Re: Muon paradox

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?
>
"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,

If the lifetime of the muons had been 2.2 μs in the Earth frame

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?

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

 

--
Paul
https://paulba.no/