Relativistic Time Dilation in Muon Decay

According to Einstein's special theory of relativity, a clock moving at a significant fraction of the speed of light with respect to an observer runs more slowly than the observer's own clock. This implies that time must be flowing more slowly in a moving frame of reference, which is referred to as time dilation. If a process (such as the decay of an unstable particle) occurs with an average lifetime of in the rest frame, the lifetime of the particle moving at speed is given by , where is the speed of light, 2.9979 × m/sec. The decay of muons has provided verification of Einstein's formula to a high degree of accuracy. The negative muon , with a mass of 105.7 MeV/, is the second-generation lepton analogous to the electron . The antiparticles and (the positron) are similarly related. The mean lifetime of free muon decay is 2.197 sec in the rest frame. The decay processes are and . Here is a neutrino and an antineutrino, each occurring in both electron and muon flavors. In finer detail, these weak-interaction processes involve bosons as intermediates.

High-energy collisions of protons produce copious numbers of pions, which, in turn, decay into muons. This all happens within the blue square in the graphic. The beam of muons thus produced is injected into a circular synchrotron, which can accelerate them to energies up to 10,000 MeV (10 GeV). The lifetimes are then determined as a function of energy. Muons accelerated to 750 MeV already travel at 99% the speed of light and have average lifetimes enhanced by an order of magnitude. At the maximum energy available in this Demonstration, speeds of 0.9999 are achieved and the muon lifetime is increased by a factor of 100.

Earlier experiments on muons produced by cosmic rays found their half-lives to be dependent on distance traveled through the atmosphere; they also exhibited relativistic time dilation.

See: Relativistic Time Dilation in Muon Decay

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Muons reveal the interior of volcanoes

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It has been recently shown that puzzling excess events observed by the LSND and MiniBooNE neutrino experiments could be interpreted as a signal from the radiative decay of a heavy sterile neutrino (nu_h) of the mass from 40 to 80 MeV with a muonic mixing strength ~ 10^{-3} - 10^{-2}. If such nu_h exists its admixture in the ordinary muon decay would result in the decay chain mu -> e nu_e nu_h -> e nu_e gamma nu. We proposed a new experiment for a sensitive search for this process in muon decay at rest allowing to definitively confirm or exclude the existence of the nu_h. To our knowledge, no experiment has specifically searched for the signature of radiative decay of massive neutrinos from muon decays as proposed in this work. The search is complementary to the current experimental efforts to clarify the origin of the LSND and MiniBooNE anomalies. Bounds on the muonic mixing strength from precision measurements with muons are discussed. See: New muon decay experiment to search for heavy sterile neutrino and also The LSND/MiniBooNe excess events and heavy neutrino from muon and kaon decays

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Some History of the Muon Experiment 

The historical experiment upon which the model muon experiment is based was performed by Rossi and Hall in 1941. They measured the flux of muons at a location on Mt Washington in New Hampshire at about 2000 m altitude and also at the base of the mountain. They found the ratio of the muon flux was 1.4, whereas the ratio should have been about 22 even if the muons were traveling at the speed of light, using the muon half-life of 1.56 microseconds. When the time dilation relationship was applied, the result could be explained if the muons were traveling at 0.994 c.

In an experiment at CERN by Bailey et al., muons of velocity 0.9994c were found to have a lifetime 29.3 times the laboratory lifetime.

See Also:

• Superluminal neutrinos from noncommutative geometry
•  No. Uh-uh. Nope. Nuh-Uh.
•  Theory Carnival: Phenomenological Quantum Gravity