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Subject: Re: Incorrect mathematical integration
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Date: Sun, 21 Jul 24 21:06:27 +0000
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From: Richard Hachel <r.hachel@wanadou.fr>
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Le 21/07/2024 à 21:26, "Paul.B.Andersen" a écrit :
> Den 20.07.2024 23:55, skrev Richard Hachel:

> So: in an inertial system K, a clock C is in inertial motion.
> 
> t is the time in K.

 No, "To" is time in K. This is chronotropy.

 Every clocks in K have not the same time (t1,t2,t3,t4,t5, etc...), only 
the same chronotropy. 
 

> A and B are two stationary, synchronous clocks in K.
> 
> At t = t₁

 You want say, at To=To1

>    C
>    A                     B
> --|---------------------|------> x
>    0                     L
> Clock A is showing t₁, clock C is adjacent to A and is set to zero.

 To(A)=0
 To(C)=0
 t(A)=0
 t(C)=0

> At t = t₂
>                          C
>    A                     B
> --|---------------------|------> x
>    0                     L


 At To2(B)=t(C)/sqrt(1-Vo²/c²)

> Clock B is showing t₂, clock C is adjacent to B and is showing τ

 Yes.

> Let L = 0.0001 light second = 29979 m

 Yes

> Let (t₂ - t₁) = T = 125 μs

 Yes

> v = L/T = 239833966.4 m/s = 0.8c

 Yes

> w = L/τ

 Yes

> What kind of time is T ?

 T=To (observable time in the laboratory, time observable but not real 
mesured by two anisochronic clocks A and B). 

 
> What kind of speed is v ?

 Observable speed Vo. 

> What is τ ? (equation, value and type of time)

 Proper time of C (real time).

> What kind of speed is w ?

 Real speed (Vr)

> What is the physical significance of w?

  Vr=AB/τ

 It is a physical notion, but not very important in Galilean relativistic 
physics, on the other hand, which becomes fundamental in the physics of 
accelerated mobiles and which we can no longer do without as soon as we 
leave basic relativistic physics.

I recognize that it is quite strange to say that it is in the laboratory 
that we measure the real distance traveled, and at the level of the 
particle that we measure the real time to travel it.

> Can it say anything about the position of C at the time τ ?

x = Vo.To = Vr.Tr = Vapp.Tapp

x=Vr.τ

R.H.