Re: Langevin's paradox again

Le 16/07/2024 à 20:33, Paul.B.Andersen a écrit :

 Den 16.07.2024 15:25, skrev Richard Hachel:
...

 > Where they will no longer be is when it is necessary to calculate Stella's own time (now Bella).
 >
 > The fact that Bella accelerates from rest in Stella's frame of reference allows us to say:
 > “If the paths are equal, and the observable times equal, then the proper times will be equal”

...

So "the travelling twin" ages less than the "stay at home twin".
 The ageing of the twins in the "twin paradox" is experimentally verified to be as predicted by SR.
 Your theory is falsified.

I tried, in vain, to explain to Richard how his claim : “If the paths
are equal, and the observable times equal, then the proper times will be
equal” is asinine :
1. Given two distincts trajectories, "equal paths" is a frame dependent
    property it CANNOT implies something which is NOT frame-dependant
    (equality of proper times)
2. "observable times equal" expresses nothing more than the equality of
    difference of time between two events with... itself
Out of Galilean Relativity, where proper times are always equal (and
then the whole claim is void), this is logically impossible.
And also I pointed out with full details how his claims implies, as
you wrote, that this leads to equal times for any twin scenario.
Guess how he reacted ? :-)