(455) HL Muon decay [IB Physics HL]

Formation:
- Created in particle accelerators and naturally in the upper atmosphere.
- Cosmic rays collide with atmospheric particles at around 10 km altitude to produce muons.
Speed and Lifetime:
- Travel at approximately 0.98 times the speed of light.
- Average lifetime of a muon is 2.2 microseconds (2.2 x 10^-6 seconds).

Expected Travel Distance:
- Using the formula for distance (distance = velocity × time):
  - Distance = 0.98 × (3 × 10^8 m/s) × (2.2 x 10^-6 s) = ~650 meters.
Detection Problem:
- A muon should only travel about 650 m before decaying, which is insufficient to reach the Earth's surface from 10 km.

Relativistic Effects:
- Time dilation indicates that muons can appear to live longer than their average lifetime due to their high speeds.
- Calculations show that they should last about 11 microseconds in the observer's frame on Earth.
Further Consideration:
- Although it takes muons 33 microseconds to reach Earth, some can still be detected because their lifetime is increased through relativistic effects.
- Length Contraction: From the muon’s perspective, the distance traveled would be contracted to about 2 km instead of 10 km.

Significance:
- The detection of muons on Earth provides strong evidence for relativistic effects such as time dilation and length contraction.
Applications:
- Understanding these concepts is crucial in advanced topics like GPS, which also incorporates relativistic principles.
Historical Context:
- Muons have been known and studied for over 100 years, affirming the validity of relativistic physics.