Time Dilation Experiments
http://home.fnal.gov/~pompos/light/light_page18.html

On the previous page I stated that time goes slower for moving
objects.

This time slowing prediction was actually VERIFIED in many many
different ways in many many experiments. One of the nicest is an
experiment with elementary particles called MUONS. These particles
are unstable and decay into electrons and other particles called
neutrinos.

The lifetime of muons, if they do not move, has been measured in
laboratories. Now, if you measure the lifetime of muons moving at a
very high speed (close to the speed of light), you notice that it is
much longer than the lifetime of the stationary muons.

It is easy to measure speed of muons. Then it is possible to
calculate their lifetime in our frame of reference. Physicists
compared the prediction from relativity theory and the results of
experiment, and they matched very well.

Another nice experiment has proved that time slows down in a moving
frame of reference. This experiment uses MUONS again and is based on
the same idea as described above. This time we use COSMIC muons. It
is a known fact that there is a flux of cosmic high-energy particles
entering our atmosphere. These cosmic particles produce high-energy
muons at a very high altitude. The lifetime of stationary muons is so
short that even if they moved with the speed of light, they could not
reach Earth. They would already decay high in the atmosphere. But
various experiments show, that there is a pretty much constant flux
of muons reaching Earth.

See: http://home.fnal.gov/~pompos/light/light_page18.html