Muon Lifetime Experiment

• What do muon decay experiments provide evidence for?

  Time dilation and length contraction
• How much heavier are muons compared to electrons?

  200 times heavier
• Where are muons produced?

  In the upper atmosphere from pion decays
• What is the speed of muons?

  0.98c
• What is the half-life of a muon?

  1.6 µs
• What is the mean lifetime of a muon?

  2.2 µs
• How far do muons travel in one half-life?

  Approximately 470 m
• At what height are muons created?

  About 10 km above the surface
• How many half-lives pass over a distance of 10 km?

  Roughly 21 half-lives
• Why do more muons reach the Earth's surface than expected?

  Due to time dilation effects
• What is the half-life of a muon in its own reference frame?

  1.6 μs
• How is the muon's half-life perceived by an observer on Earth?

  It is dilated due to high speed
• What is the time dilation equation?

  ∆t = γ∆t0
• What is the gamma factor for a speed of 0.98c?

  5
• How long do muons appear to live from Earth's reference frame?

  8 µs
• How long does it take for muons to travel 10 km at 0.98c?

  34 μs
• How many half-lives do muons experience according to an observer on Earth?

  4.3 half-lives
• What is the distance covered by muons from their reference frame?

  Shorter due to length contraction
• What is the length contraction equation?

  L = L0/γ
• What distance do muons perceive they travel to reach Earth?

  2000 m
• How long does it take muons to travel 2000 m?

  6.8 µs
• What is proper time?

  Time measured in the stationary reference frame
• What is proper length?

  Length measured in the stationary reference frame
• How many half-lives do muons experience according to Newtonian mechanics?

  9 half-lives
• What fraction of muons reach the Earth's surface according to Newtonian mechanics?

  0.2%
• What fraction of muons reach the Earth's surface according to special relativity?

  29%
• How does an observer moving with the muons perceive the distance to the surface?

  Shorter by a factor of 5
• What is the distance to the surface according to the muon's reference frame?

  850 m
• How long does it take for muons to travel 850 m?

  2.9 × 10^-6 s
• What are the key equations used in muon decay experiments?

  • Time dilation: ∆t = γ∆t0
  • Length contraction: L = L0/γ
  • Speed: speed = distance/time
  • Half-lives: 1/2^n remaining after n half-lives
• What are the implications of time dilation and length contraction in muon experiments?

  • Time dilation: muons live longer from Earth's perspective
  • Length contraction: muons travel shorter distances in their frame
  • Both effects explain the number of muons reaching Earth
• What is the relationship between half-lives and the fraction of muons remaining?

  • After 1 half-life: 1/2 remain
  • After 2 half-lives: 1/4 remain
  • After 3 half-lives: 1/8 remain