Relativistic Time Dilation in Muon Decay
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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.
Contributed by: S. M. Blinder (March 2011)
Correction by Howard Landman
Open content licensed under CC BY-NC-SA
Snapshots
Details
Permanent Citation