"The effects of relativity are symmetrical by permutation of referential".

To put it better: there is no privileged frame of reference.

In the episode of the Langevin twins, many (if not everyone) do not seem
to understand that the situation is symmetric going out and back, and that
each has a positive chronotropy with respect to the other twin without
this leads to an obvious final paradox.

To better understand, it is necessary to give an example that is easy to
integrate.

The equation, everyone knows it.

t'=t.(1+cosµ.v/c)/sqrt(1-v²/c²)

Either on the way : t'=t.sqrt[(1+v/c)/(1-v/c)]
and on return : t'=t.sqrt[(1-v/c)/(1+v/c)

Thus, on the outward journey, each of the two twins sees the other's clock
turn more slowly, ie (take Vo=0.8c) three times slower; and, on the way
back, the equation is reversed.
Each sees the other's watch spinning three times faster.

So why are the two twins not the same age in the end?

Because when the twin turns, he is nine years old, and he sees his earthly
brother (he has a good telescope) who is only three.
It's logic.
But for the other, when the brother turns, the brother is nine years old.
But he has twenty-seven!

That is to say that the equation is reversed for the first when he is nine
years old, but that it is reversed for the other only when he is 27 years
old.

The situation therefore becomes unequal, not in the sense that the two
equations are not symmetrical, but in the sense that they do not reverse
"at the same time". The twin of the stars being warned directly that he is
turning (obviously), but not the other, for whom the other is always on
the way.

For both, the watches of the other then begin to turn three times faster.

The earth twin sees his brother come back for three years at full speed
and age nine years
additional.

The twin of the stars for whom the terrestrial twin was only three years
old sees returning to him, for nine years, an earth whose needles turn
three times faster.

For the two, in total, we have a twin aged 18 and the other 30 years old.

It is very simple when you understand.

It remains to understand the relativistic zoom effect that nobody in the
world explains, unfortunately correctly (elasticity of distances) to
finally admit (but here the problem is YOU).

We then understand, if we make the effort to follow what I say, that each
sees the other returning at an apparent speed of 4c.
But especially that the twin of the stars sees the earth travel 36 al.
It is this fantastic spatial zom-effect during the twin's U-turn (and
which obviously concerns only him) that relativists around the world do
not seem to be able to understand. If they are told that the rocket
observed from the terrestrial reference frame seems three times larger,
they understand.
But if, conversely, they are asked to understand that for the other, it is
the distance to the earth that will seem three times greater to them, they
lose control.
As if the intellectual effort exceeded them.
I never understood why it exceeds them.
It's not that hard to understand though.

In relativity, you have to apply the symmetries, and apply them to the
end.

We then have a perfectly logical theory.

I will speak later of the traveler of Tau Ceti in uniformly accelerated
rectilinear motion.

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R.H.

--
"Mais ne nous y trompons pas. Il n'y a pas que de la violence
avec des armes. Il y a des situations de violence".
Abbé Pierre.
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