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Subject: Re: Langevin and Doppler effects...
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From: Richard Hachel <r.hachel@wanadou.fr>
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Le 07/09/2024 à 21:14, "Paul.B.Andersen" a écrit :

> Is the Langevin paradox solved?

Absolutely not.

We had a very interesting discussion, you and I, on the relativistic 
Doppler effect.

We are neither you nor I, cretins, bandits, thugs, war criminals.

Each of us agrees that we wish to understand, master, and teach Henri 
Poincaré's theory of relativity (the most beautiful theory ever to have 
germinated in a human mind) in the most correct way possible.

We have just, by a very simple example, shown the relativity of pulsatile 
frequencies, and there is no doubt, for me, as for you, that if these 
things can one day be tested, they will give strictly the results that we 
have proposed, and which are perfectly in agreement in your vision of 
things, and in mine.

But this is only the first approach. This is NOT the complete resolution 
of the Langevin paradox, because we talked about the relativity of the 
pulsatile frequency, but we never
talked about the relative distances traveled by the two protagonists.

And that is the main point of the subject (the Doppler effect is just the 
appetizer).

I have never stopped saying, for forty years, that we must respect the 
word of our old physicists, and the difficulty they had at the time to 
believe in the theory of relativity because we could not say on the one 
hand that there was no absolute frame of reference, and on the other,
say that Stella, in her own frame of reference, came back younger than 
Terrence, which is absurd, since constantly, AS MUCH on the way out, 
DURING the U-turn, and AS MUCH on the way back, second after second,
for her, Terrence's time passes less quickly.

There must be something wrong.

Because that's the reality of things, always, always, always, chronotropy 
is of the type To'=To/sqrt(1-Vo²/c²) for both participants. Always, 
always, always, the relative speed will be v=0.8c (even during the 
half-circle of the U-turn) between the two, and always, always, always, 
Stella will observe Terrence's chronotropy lower than hers, and Terrence 
will observe that it is Stella's chronotropy that is lower.

So what's going on?

The Doppler effect solves part of the things, but not ALL of the things, 
and in this, a problem persists: the Langevin paradox.

It is ONLY partially clarified.

Because there will persist, on Stella's side, a theoretical enormity that 
physicists cannot explain, and which will then be denied (by human 
reflex).

We know that Terrence will observe Stella moving at Vapp=0.4444c,
on the way there, and for 27 years (he receives half of the beeps during 
this period).

What distance will he measure? x=0.4444c*27=12al.

On the way back, he will measure x=4c*3=12 al

It is undeniable and mathematical.

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.

It is on this incredible relativity of distances that the paradox is 
based, BUT she does not travel a shorter distance (which is absurd because 
she would have a longer time) but a longer one.

That is why in total she has a shorter time than Terrence.

I beg you to UNDERSTAND what is really happening.

This "time-gap" story is just dust swept under the carpet.

There is NO time-gap in Hachel, because we do not need it, and it is 
totally false.

In Stella's frame of reference the earth will travel x=0.4444*9=4ly on the 
way out.

And x=4c*9=36al on the way back.

This is the phenomenon of elasticity of relative distances well 
understood.

During the U-turn, nothing changes for Stella in terms of time.

I beg you to understand this.

She notes 9 years on her clock, at the entrance to the U-turn, and 9 years 
at the exit.

She sees the earth, over there, at 4ly, which marks 3 years, when she 
enters her U-turn (which she will do in 24 hours of proper time), and at 
the exit, the earth still marks 3 years.

There is no time gap.

She will therefore see the earth come back to her in 9 years of proper 
time, but with an earth clock that turns three times faster.

The key to the problem is not explained by the time gap, but not the 
space-zoom.

During her U-turn, she sees the earth go from 4 ly, to 36 ly, in her frame 
of reference.

THIS is what explains the Langevin paradox.

Not the time-gap, which is false, ridiculous, and a filthy attempt to 
sweep dust under the carpet.

R.H.