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From: clzb93ynxj@att.net (LaurenceClarkCrossen)
Newsgroups: sci.physics.relativity
Subject: Re: Muon paradox
Date: Tue, 1 Apr 2025 19:19:38 +0000
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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?
>>>
>>> "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?
>>
Can you guess which muon lifetime is closest to what is observed?