Explain how cosmic muons work...?

Question

I don't understand cosmic muons! Do they travel close to the speed of light? How is that even possible? In respect to a person on the ground how far does a muon travel before decaying if it's traveling 99.9995% the speed of light and lives for exactly one millionth of a second as measured in the muon's frame? How is a muon's reference frame different than ours?

Answer 1

"Do they travel close to the speed of light?" - They do when produced by the cosmic rays in our atmosphere..



"How is that even possible?" - many elementary particles can travel close to the speed of light, it's nothing unusual.



Travelling at close to the speed of light causes time dilation. This means that for the travelling object time passes slower than for the stationary observer. In the atmosphere very fast moving muons are introduced by cosmic rays. The lifetime of a muon travelling at 98% of the speed of light is about five times longer than a "stationary" muon produced in a lab.

Answer 2

I don't understand cosmic muons! Do they travel close to the speed of light?



Perfectly possible. Any massive particle can be accelerated up to close to the speed of light, provided they don't exactly reach it. The total energy necessary to push it to the speed of light increases asymptotically to infinity. Think about the fable of Zeno and the turtle.



However, muons are unstable particles. Even when travelling at relativistic speeds, they'll inevitably decay. What we observe here on Earth rather tends to be secondaries created from the collision of cosmic rays with the atmosphere. Those cosmic rays tend to be "stabler" particles such as protons, electrons or gamma rays (photons).





In respect to a person on the ground how far does a muon travel before decaying if it's traveling 99.9995% the speed of light



For beta=0.999995 you get the relativistic factor gamma=1/sqrt(1-beta^2) = 316.23. Therefore, since in its frame of reference the muons' half-life is 2.2 microseconds, then half of them will survive for 2.2E-6 * 316.23 = 0.7 miliseconds, or 7E-4 seconds. In that time, travelling at (close to) the speed of light, they can cover a distance of 7E-4 * 3E8 = 2.1E5 meters, or 210 kilometers (or about 130 miles). Muons decay all the time, but on average half of them will survive long enough to transverse that distance. Then, half of the remaining muons travelling at that speed will survive another distance equal to that (another 210 kilometers), and so on.



Provided that such muon is created in the atmosphere (as a secondary from a cosmic ray collision with some atom in our atmosphere), this muon should survive long enough to reach the surface and be detected.





How is a muon's reference frame different than ours?



The frame of reference moves relative to ours. The muon doesn't move in its own frame of reference.

You can relate quantities (time, distance) measured in a frame of reference with the same quantities measured in another frame of reference by using the Lorentz transform:

http://en.wikipedia.org/wiki/Lorentz_transformation

Answer 3

Inform yourself about special relativity, in particular study what absoluteness of the speed of light means, how velocities are added, what the Lorentz transformation is and time dilation. Then you will understand the "muon phenomenon". It is definitely too much to put into a textbox here.

Answer 4

Adding to the above.....The interesting thing about muons is how it helps verify special relativity because without the time dilation we would not see these particles hit the surface.