Re: Langevin's paradox again

Den 14.07.2024 23:49, skrev Richard Hachel:

Le 14/07/2024 à 22:25, "Paul.B.Andersen" a écrit :

 If Stella leaves Terrence with the initial speed 0.8c
and accelerates toward Terrence (brakes) with a constant
proper acceleration, her speed in Terrence rest frame will
diminish with time to zero, and then increase until she
passes (hits?) Terrence with the speed 0.8c.
 Everybody but complete morons will understand that the acceleration
will affect Stella's proper time when she is back at Terrence.

 MAIS NON !!!
 Oh my god!
 Stella's acceleration does not change its own time in any way.
Breathe in, breathe out...
Damn it!
What will vary is not its own time, which is only related to its chronotropy, and it is always immobile in relation to itself.
There is no absolute frame of reference, and time passes in the same way in ALL frames of reference, that is to say by one second every second.
It is only for observers placed elsewhere and measuring with different watches that proper time becomes relative. But proper time is in itself invariant.
When Bella (the traveler from Tau Ceti) leaves the earth, her own time does not change in any way. She will reach Tau Ceti in 4,776 years, and throughout the journey her time remains one second per second, as it was before she left. Only in the Earth's frame of reference does time seem to expand more and more, and acceleration seems to decrease more and more. I gave the equations.
In relativity, everything happens as if the observers were always stationary, and that it was "others" who were moving in relation to them. Even in rotating frames of reference (the most difficult concept) the rotating object observes the universe as if it were the universe rotating around it. In relativism everything always happens like this.
 R.H.

So you have addressed my scenario quoted above with
a lot of general words.
But a stupid relativist like me doesn't understand
what your wise words have to say about my scenario,
so please give a _concrete_ analysis of my scenario.
The scenario is:
Terrence is inertial.
Stella passes Terrence with the speed 0.8c relative to Terrence.
At the instant when Stella is adjacent to Terrence they both set
their clocks to zero, and Stella starts her rocket engine so that
she accelerates at the constant acceleration c per year (≈ 0.97g)
towards Terrence.
Some time later, Stella will again pass Terrence at the speed 0.8c.
The only question I want answered is:
What do Stella's clock and Terrence's clock show
at the instant when Stella passes Terence the second time?
It's two invariant proper times, so they are "absolute".
-----------------------
I would also like you to break down the evolution, observer
by observer, segments by segments and explain correctly and with essential mathematical precision why Terrence and Stella ages as
you have calculated that they do.
Since you have explained this hundreds of times, it should be easy
for you to do it one more time with my specific scenario.
Or is it to boring?
--
Paul
https://paulba.no/