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Exercise:
A muon half-life taO created hO above the surface of the Earth reaches the surface at the of its half-life. Calculate the distance to the Earth in the muon’s rest frame.

Solution:
The proper distance i.e. the distance in the rest frame of the Earth can be expressed as lambda v t v gamma tau beta c gamma tau sqrt-fracgamma^ gamma ctau sqrtgamma^- ctau It follows for the Lorentz factor gamma sqrt+leftfraclambdactauright^ The contracted length i.e. in the rest frame of the muon is thus ell fraclambdagamma fraclambdasqrt+leftfraclambdactauright^ hmF leftsqrtfrach^+fracncctimesta^right^- resulthmP This is only slightly less than the distance the muon could travel within its half-life if it was moving at the speed of light: sscellmax lmaxF ncctimesta lmaxP
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Exercise:
A muon half-life taO created hO above the surface of the Earth reaches the surface at the of its half-life. Calculate the distance to the Earth in the muon’s rest frame.

Solution:
The proper distance i.e. the distance in the rest frame of the Earth can be expressed as lambda v t v gamma tau beta c gamma tau sqrt-fracgamma^ gamma ctau sqrtgamma^- ctau It follows for the Lorentz factor gamma sqrt+leftfraclambdactauright^ The contracted length i.e. in the rest frame of the muon is thus ell fraclambdagamma fraclambdasqrt+leftfraclambdactauright^ hmF leftsqrtfrach^+fracncctimesta^right^- resulthmP This is only slightly less than the distance the muon could travel within its half-life if it was moving at the speed of light: sscellmax lmaxF ncctimesta lmaxP
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special relativity
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length contraction, lorentz factor, muon
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(3, default)
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ENG (English)
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Calculative / Quantity
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