### Relativity and muon decay

#### What are muons?

Muons are leptons, like electrons with a negative charge but a much greater mass. As with all leptons and quarks, they are part of the group of particles called “fermions”.

Muons can be produced in a particle accelerator and are produced naturally by cosmic rays striking the upper atmosphere. Muons are unstable, they will decay having a half life at rest of about 1.5µs

The deep penetration of heavy muons into dense material makes them useful for imaging the interiors of large masses.

#### What have muons got to do with relativity?

The half life of muons was studied as they travelled from the edge of the atmosphere to the ground becoming a major experiment helping to confirm Einsteins Laws of Special Relativity. For example, measurements are made of the number of muons at 2000 metres above

ground level, during the time that they take to travel to the ground, travelling at almost the speed of light, we would expect that most would decay. That time taken is equal to about four half lives so we would expect only 1/16 of the original number to remain.

However, when measurements are made about half of those muons reach the ground. For the muons either the time they have been travelling seems to be much less than we calculate as outside observers or the distance they have travelled is much less. The effect can be explained by using Einstein’s Laws of Relativity in two possible ways.

A clock travelling along with the muon would, to an outside observer, seem to be running slow. That is time dilation.

If an observer was travelling with the muon, the ground would seem to be rushing up towards them and distance to the ground would seem to be a lot shorter. That is length contraction.

The most common muon decay is shown here, the decay is by the weak interaction. Because lepton numbers are conserved one product is a muon neutrino and the other an electron-type antineutrino together with an electron.