Muon Decay and Special Relativity

Document Sample
Muon Decay and Special Relativity Powered By Docstoc
					                    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

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:48
posted:11/11/2010
language:English
pages:1
Lingjuan Ma Lingjuan Ma MS
About work for China Compulsory Certification. Some of the documents come from Internet, if you hold the copyright please contact me by huangcaijin@sohu.com