Re: Albert in Relativityland

On Fri, 4 Apr 2025 10:33:37 +0000, Paul.B.Andersen wrote:

Den 03.04.2025 23:06, skrev LaurenceClarkCrossen:

On Thu, 3 Apr 2025 9:08:46 +0000, Paul.B.Andersen wrote:

>
The measured mean lifetime of a stationary muon is 2.2 μs
The measured mean lifetime of a muon moving at 0.999668⋅c is 85.36 μs.
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These are measured facts, not math.
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Can you give another interpretation of the facts than "time dilation"?
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I did not say the time dilation must be the same for the same speed.
I asked why relativity says it's different.
What is the alleged cause?
When are you going to try to understand?

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Your confused nonsense can't be understood.
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Time dilation is not a difference in lifetime.
I never denied the measured lifetimes.
I only disagreed with your interpretation that it is time dilation.
They just live longer. But why?

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Everything you say shows that you have no idea of
what time dilation is.
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So let's take it from the beginning.
Time dilation is the phenomenon that the measured time
between two events on an objects world-line depend
on the frame of reference in which it is measured.
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In the following example there is but one muon with one life.
Let the two events on the muon's world-line be its creation and decay.
If this life is measured to last 2.2 μs in the muon's rest frame,
then _the same life_ would be measured to last 85.36 μs in
a frame of reference where the speed of the muon is 0.999668⋅c.
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But we can only measure times in the lab-frame (or Earth-frame).
So it is impossible to measure the lifetime of the same muon
in two different frames, so we must measure the lifetime
of a stationary muon, and we know that the proper mean lifetime
of the moving muon is the same, 2.2 μs.
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(Proper lifetime is the lifetime measured in the rest frame
  of the muon.)
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That the proper mean lifetime of a muon is τ = 2.2 μs
doesn't mean that all stationary muons will live 2.2 μs.
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If a muon is known to exist, then the probability that it still
exists a time t later is exp(-t/τ).
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Now you can read my original post in this thread:
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| The speed of muons is v = ~ 0.999668⋅c through the atmosphere
| which also is within the laboratory.
| γ = 38.8.
|
| The mean proper lifetime of a muon is t₀ = 2.2 μs.
| But measured in the Earth's rest frame the mean 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 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 measured in the Earth
frame,
| then the part of the muon flux that 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?
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Since it is impossible to measure the muon flux at 15 km,
the experiment would have to be modified to be done in the real world.
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Here is how:
https://paulba.no/paper/Frisch_Smith.pdf
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Because you can't understand it is confusing to you.
It is easy to understand what time dilation is. It is not a different
lifetime. It is an interpretation that denies the lifetime is different.
Time is the same everywhere so you require a nonsensical definition of
time.