Re: Langevin's paradox again

Den 14.07.2024 04:02, skrev Richard Hachel:

Le 14/07/2024 à 01:29, "Paul.B.Andersen" a écrit :

<unsnip>:

As long as Stella's speed is constant, the shape of Stella's path is irrelevant, it can be circular, elliptic, partly straight and partly curved, or whatever shape you might like. (But no sharp corners, the path must be an analytic function.)

<unsnip end>

Of course Stella must accelerate at some part of the journey in
order to get back to Terrence, but when the speed is constant
the acceleration is transversal and will have no effect on her
proper time.

It's obvious from the following that you haven't understood
my statements above. You probably haven't even read them.

 < snip irrelevant talk about Langevin>

You have changed the scenario from the one I was responding to.
But let us consider this one.

So I assumed that the journey would last 18 years for Stella, and 30 years for Terrence (Vo=0.8c and D=2*12 al in R) which everyone agrees with.
 I placed a small acceleration phase at the aphelion of Stella's journey which will make a vast half-turn on a semi-circle while keeping its tangential speed of 0.8c in R, and this for 40 hours (we admit that momentary and monstrous accelerations are physically technically possible).

The acceleration isn't momentary, it lasts for 24 hours,
and of course it is technically impossible.
But it doesn't matter, this is a thought experiment.

In Stella's repository, exactly 24 hours (one day) will pass.
This value is absolute, and the two twins agree that for this concrete phase, it is 24 hours for Stella, and 40 hours for Terrence.
 I ask you to kindly grant me these bases.

I accept your definition of the scenario.
I will assume that the 24 hours are included in the 18 years,
and the 40 hours are included in the 30 years.

 Because afterwards, it gets complicated, and it seems that apart from me, no one in the world has had the trigger for the complete explanation of the Langevin traveler.

What do you mean by "complete explanation"?
Do you know the "complete explanation" for why
the Earth is orbiting the Sun?
Newton's gravitation theory and GR both predict that the Earth
will orbit the Sun, given the right initial condition.
Is this "the complete explanation" or have you another?
The only sensible question is:
What does the theory predict will happen?
And:
Is this in accordance with what really happens?
I will tell you what SR predicts for the scenario.
--------------------------------------------------
It is trivially simple.
Stella's speed in Terrence's inertial rest frame is
_constant_ 0.8c throughout the whole journey, so γ = 1/0.6.
So if Terrence proper time is 30 years, Stella's proper time
is  30/γ = 18 years.
(This follows from the metric or Lorentz transform.)
See: https://paulba.no/pdf/TwinsByMetric.pdf
I explained in my previous posting (quoted above) why
the acceleration is irrelevant in this case:
As long as Stella's speed is constant, the shape of Stella's path
is irrelevant, it can be circular, elliptic, partly straight and
partly curved, or whatever shape you might like.
(But no sharp corners, the path must be an analytic function.)
Of course Stella must accelerate at some part of the journey in
order to get back to Terrence, but when the speed is constant
the acceleration is transversal and will have no effect on her
proper time.
If Stella was accelerating longitudinally, the speed would change
and γ would be a function  of time, so the acceleration would
obviously affect Stella's proper time.
https://paulba.no/pdf/TwinsByMetric.pdf

 I therefore ask you to agree on the basics, because then you will have to admit true, but astonishing things, which can shock the human mind, in the same way as saying that the earth is a big blue ball to a peasant from the 11th century.

I can tell you that SR's prediction that the twins will age
differently doesn't chock me at all, because I know that
the prediction is demonstrated to be correct in the real world.

 It's true, but it can be shocking when you're not there, or worse, when you're poorly prepared.

Quite.
SR's predictions are chocking for people ignorant of physics.
--
Paul
https://paulba.no/