Re: Incorrect mathematical integration

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.