Muons are subatomic particles formed by high energy collisions of cosmic rays with air molecules in the earth’s atmosphere about 15 km from the surface. These particles have an average lifetime of 2.2 microseconds. How do you know about muons? Because you can measure their presence using particle detectors.
Do you see anything weird with the above statements? Well, take out your pen and paper and calculate the distance a muon travels before it’s finished. And use the maximum speed, the speed of light.
speed = 300,000 km/s
time = 2.2 x 10-6 s
distance = speed x time = 0.66 = 660 m
So, what’s going on here? The muons should be done in the first 660 metres after their journey from 15 km high. But they do come home. Think of it this way: that is only possible if their time of 2.2 microseconds is slower than ours or our distance of 15 km is shortened for them.
Since they are travelling pretty fast, their time passes slowly, like the following:
Put v = 99.9% of speed c, the speed of light, and you get 22 microseconds. So, for a muon that travels at 99.9% the speed of light, it will live for 22 microseconds (for us), and during that time, it can travel 6 km!
By the way, we just proved Einstein’s theory of special relativity.
From a muon’s perspective, we are moving closer to them at 99.9% speed of light. And when that happens, the distance contracts by the following formula.
This Paradox Proves Einstein’s Special Relativity: Up and Atom
