825.3 consequences of Einstein's postulates Microscopic clock: Muons are unstable elementary particles with a(proper) lifetime of 2.2 As they are produced with very higl speeds in the upper atmosphere when cosmic rays collide with air molecules. Take the height Lo of the atmosphere to be 90 km in the reference frame of earth, if the average speed of the muons is 0.999978c can the muons arrive the surface of the earth? 8 25.3 consequences of Einsteins postulates Solution: According to Newton's mechanics L=0.999978×3.0×103×22×10=660m The muons can not arrive the surface of the earth According to relativity, the life-time of the muon is 2.2 3317 (0.999978 The distance that muon can travel is 0.999978×3×10°×3317×10=995078m The muon can arrive the surface of the earth14 Microscopic clock: Muons are unstable elementary particles with a (proper) lifetime of 2.2 µs. they are produced with very high speeds in the upper atmosphere when cosmic rays collide with air molecules. Take the height L0 of the atmosphere to be 90 km in the reference frame of earth, if the average speed of the muons is 0.999978c, can the muons arrive the surface of the earth? §25.3 consequences of Einstein’s postulates Solution: 0.999978 3.0 10 2.2 10 660 m 8 6 = × × × × = − L According to Newton’s mechanics The muons can not arrive the surface of the earth. According to relativity, the life-time of the muon is 331.7µs 1 (0.999978) 2.2 1 ( ) 2 2 2 0 = − = − = v c τ τ The distance that muon can travel is 0.999978 3 10 331.7 10 99507.8m 8 6 × × × × = − The muon can arrive the surface of the earth. §25.3 consequences of Einstein’s postulates