Re: Incorrect mathematical integration

Den 24.07.2024 00:19, skrev Richard Hachel:

Le 23/07/2024 à 23:29, "Paul.B.Andersen" a écrit :

Den 22.07.2024 23:37, skrev Richard Hachel:

Le 22/07/2024 à 21:34, "Paul.B.Andersen" a écrit :

>
Let's look at the LHC again.
>
The length of the circuit is L = 27 k, γ = 7460
The real speed of the proton in the lab frame is
v = 0.999999991·c
>

 When calculating velocities the distance and time must be measured
in the same frame of reference.
The distance in one frame and the time in another frame is not
a speed of anything if the frames are moving relative to each other.

 I know it may seem very strange (relativistic physics is a bit strange but unavoidable) but that's how it happens.
It is the observing frame of reference that has the right distance, but it is the particle or rocket that has the right time.
Observable time being only an anisochronous illusion.

It isn't only "strange", it is idiotic nonsense.
Measured in the lab frame the proton is moving around
the L = 27 km long ring in T = 90.0623065140618 μs.
The very real speed of the proton relative to the lab is
v = L/T =  0.999999991·c
γ = 7460
Measured in the proton frame, the length of the ring is
L' = L/γ = 3.6193029490616624 m.
The proton is moving around the L' long ring in the time
  τ = T/γ = 12.072695243171824 ns
The very real speed of the lab relative to the proton is
v =  L'/τ = (L/γ)/(T/γ ) = L/T = 0.999999991·c
This should be blazingly obvious for anybody but complete morons:
If the proton is passing a point in the ring with the speed v
relative to the point, then the point in the ring is passing
the proton a the speed v relative to the proton.

>

The proton is moving at the speed 0.999999991·c relative to the lab,
and the lab is moving at the speed 0.999999991·c relative to the proton.

Because the distance and time are measured
in the same frame of reference.

>
That what I say.

 No, that is not what you say.
You say the proton is moving at the speed 6947c relative to the lab.

Which is the "proper speed" L/τ.
But L/τ  is not the speed of anything because it is the distance
in the lab frame divided by the time in the rest frame of the proton.

And you thought that the real speed speed of the proton in the lab frame
was 6947c and therefore you "tell them [the physicists at CERN]  that
the proton rotates 78 million times per second".
>
Which is 6933 times the real number,  ≈ 11.25 thousand times per second.

 Give it up, Richard.
The physicists at CERN measures that the proton 'rotates'
11.25 thousand times per second, you "tell them that the proton
rotates 78 million times per second."

Don't tell me you don't understand that the proton rotates 11.25 million times per second in the laboratory frame but 78 million times per second in the proton frame.
 This is called time dilation.

"The proton rotates 11.25 million times per second in the laboratory frame but 78 million times per second in the proton frame"!
Good grief, this is way toooo stupid!
But it is funny! Hilarious! The involuntary jokes are often the best.
ROFL (not really, but it was close!)
--
Paul
https://paulba.no/