Re: Muon paradox

Den 31.03.2025 22:40, skrev LaurenceClarkCrossen:

Do muons move at a different velocity in the laboratory than in the
atmosphere?
 "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.
 Then why would they "time dilate" in the atmosphere?

The speed of muons is v = ~ 0.999668⋅c through the atmosphere
which also is within the laboratory with open roof.
γ = 38.8.
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!).
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.
If the lifetime of the muons had been 2.2 μs, 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.
Can toy guess which of them is closest to what is observed?
--
Paul
https://paulba.no/