3. Muon Decay

Definitions

Muons move at speed of about

v = 0.99c

if we place two detectors MR1 and MR2, $d = 2000$ m apart

the time it takes for the muons to go from MR1 to MR2 is

t = \dfrac{2000}{0.99c} = 6.73 \mu s

notice that this time is much larger then the half life of a muon about $4.4$ half-lives

however typical measurements say we get

\text{MR1} = 500 \; \text{per min}, \quad \text{MR2} = 325 \; \text{per min}

based on the fact $4.4$ half-lives should have occured, we should expect a count of about

\text{MR2} = 25 \; \text{per min}

now lets look from a special relativity point of view

from the muons frame of referernce ( $t_0$ )

t = \gamma t_0, \quad t_0 = \dfrac{t}{\gamma}, \quad t = 6.73 \times 10^{-6} s

6.73 \times 10^{-6} \times \sqrt{1 - \dfrac{(0.99c)^2}{c^2}} \approx 0.95 \mu s

which for the muons is less than their half life

this means that less time has elapsed for the muons

and from the point of view of the observer it appears their half life has been extended