Re: Muon paradox

On Tue, 1 Apr 2025 18:44:39 +0000, Paul.B.Andersen wrote:

Den 01.04.2025 19:56, skrev Paul.B.Andersen:

Den 31.03.2025 22:40, skrev LaurenceClarkCrossen:

Do muons move at a different velocity in the laboratory than in the
atmosphere?
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"No, muons generally do not move at a different velocity in a laboratory
setting compared to their velocity in the atmosphere; they both travel
at speeds very close to the speed of light, typically around 99.8% of
the speed of light" - Google search AI.
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Then why would they "time dilate" in the atmosphere?

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The speed of muons is v = ~ 0.999668⋅c through the atmosphere
which also is within the laboratory with open roof.
γ = 38.8.
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The mean proper lifetime of a muon is t₀ = 2.2 μs.
But measured in the Earth's rest frame the lifetime of the muon
is  tₑ = 2.2e-6⋅γ s = 85.36 μs (time dilation!).
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Since muons are created at a height ~15 km, and the time for
a muon to reach the earth is t = 15e3/v = 5.005 s,
then the part of the muon flux that will reach the Earth is
  N/N₀ = exp(-t/tₑ) = 0.556, so 55.6% of the muons would reach the
Earth.
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If the lifetime of the muons had been 2.2 μs,

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If the lifetime of the muons had been 2.2 μs in the Earth frame
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then the part of
the muon flux that will reach the Earth would be:
  N/N₀ = exp(-t/t₀) = 1.32e-10.
So only 0.0000000132% of the muons would reach the Earth.
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Can toy guess which of them is closest to what is observed?

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Can you guess which of them is closest to what is observed?

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Can you guess which muon lifetime is closest to what is observed?