Re: Langevin's paradox again

Le 16/07/2024 à 20:28, "Paul.B.Andersen" a écrit :

 Den 16.07.2024 15:25, skrev Richard Hachel:

So your theory predicts that Stella and Terrence ages equally.

 

 According to SR Stella's proper time is τₛ ≈ 2.19722 years.
 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.

This is what I keep repeating to relativistic physicists, who can read what I write on usenet (but I don't think they are interested).
In this very specific case, we come across an equality of improper times, which everyone admits (except the cranks who understand nothing about it).
But we also come across an equality of proper times, because there is a small difference between special relativity, and special relativity haxel in a few points of the theory.
I told you in a recent post, the way you do it is mathematically very correct. You have made a very correct integration (where I circled it with a big red circle), but there is a trap there.
The trap is here:
<http://news2.nemoweb.net/jntp?xLBGlqr9FmVi45Mlcw6nJbdFqqM@jntp/Data.Media:1>
If you look closely, you have the red line which marks the improper time To in the Galilean movement. Tr (tau) is found
on the vertical axis.
In accelerated motion you still have the red line which represents To relative to Tr (tau) which is still on the horizontal axis. We then see time passing, and the relationship between To and Tr over time.
The confusion, and the trap in this very specific case where the departure is stopped, is to think that the blue line is the improper time To.
But no, the imporpre time To always IS, moment after moment To. The red line grows constantly as a function of Tr and Et (distance traveled = universal anisochrony). The blue line does not represent anything special, and will give a To too large, that is to say, by simple comparison a Tr (tau) too small.
This is what I keep saying when saying where the problem is (as in Langevin's traveler in apparent speeds) but no one seems to understand.
Ditto for the deformations of the cubes in geometry from the TL which are correct, but misinterpreted. I asked to show me for example where M' was in R', no one can do it, even though I gave the matching equation (and its very simple reciprocal) point by point.
This is all very tiring.
R.H. <http://news2.nemoweb.net/?DataID=xLBGlqr9FmVi45Mlcw6nJbdFqqM@jntp>