From: roland.franzius@uos.de   
      
   Am 29.07.2017 um 14:10 schrieb LuigiFortunati:   
   > The traveling twin starts and goes back to Earth where he finds his   
   > 80-year-old brother aged as he is only 10 years old.   
   >   
   > The wristwatch on the twin traveler's wrist marks (of course) the   
   > 10-year time.   
   >   
   > The earth twin during the years of the trip has been flashing every 10   
   > years (his).   
   >   
   > The last lightning is emitted at the time of the return of the ship,   
   > when the Earth clock marks the 80-year time and the wrist watch on   
   > the twin traveler marks 10 years.   
   >   
   > Calculation (perhaps) impossible is this: at the ejection of the   
   > penultimate lightning (when the Earth clock marked 70 years) what time   
   > was the watch on the wrist of the traveling twin?   
   >   
      
   There is a Lorentz frame (t,x) of the sun at rest. The orbiting earth as   
   a rotating light house at constant angular speed emits a flash every   
   year. This flash is represented by a series of immediate time-forward   
   cones (t-k)^2=x^2+y^2+z^2, t>k, k=0,1,2.. and so on covering the inner   
   of the first flasch cone over all of space-time.   
      
   Any traveller starting at (t,x,y,z)=0 and returning to that straight   
   world line at a point later (k,0,0,0) on a continous path intersects   
   each forward light cone once.   
      
   This is the kernel of causality: In a flat universe without timelike   
   closed world lines one cannot miss a light flash signal and one cannot   
   catch a signal twice as long as on moves on timelike world lines.   
      
   The inverse is also true: The traveller moving outward on a straight   
   world line flashes a signal each year and each signal reaches earth   
   before his arrival back home. The the same with the inward travel.   
      
   The relative clock rates are given by the (hyperbolic functions of the)   
   angles, by which the world lines of earth and traveller intersect the   
   flash cone surfaces.   
      
   As Minkowski told us, you never may grasp and imagine the simple laws of   
   the special relativistic kinematics, if you dont switch from meter   
   sticks, 3d-curves and clocks to the picture of world lines in   
   fourdimensional space-time with a vector norm representing the lenght of   
   a time intervall of a tangent vector.   
      
   This is very similar to the complexity considering curves as y=f(x) like   
   Kepler did for planets instead of the trivial vector representation in a   
   plane (x(t),y(t)) as has been considered by Newton.   
      
   --   
      
   Roland Franzius   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)