Time dilation for muons
Question 120S: Short Answer		

Muons are unstable subatomic particles created near the top of the Earth’s atmosphere (about 60 km above the surface) by cosmic rays. They travel down toward the surface of the Earth at a velocity close to the speed of light. However, muons have a half-life of about 2 ms so some will decay before they reach the surface.

1.	What is the maximum distance a muon can travel during one half-life?

2.	As seen from the Earth, how long would it take a muon travelling at the speed of light to reach the surface of Earth, 60 km below? Express your answer in muon half-lives.

3.	Use your result from question 2 to estimate the fraction of muons created at 60 km that reach the surface. Comment on your result.

4.	In fact about one in eight muons created at 60 km do reach the surface. How is this possible?

5.	If one in eight muons reach the surface, how many half-lives must have passed, so far as the muons are concerned? Compare this with the answer to question 2 to find g, the time dilation factor, for these muons.

6.	How fast are the muons travelling? Use

7.	If you were travelling with the muon you would pass through the Earth’s atmosphere in about 6 s and yet you would agree with a terrestrial observer that your relative speed is about 0.9995 c. How is this possible?