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Date: Wed, 24 Apr 24 12:44:13 +0000
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From: Richard Hachel <r.hachel@wanadou.fr>
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Le 24/04/2024 à 03:08, Richard Hachel   a écrit :
> We set To²=Tr²+Et²
>  
> It’s great, life is above all very easy.
>  
> We take Stella, we calculate her proper time (Tr=4.776 years), her improper time 
> (validated by Terrence, To=12.915 years), her constant speed Vo=0.929c, her 
> distance traveled to Tau Ceti (12al).
>  
> We take Bella, in an accelerated reference frame at 1.052 ly/year², we 
> calculate its proper time, its improper time, and the distance traveled.
>  
> In RRH (Hachel's special relativity), if we place the proper time in y, the 
> distance traveled in x,
> and the improper tense on the LENGTH of the hypotenuse, all this still works 
> very well.
>  
>   Even in accelerated frames of reference as long as you pay close attention to 
> what you do.
>  
>   Furthermore, what is the slope of this hypotenuse for Stella? Unlike the speed 
> Vr.
>  
>   But what can we say for Bella, who will trace a curve since her movement is 
> accelerated?
>  
>   What becomes of To for her?
>  
> It is the length of the line which links, at each moment, the origin O
>   and the point we find ourselves on the curve. That's it, To. Bad weather.
>  
>   And what happens to Vr at each moment? It is the inverse of the slope of the 
> tangent at the given point.
>  
>   This may seem very strange.
>  
>   But it is nevertheless mathematical.
>  
>   The most complex thing to understand (it took me decades to find the tilt) is 
> that in the case
> of the accelerated twin, the line which links the origin to the chosen point of 
> the curve IS To, and that this line is obviously NOT the curve itself.
>  
>   And that on the other hand the real instantaneous speed (Vr) is given by the 
> inverse of the slope of the tangent to the curve, speed which must then be 
> transcribed into Vo. Vo=Vr/sqrt(1+Vr²/c²)
>  
>   Everything then enters into a sumptuous logic and a great conceptual beauty.
>  
>   We then obtain the following two equations, which physicists nevertheless 
> deny, because they do not understand the beauty of reasoning, and persist in 
> posing totally false equations.
>  
>   For the instantaneous speed of the accelerated mobile as a function of x and 
> a:
>   Voi/c=[1+c²/2ax]^-(1/2)
>  
>   For the improper time of the particle or the mobile:
>   To=(x/c).sqrt(1+2c²/ax) Validated by physicists that.
>  
>   For the proper time Tr=sqrt(2x/a) quite simply.
>  
>   There, a terrible incomprehension can shake the biggest minds in physics, 
> because they will ask:
> Voi=Δx/ΔTo
>  
>   However, as obvious as it may seem, it is completely false.
>  
>   Something that would drive the greatest theoreticians crazy if they're not 
> careful.
>  
>   Because Voi, it is given by the inverse of the SLOPE of the tangent to the 
> curve at the given point,
>   (and Voi transcribed from Vri), and not by the slope of the line which joins 
> the origin to this point, the only use of which is the length which corresponds 
> for each point to To.
>  
>   Breathe, breathe...
>  
>   Grab three cups of coffee, edit this post, and think for an hour or two about 
> what I'm trying to explain to you in a few words.
>  
>   R.H.

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R.H.