Re: Muon paradox

Den 09.04.2025 16:07, skrev gharnagel:

On Tue, 1 Apr 2025 17:56:05 +0000, Paul.B.Andersen wrote:

>
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?

 The problem with AI apps that Crossen used is that it's not accurate.
Crossen finds one source that agrees with his bias and stops looking,
then makes post after post after post believing he has discovered the
ultimate truth!

The muons in the laboratory which the AI-app said travel at speeds
very close to the speed of light was probably muons in a storage ring.
I chose the "laboratory" to be the lab where the atmospheric muons
were counted. So the muons don't only have the same speed, they are
the same muons.
What kind of reasoning is behind Laurence's question:
"Then why would they "time dilate" in the atmosphere?"
beats me.

 Well, he has merely scratched the surface and his AI app is wrong
about muon lifetime in the laboratory.  Muon-electron "atoms" are
not formed by muons travelling at relativistic speeds and the
lifetime of the muon is 2.2 usec:
 https://www.quirkyscience.com/muonium/

--
Paul
https://paulba.no/