Question

The muon is an unstable elementary particle that decays via a weak-force interaction process into an electron and two neutrinos. The life time of muons in their rest frame is 2.197µs ≡ 2.197×10−6 s. Nuclear reactions in the upper atmosphere, precipitated by the impact of highly energetic cosmic rays ,generate fast-moving muons about 10km above sea level. Some of these particles are detected in labs at about sea level. This is possible because the life time of muons moving with respect to the Earth’s surface is dilated. (a) Estimate the muons’ speed relative to Earth from the fact that they travel 10.0km between their point of creation in the atmosphere until seen to decay in ground-based labs. (b) The proper distance travelled by the muons considered in part (a) is 10.0 km. Calculate the length of this distance as it would be measured in the muons’ rest frame. Explain how your result, if interpreted using Galilean relativity, would be at odds with finding cosmic-ray muons at the Earth’s surface.

Answer 1