muon at 1 meter above the ground
and the same muon at 30,000 meters, muons are 29,999 meters long.
Arthur Dent.