A particle known as a pion lives for a short time before bre

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.989c, and an observer who is stationary in a laboratory measures the pion\'s lifetime to be 3.5 × 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

Solution

A. the time interval is given by

dt = t*sqrt(1 - v^2/c^2)

t = time in the observer\'s frame

dt = time in moving system\'s frame

dt = 3.5*10^-8*sqrt(1 - 0.989^2*c^2/c^2)

dt = 3.5*10^-8*sqrt(1 - 0.989^2)

dt = 5.177*10^-9 m/sec

B. Now the laboratory appears to move toward the pion at v = 0.989c, so distance will be given by

x = V0*dt = 0.989*c*dt

x = 0.989*3*10^8*5.177*10^-9

x = 1.536 m