Posted by pooja on Wednesday, May 2, 2012 at 8:31pm.
The π meson’s lifetime in its own frame is the proper time
interval, tₒ =2.6•10^−8 s. An earthbound observer measures a longer dilated time interval t . If β =0. 985,
t = tₒ/sqrt(1-β²) = 2.6•10^−8 /sqrt(1-0.985²) =1.5•10^-7 s.
The distance the π meson travels in the earthbound observer’s reference frame is the π-meson’s velocity multiplied by the time interval measured by the earthbound observer. (Note that this is the relative velocity)
d = v•t =0.985•c•1.598510^-7 = 0.985•3•10^8•1.5•10^-7 = 44.5 m,
Without time dilation, the distance traveled would just be the proper lifetime multiplied by the meson’s velocity:
s = 0.985• c•2.6•10^−8 =7.68 m.
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