Re: Langevin and Doppler effects...

Den 11.09.2024 23:15, skrev Richard Hachel:

Le 11/09/2024 à 22:18, "Paul.B.Andersen" a écrit :

Den 09.09.2024 20:54, skrev Richard Hachel:
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Example #2:
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Terrence will move away at the speed 0.8c in Stella's frame.
When Stella's clock shows 9y, Terrence will be at the position
x = 0.8c⋅9h = 7.2 ly in Stella frame. (Stella is at x = 0ly)
Terrence clock will run at the rate 1/γ so it will show 9h/γ = 5.4y
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When Stella's clock show 9y 12h, Terrence will be at the position
x = 12 ly in Stella's frame. Terrence clock will now show 15 y.
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When Stella's clock shows 9y 24h, Terrence will now be at the position
x = 0.8c⋅(9y 24h) = (7.2 ly + 19.2 lh)  in Stella's frame.
Terrence clock will now show (30y 40h) - (9y 24h)/γ = 24.6y 25.6h
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When Stella's clock shows 18y 24h, Stella is back.
Terrence will now be at the position x = 0 ly.
Terrence clock will now show (24.6y 25.6h) + (9y 24h)/γ = 30y 40h
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Note that when Stella's clock show 9y, Terrence clock simultaneously
in Stella's frame show 5.4y, and when Stella's clock show 9y 12h, Terrence clock simultaneously in Stella's frame show 15y.
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That means that Terrence clock runs (15-5.5)y/12h = 7012.8 times
faster than Stella's clock during the first part of the U-turn.
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But nothing happens to Terrence clock, it runs normally.
It is _only_ Stella's idea of what is simultaneous that
make it appear that Terrence clock run fast.
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 Same as for the previous post.
 You use observers M1 and M2 and not Terrence himself.
 Here, Terrence always remaining in the same inertial frame of reference, M1 and M2 are the same external reference point.
 But it is not Terrence.
 Of course, I may give you the impression that I am quibbling, but that is not the case.

You are not quibbling, you are babbling.
According to SR:
I have shown you Terrence's, speed, position and proper time
measured in Stella's rest frame, as a function of Stella's time.
It is quite simple:
During Stella's time 0y -> 9y, Stella is inertial and so is her frame.
MEASURED IN STELLA'S FRAME, Terrence is moving away at the speed 0.8c, his clock runs slow by 1/γ, and his position is x = 0.8c⋅t_Stella'
So when Stella's clock show 9h, t_Terrence = 5.4y and x = 7.2 ly
During Stella's time 9y -> 9y + 24h, Stella is accelerating towards
Terrence, so Stella's frame is an accelerated frame.
MEASURED IN STELLA'S ACCELERATED FRAME, Terrence will move away
from Stella at high speed, and his clock will run thousands of times
faster than Stella's.
So when Stella's clock shows 9h 12h, t_Terrence = 15y and x = 12ly
When Stella's clock shows 9h 24h, t_Terrence = 24.6y 25.6h
and x = 7.2ly + 19.2lh
During Stella's time 9y 24h - 18y, Stella is inertial and so is her  frame.
MEASURED IN STELLA'S FRAME, Terrence is moving away at the speed 0.8c, his clock runs slow by 1/γ, and his position is
x = 7.2ly + 19.2lh + 0.8c⋅t_Stella'
At Stella-s time 18y + 24h Terrence is back.
What is it that you don't understand?

 Things must be said so that it is both infinitely beautiful and infinitely true.
 The measurements that you give here, with this concept M (which is not known since you really think that you are talking about Stalla, then Terrence, and not very distant lateral points) are not beautiful, even if, for the moment, they are true.
 The blow of the baton can only come later.
 When you are going to talk about the same things, but with accelerated frames of reference, it will no longer be beautiful or true.

| Den 07.09.2024 23:42, skrev Richard Hachel:
|> But for Stella, and this is the great key to the paradox, and the brilliant explanation, the distance traveled by the earth will NOT be 12 al, neither on the way there, nor on the way back, because it is not in the same frame of reference.
This is the statement I responded to.
It was YOU who introduced Stella's view ("for Stella").
You even called it "the key to the paradox" and "the brilliant explanation".
If Stella shall return to Terrence, she _must_ accelerate during
her journey, so Stella's frame is always an accelerated frame of reference (in flat spacetime).
But it isn't beautiful, even if it true.
Stella's view is rather pointless.
As I said:
Nothing happens to Terrence clock, it runs normally.
It is _only_ Stella's idea of what is simultaneous that
make it appear that Terrence clock run fast.
If you change Stella's path in Terrence frame a little,
Stella's view of Terrence may change it a lot, because
Stella's idea of what is simultaneous changes.
(You can change the path without changing Stella's and Terrence's proper times.)
If we describes the "twin paradox" in Terrence's inertial frame,
Stella's view adds nothing of interest.
So we can do without Stella's view of Terrence.
It is certainly not "the key to the paradox".
--
Paul
https://paulba.no/