From: fortunati.luigi@gmail.com   
      
   Roland Franzius alle ore 08:54:12 del 03/08/2017 ha scritto:   
   >> 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.   
      
   Ok.   
      
   But I ask for a very simple thing to which you did not answer: what time   
   marks the twin traveler watch when a terrestrial brother emits his   
   penultimate ray?   
      
   --   
   Luigi Fortunati   
      
   Credere e' piu' facile che pensare   
   Believing is easier than thinking   
      
   --- SoupGate-Win32 v1.05   
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