Muon Decay and Special Relativity

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					                    Muon Decay and Special Relativity
                             John R. Newport Ph.D., Spring 2007

Muon decay is the reaction: +  e+ +  + e.

Lab experiments:

(muon initially at rest)
calculated lifetime from quantum mechanics:            = k/m5, k = 1923h7/(G2c4)
measure lifetime from PDG:                             = 2.197034x10-5 s

Atmospheric experiments:

*      mechanism of muon production:
               very high energy protons from sun =>
               protons collide with air molecules in upper atmosphere =>
               collision produces pions, electrons,....
               pions decay to muons
* measured kinetic energy of muons at surface of earth (average), 4GeV,
       so =E/mc2 = 37.7 (extremely relativistic!)
               => v/c = 0.99965
* decay length (no special relativity).
       L = c = 660 m;
       the collision typically occurs at altitudes around 15km
               (verified by detectors placed at various altitudes)
       prediction: should be no muons reaching the surface
       actual: about 1 muon per minute, per cm2 of surface area
* decay length (with special relativity)
        => , L => L = 38*660m = 25 km.
       prediction: lots of muons reaching the surface! consistent with actual

some details:
      event A:        muon born
      event B:        muon dies (decays)
              the reference frame of the muon is proper;
              the proper time interval is t0 = 
      in the reference from of the earth, t = t0 = .

other explanations:
*      muons actually created 660 m above surface:
              easy to verify that this does not happen, move detectors to mountain top,
              result is flux very close to surface value
*      increase in kinetic energy
K = mgh = mc2 (gh/c2) = E0(gh/c2) = E0(1.6 x 10-12) for h = 15km
       (allowing g to vary with height makes it even smaller)
       => particles do not significantly increase speed due to fall

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