This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
These amazing consequences of relativity do have experimental
foundations. For example, using atomic clocks and super-sonic jets, we have
been able to confirm the effects of time dilation just as relativity
predicts. Another experimental confirmation involves the creation of
particles called muons by cosmic rays (from the sun) in the upper
atmosphere. These muons then travel at very fast speeds towards the earth.
In the rest frame of a muon, its life time is only about 2.2E-6 seconds.
Even if the muon could travel at the speed of light, it could still go only
about 660 meters during its life time. Because of that, they should not be
able to reach the surface of the Earth. However, it has been observed that
large numbers of them do reach the Earth. From our point of view, time in
the muon's frame of reference is running slowly, since the muons are
traveling very fast with respect to us. So the 2.2E-6 seconds are slowed
down, and the muon has enough time to reach the earth.
We must also be able to explain the result from the muon's frame of
reference. In its point of view, it does have only 2.2E-6 seconds to live.
However, the muon would say that it is the Earth which is speeding toward
the muon. Therefore, the distance from the top of the atmosphere to the
Earth's surface is length contracted. Thus, from the muon's point of view,
it lives a very small amount of time, but it doesn't have that far to go.
This is an interesting point of Relativity--the physical results (e.g. the
muon reaches the Earth's surface) must be true for all observers; however,
the explanation as to how it came about can be different for different
frames of reference.
Another verification of special relativity is found all the time in
particle physics. In particle physics, large accelerators push particles to
speeds very close to the speed of light, and experimenters then cause those
particles to strike other particles. The results of such collisions can be
understood only if one uses the momentum and energy equations which were
predicted by relativity (for example, one must take the total energy of the
particle to be E = gamma*m*c^2, which was predicted by relativity).
These are only a few examples that give credibility to the theory of
relativity. Its predictions have turned out to be true in many cases, and to
date, no evidence exists that would tend to undermine the theory in the
areas where it applies.
In the above discussion of relativity's effects on space and time we
have specifically mentioned length contraction and time dilation. However,
there is a little more to it than that, and the next section attempts to
explain this to some extent.
 
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