Lucifer's Question Of The Day:-

An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c. What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?

Question

Lucifer's Question Of The Day:-

An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c. What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?

anonymous · Answer

Only God or nerds...

jamesj · Answer

from out perspective, the elapsed time of the particle's life is
t = distance/speed = 0.00105/0.992c

Now adjust this back into the particles frame of reference to find the life time of
$$ t' = t \sqrt{1-(0.992)^2} $$