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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Langevin and Doppler effects...
Date: Fri, 6 Sep 2024 21:04:43 +0200
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Den 05.09.2024 23:45, skrev Richard Hachel:
> 
> Paul B. Andersen :
> 
> https://paulba.no/pdf/TwinsByDoppler.pdf
> 
> Well.
> There are often few numerical applications in the
> developments of relativistic theorists, because this can pose some 
> problems of contradiction, or even absurdity.
> 
> We will return to the eternal problem, which has scared away all the 
> contributors I have dealt with for 40 years, although the opposite is 
> always said, and that I am the one who would be a wimp.
> 
> So we return to the problem, which is nevertheless very simple.
> 
> Stella goes into the stars for a journey of 24 light years.

> 
> The speed is 0.8c on the way there (12 ly), and 0.8c on the way back (12 
> ly).
> 
> We quickly obtain the following data by the Doppler effect.
> 
> Stella and Terrence agree to beep every month.


You will find the answer here:
https://paulba.no/pdf/TwinsByDoppler.pdf
L = 12 ly
c = 1 ly/y
f = 12/y
v = 0.8c
γ = 5/3

But since you never read anything, I will repeat it here.

> 
> It is clear that, for Stella, on the way there, as on the way back, she 
> will beep
> 108 times (216 times in total). >
> SO, Terrence will receive 216 beeps.

OK. Stella has aged Tₛ = 2L/vγ = 18 y
Number of received beeps Ns = Tₛ⋅f = 216

> 
> For his part, Terrence will beep for 30 years. He will therefore send
> 360 beeps.

OK

> 
> Except that if Terrence receives the same number of beeps on the way 
> there as on the way back (108 each time), Stella receives many more 
> beeps on the way back than on the way there.
> 
> It is then interesting to know how many beeps Stella receives on the way 
> there, and how many she receives on the way back.


Doppler shift when Stella is moving out  Do = √((c−v)/(c+v)) = 1/3
Doppler shift when Stella is moving back Db = √((c+v)/(c-v)) = 3
So number of received beeps Nt = Tₛ⋅f⋅Do/2 +  Tₛ⋅f⋅Db/2 = 36 + 324 = 360

> 
> Once this is done, we can still progress in understanding things.
> 
> We just have to not be afraid, and have a playful spirit.

Terrence will age C = 2L/v = 30y

Am I guessing wrong when I guess that you will present us with
the paradox that Terrence will receive
Tₜₛ⋅f⋅Do/2 + Tₜₛ⋅f⋅Db/2 = 60 + 540 = 600 beeps ? :-D

Hint:
https://paulba.no/pdf/TwinsByDoppler.pdf

> 
> R.H.

-- 
Paul

https://paulba.no/