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akennedy
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Homework Statement
The muon is an unstable elementary particle that decays via a weak-force
interaction process into an electron and two neutrinos. The life time of muons in their rest
frame is 2:197 s 2:197106 s. Nuclear reactions in the upper atmosphere, precipitated by
the impact of highly energetic cosmic rays, generate fast-moving muons about 10 km above sea
level. Some of these particles are detected in labs at about sea level. This is possible because
the life time of muons moving with respect to the Earth's surface is dilated.
(i) Estimate the muons' speed relative to Earth from the fact that they travel 10.0 km between
their point of creation in the atmosphere until seen to decay in ground-based labs.
(ii) The proper distance traveled by the muons considered in part (a) is 10.0 km. Calculate
the length of this distance as it would be measured in the muons' rest frame. Explain
how your result, if interpreted using Galilean relativity, would be at odds with nding
cosmic-ray muons at the Earth's surface.
Homework Equations
gamma = 1/SQRT(1-v^2/c^2)
Time = gamma*proper time
The Attempt at a Solution
Honestly I'm clueless. I am really struggling with relativity but here's my current understanding of the problem (i). The muon is traveling at high speeds so it experiences time dilation and is able to travel to the surface of the Earth without decaying.
The proper time would be the time as measures on the Earth as it is, for all purposes, at rest right?
I'm having trouble understanding the whole dilation aspect... If the particle experiences time dilation does that mean it's only undergone that time above to travel 10KM? Wouldn't that mean it was traveling faster than c?
Is the 2.197x10-6 the proper time or the dilated time? :|
Sorry I really don't know where to start.