Chapter 20 - Relativity - Davidson Physics

Announcements Review The Twin Paradox Length Contraction Final QuestionsMuons: continuedHowever, a hypothetical observer on the muon would not invoke time dilation, because in their frame ofreference they are not moving!For the imaginary observer on the muon, the time it takes before the muon decays is still∆t 0 = 2.20 × 10 −6 secondsHowever, the observed distance (length) that the muon needs to travel to reach the Earth’s surface isshorter (length contraction)√L = L 0√1 − v 2 /c 2 = (10 km) 1 − (0.998) 2 = 0.633 km = 633 metersTo travel that distance would take a timet = L v =633 m0.998 ( 3 × 10 8 m/s ) = 2.11 × 10−6 sThis time is roughly the same as the muon’s lifetime, so both observers agree that many muons will reachthe Earth’s surfaceRelativity