Time dilation of moving particles
Time dilation of moving particles as predicted by special relativity can be measured in particle lifetime experiments. According to special relativity, the rate of clock C traveling between two synchronized laboratory clocks A and B is slowed with respect to the laboratory clock rates. This effect is called time dilation. Since any periodic process can be considered a clock, also the lifetimes of unstable particles such as muons must be affected, so that moving muons should have a longer lifetime than resting ones. Variations of experiments that actually confirmed this effect took place in the atmosphere or in particle accelerators. Other time dilation experiments belong to the group of Ives–Stilwell experiments measuring the relativistic Doppler effect. See also Tests of special relativity.
The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. The probability that muons can reach the Earth depends on their half-life, which itself is modified by the relativistic corrections of two quantities: a) the mean lifetime of muons and b) the length between the upper and lower atmosphere (at Earth's surface). This allows for a direct application of length contraction upon the atmosphere resting in inertial frame S, and time dilation upon the muons resting in S′.
Length of the atmosphere: The contraction formula is given by , where L0 is the proper length of the atmosphere and L its contracted length. As the atmosphere rests in S, we have γ=1 and its proper Length L0 is measured. As it is in motion in S′, we have γ>1 and its contracted length L′ is measured.
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