Date: Tue, 15 Apr 2025 23:39:00 +0200
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Subject: Re: Muon paradox
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On 4/15/2025 10:10 PM, Paul.B.Andersen wrote:
> Den 10.04.2025 22:02, skrev Aether Regained:
>> Paul.B.Andersen:
>>>
>>> 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 you 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):
>>
>> 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.
> 
> Nothing but the mean lifetime is really measured in my scenario above.


In your scenario? Sure. Most  or the
"measurements" invoked by relativistic
idiots are imagined; real measurements
of course are t'=t, you're even stupid
enough to admit it.