The muon is traveling with a speed of \(v=0.9c\) relative to the Earth, thus the gamma factor is given by: \[\begin{aligned} \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} =\frac{1}{\sqrt{1-0.9^2}}=2.29\...The muon is traveling with a speed of \(v=0.9c\) relative to the Earth, thus the gamma factor is given by: \[\begin{aligned} \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} =\frac{1}{\sqrt{1-0.9^2}}=2.29\end{aligned}\] The amount of time that goes by in the frame of reference of the Earth, \(\Delta t\), when \(\Delta t'=2.2\mu\text{s}\) has gone by in the muon’s frame of reference will be dilated by the gamma factor. \(\Delta t'\) is the proper time in the muon frame’s of reference, which correspon…
