Re: Muon paradox

On Thu, 10 Apr 2025 20:02:00 +0000, Aether Regained wrote:

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, 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?
>

>
@PaulBAndersen
>
There is one flaw I find in the SR explanation, can you confirm if it is
true:
>
What is really measured are these (the facts):
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1. The mean proper lifetime of a muon is t₀ = 2.2 μs.
2. muons are created at a height ~15 km
3. The speed of the muons is ~c, so travel time is ~50.05 μs
4. muon flux measured on the Earth's surface is about 55.6% of what it
is at 15km.
>
From 1, 2 and 3, the expected muon flux on the Earth's surface is:
>
N/N₀ = exp(-t/t₀) = exp(-50.05/2.2) = 1.32e-10 = 0.0000000132%
>
The important point (the flaw) is that the speed of the muon has not
actually been measured to be 0.999668⋅c, but instead is computed.
>
N/N₀ = exp(-t/γt₀) = .556 => γ = 38.8 => v = 0.999668⋅c
>
The SR explanation would have been more convincing, if the speed had
actually been measured to that many significant figures.

Time dilation is an absurdly illogical interpretation that cannot be
proven by any evidence. There can easily be many reasonable and
scientific explanations.
 "Another example he gives is that muons created by cosmic radiation in
high atmosphere are seen to travel longer than their half-time would
allow. But half-time is only the time when half of the muons break up.
There are muons that last longer. Should one measure the muon half-time,
it might show the claim, but that calculation requires knowing the
distribution and intensity of cosmic radiation, the distribution of the
velocities of muons created by this radiation, and an estimation how
many are detected in a given speed range. This calculation has many
uncertainties." - "The final blow to the relativity theory" -Jorma
Jormakka
jorma.o.jormakka@gmail.com
Aalto University, (Adjunct Professor in the Department of
Communications and Networking, retired), Espoo, Finland
"AI Overview
The chance of something lasting ten half-lives is exceptionally low.
After each half-life, the amount of the substance remaining is halved.
After ten half-lives, approximately 0.1% of the original substance would
be left. This means there's a very low chance of anything surviving ten
half-lives."