2.6 Muon Time
Experimental evidence lends powerful support to the Special Relativity theory.
All of this stuff about time dilation we have inferred as a logical consequence of the postulate that the speed of light is a constant, irrespective of frame of reference . However, as always in science, we need supporting experimental evidence, otherwise we can never have any real confidence in the theory, especially when its implications are as weird as in this case. So Nefertiti and Cormorant will recreate for you a classic experiment:
Muons are unstable particles which are formed by the interaction of cosmic rays with molecules in the upper atmosphere. They are formed with very high velocities and some of them head down towards the Earth’s surface. They rapidly decay into other particles with first order kinetics, meaning that if at some point in time you have a population N0 of muons, then after time t the population will have decreased to N, according to the equation
N = N0e-kt
When muons are studied in the lab, in situations where their velocities are negligible, the value of k is measured to be 4.545 x 105 s-1.
In their experiment, which you can see beautifully illustrated below, Nefertiti stands on the beach with her muon detector, while Cormorant hovers overhead at an altitude of 5000 m, with his detector. Each counts the number of muons per square metre per second arriving at their detector.
Figure II-vii
Hopefully this result – which is based on experiments that were actually done in the 1950s to test special relativity (though with less cormorant involvement) – leaves you feeling as close to comfortable as you’re ever going to with time dilation, but we aren’t anywhere near finished with special relativity yet. The next issue to deal with is conveniently raised by the very experiment we’ve just been considering.