Re: Incorrect mathematical integration

Den 25.07.2024 21:50, skrev Richard Hachel:

Le 25/07/2024 à 21:17, "Paul.B.Andersen" a écrit :

 I see you have given up responding to my post.
 So let us terminate this discussion with the following
demonstration of the geniality of Doctor Richard Hachel:
  | Den 24.07.2024 00:19, skrev Richard Hachel:
|> Don't tell me you don't understand that the proton rotates
|> 11.25 thousand times per second in the laboratory frame but
|> 78 million times per second in the proton frame.
|>

Richard Hachel's statement:
"The proton rotates 11.25 thousand times per second in
  the laboratory frame but 78 million times per second
  in the proton frame."
is quite genial, because it sums up Richard Hachel's
confusion and stupidity in one single sentence!
Well done, Richard!:-D

 When a proton moves around the circuit once, a stationary clock
in the circuit will measure the one round around the circuit to
last the time T = 90.0623 μs
The proton (if it had a clock) will measure the one round around
the circuit to last the time τ = 12.0727 ns
 Does this mean that when the proton moves around the circuit once,
then it moves once around the circuit in the lab frame while
it moves T/τ = 7460 times around the circuit in the proton frame?

 But no!
 It's stupid.
 The proton only goes around once, and the time it takes, measured by the laboratory clock (which is actually TWO clocks A and B combined into one) is T = 90.0623 μs.
 I write To = 90.0623 μs to say that this is the observable time in the laboratory reference frame.
 But if I measure with the watch that the proton wears on his left wrist, I will measure a time of τ = 12.0727 ns.

Why do you repeat what is quoted above?

 Thus, for the proton, the distance AB (in the laboratory reference frame) was crossed 7460 times faster.

So we can change the wording of your genial statement above to:
"The proton rotates once per 90.0623 μs in the laboratory frame
  but 7460 times per 90.0623 μs in the proton frame."
Even better!

I call this notion the real speed of the proton, even if it sounds funny when you're not used to seeing things that way.
The speed usually measured, and observed in the laboratory, which is the distance in the laboratory per laboratory time, I call it v (like the physicists) or better, Vo, to point out that we only ever observe one notion of things, and not real things, distorted by the nature of local space-time, of the local frame of reference.
 

'nuff said! :-D
A hint:
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
--
Paul
https://paulba.no/