From: relativity@paulba.no   
      
   Den 18.10.2025 15:37, skrev Richard Hachel:   
   > Le 18/10/2025 à 11:37, "Paul B. Andersen" a écrit :   
   >>   
   >> see: 2.4 Concrete example   
   >> -------------------------   
   >> Twin A stays inertial   
   >> Twin B travel 10 ly and back with constant acceleration 1c/year   
   >> Twin A ages 23.664 years   
   >> Twin B ages  9.912 years   
   >>   
   >> This follows inevitably from the metric,   
   >> so it is a _fact_ that this is what SR predicts.   
   >>   
   >> There is nothing to "explain".   
   >>   
   >> Your opinion is irrelevant.   
      
   You snipped this:   
      
   The Special Theory of Relativity (SR) is precisely defined   
   by the metric:   
         (c⋅dτ)² = (c⋅dt)² − dx² − dy² − dz²   
      
   What follows from this metric is what SR predicts.   
      
   See:   
   https://paulba.no/pdf/TwinsByMetric.pdf   
      
   Read it, and you will see that it is a fact that   
   in the scenario described in 2.4 Concrete example,   
   The Special Theory of Relativity predicts that   
   twin A ages 23.664 years while twin B ages  9.912 years   
      
   >   
   > To fully understand the theory of relativity, we must begin with the   
   > Poincaré-Lorentz transformations and visualize as precisely as possible   
   > what they imply in our minds.   
      
   The Lorentz transformation follows from the metric, and give   
   the same answer to my scenario above, namely that   
   twin A ages 23.664 years while twin B ages  9.912 years.   
      
   It is not possible to make SR predict anything else than the above.   
      
   It is nothing to "research" or "understand", the prediction above   
   follows from the metric (and thus from the Lorentz transform).   
   It is plain and simple mathematics.   
      
   Since you think SR predicts otherwise than it factually does,   
   you are wrong.   
      
      
   > To research these transformations, there are two simple methods: the one   
   > used by Henri Poincaré and Richard Hachel (known as the French method)   
   > and the one used by Albert Einstein and Hermann Minkowski (known as the   
   > Mittleuropa method).   
   > The first involves observing a train car moving from left to right; the   
   > second involves imagining oneself in the train car and observing the   
   > landscape moving from right to left.   
   > The transformations are then said to be positive or negative. In   
   > positive form (Poincaré, Hachel), we have:   
   > x'=(x+v.To)/sqrt(1-Vo²/c²)   
   > y'=y   
   > z'=z'   
   > t'=(t+x.Vo/c²)/sqrt(1-Vo²/c²)   
   > In negative form, we have:   
   > x'=(x-v.To)/sqrt(1-Vo²/c²)   
   > y'=y   
   > z'=z'   
   > t'=(t-x.Vo/c²)/sqrt(1-Vo²/c²)   
   > It's just the same thing, said differently.   
   >   
   > But from this point on, we disagree.   
   >   
   > Einstein's concepts then lead to equations and results that are   
   > different from mine.   
   >   
   > For example, here, in the quantification of times measured during   
   > accelerations, where I give a slightly longer time each time, explaining   
   > that we should not measure the length of the blue curve on the Cartesian   
   > reference frame, but the red segment in continuous rotation during   
   > acceleration (the speed being continuously increasing).   
      
   You should read:   
   https://paulba.no/pdf/TwinsByMetric.pdf   
   The math is correct.   
      
   Your math is simply wrong.   
   You are ignorant of elementary calculus.   
      
   --   
   Paul   
      
   https://paulba.no/   
      
   --- SoupGate-Win32 v1.05   
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