What you need to know about Muons:
Muons are leptons - a type of subatomic particle. They are created created in the atmosphere, 10 km from the surface of the Earth. The cosmic rays from the sun hit the atmosphere and can create muons that travel up to 0.99c.
So the maximum distance a muon can travel is 2.2 x 10-6 x 3 x 108 = 660m
Awwwww, isn't it cute?
The thing is, eventhough the muons are not supposed to reach anywhere near Earth, we are still able to detect them. (using the cute-o-meter...joke)
So, remember that anything moving at the speed of light (in this case it s 0.99c) will experience the effects of special relativity.
A muon moving at 0.99c has a Lorentz factor of 7.1.
In terms of time dilation:
From the muon's frame of reference: the muon measures proper time. 2.2 x 10-6 seconds.
From the Earth observer's frame of reference: the muons move towards the stationary observers at 0.99c and is thus time dilated to 7.1 x 2.2 x 10-6 seconds = 1.562 x 10-7 seconds
Remember that time dilation is concered with longer time periods while length contraction is concerned with shorter distances.
In terms of length contraction:
From the muon's frame of reference: everything around the muon will now appear shorter (but not the muon - imagine sitting on the muon like a train, everything on the train stays the same) due to length contraction by a factor of 7.1.
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