Re: Albert in Relativityland

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.
>
These are measured facts, not math.
>
Can you give another interpretation of the facts than "time dilation"?
>
>

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?

Your confused nonsense can't be understood.

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?

Everything you say shows that you have no idea of
what time dilation is.
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.
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.
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.
(Proper lifetime is the lifetime measured in the rest frame
  of the muon.)
----------
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.
If a muon is known to exist, then the probability that it still
exists a time t later is exp(-t/τ).
Now you can read my original post in this thread:
| 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?
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.
Here is how:
https://paulba.no/paper/Frisch_Smith.pdf
--
Paul
https://paulba.no/