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spaghetti3451
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Homework Statement
The muon has been measured to have a mass of ##0.106\ \text{GeV}## and a rest frame lifetime of ##2.19 \times 10^{-6}## seconds. Imagine that such a muon is moving in the circular storage ring of a particle accelerator, ##1## kilometer in diameter, such that the muon's total energy is ##1000\ \text{GeV}##. How long would it appear to live from the experimenter's point of view? How many radians would it travel around the ring?
Homework Equations
The Attempt at a Solution
Proper time runs in the muon's rest frame. Therefore, the experimenter observes a dilated lifetime of the muon.
Therefore, from the experimenter's point of view,
lifetime ##= \gamma \tau = \frac{E}{mc^{2}} \tau = \big(\frac{1000}{.106}\big)(2.19 \times 10^{-6}) = 20.7 \times 10^{-3}## seconds.Using the invariant interval in the muon's rest frame, and the experimenter frame,
##- (\delta \tau)^{2} = - (\delta t)^{2} + (\delta x)^{2}##
##\delta x = \sqrt{(\delta t)^{2}- (\delta \tau)^{2}}##
##\delta x = 0.0207## m.
Therefore, number of radians ##= \frac{0.0207}{500} = 4.14 \times 10^{-5}##.
Are my answers correct?
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