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Subject: Re: Langevin's paradox again
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Date: Thu, 11 Jul 24 00:02:53 +0000
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From: Richard Hachel <r.hachel@tiscali.fr>
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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.