Muons are created high in the atmosphere, typically at altitudes of about 10-15 km. Their mean lifetime at rest is only about 2.2 microseconds, so without relativistic effects almost none would reach sea level.
Because muons travel at speeds close to the speed of light, special relativity causes their clocks to run slower (time dilation), greatly increasing the fraction that survive.
A rough estimate:
- At about 15 km altitude, around 100% are present at production.
- At sea level, the vertical muon flux is about 10-20% of the flux near the main production region.
So a commonly quoted figure is that roughly 10-20% of muons produced in the atmosphere survive to reach sea level.
The exact percentage depends on:
- The altitude where the muon was created.
- Its energy (higher-energy muons survive much better).
- The angle of travel (slant paths are longer).
For example:
- A low-energy muon may have less than a 1% chance of reaching sea level.
- A several-GeV muon can have a survival probability of 50% or more.
- Very energetic muons can easily reach the ground and even penetrate underground.
This survival of atmospheric muons is one of the classic demonstrations of the Special Relativity prediction of time dilation. Without relativity, the expected survival fraction would be only a tiny fraction of a percent.