Re: Langevin's paradox again

Le 10/07/2024 à 20:56, "Paul.B.Andersen" a écrit :

Den 09.07.2024 15:47, skrev Richard Hachel:
Let's look at the following scenario:
 - Twin A and twin B are inertial and co-located.
- Twin B accelerates at the proper acceleration 2 c/year
   away from A for 1 light year [ly] in A's rest frame.
- Twin B  coasts (no engine) for 8 light years until he is 9 ly from A.
- Twin B accelerates at 2 c/year towards A. He will reach 10 ly and
   go back to 9 ly when he stops the engine.
- Twin B coasts from 9 ly to 1 ly-
- Twin B accelerates at 2 c/y until he is co-located with A.
  Note:
While B is coasting and inertial we have two inertial twins
moving at the constant speed 0.943 c relative to each other,

This value is calculated starting from Minkowsky's four-dimensional space-time which is only one of the possible understandings of Lorentz transformations and the relationships between space and time.
Mine is directly calculated with the new and direct equation Voi/c=[1+c²/2ax]^-(1/2)
And I find Vo=0.8944c and not Vo=0.943c. The values ​​given are always too high among relativists for instantaneous observable speeds.

Yet B ages 9.18 years while A ages 22.63 y.

That's not what I find.
Tr=11.155 years
To=23,544 years.
The fact that in my opinion there are two errors comes from the fact that, as I have always said, the instantaneous observable speeds are given too high, this makes an error for To; and the natural times of the accelerated objects are given a little too low, this gives an error for Tr.
R.H.