From: fortunati.luigi@gmail.com   
      
   Tom Roberts alle ore 08:47:53 del 04/08/2017 ha scritto:   
   > Your "quiet" is a HIGHLY unusual phasing. I assume that when you say "quiet"   
   > you  mean that S is at rest in the same inertial frame as earth. Compared to   
   > the  traveling twin, the earth and S are accurately at rest in an inertial   
   > frame.  When you say "zero time" for both earth and S, I assume that the   
   > earth and S  clocks are synchronized in their inertial frame (i.e. they both   
   > display that  frame's time coordinate, for which t=0 at the traveling twin's   
   > departure).   
   >   
   > The general formula for elapsed proper time of an object moving relative to   
   > an  inertial frame is:   
   > 	T_obj = \integral dt / gamma(v)   
   > where the integral is taken over the path of the moving object, v is its   
   > speed  relative to the frame (as a function of t), t is the time coordinate   
   > of the  frame, and gamma(v)=1/sqrt(1-v^2/c^2).   
   >   
   > So in the above formula, T=5 years, and gamma(v)=8. Since gamma(v) is   
   > constant  the integral is trivial, with result   
   > 	t_elapsed = 5 years * 8 = 40 years.   
   >   
   > t_elapsed is the elapsed time in the inertial frame, which is also the value   
   > of  the clock at S.   
   >   
   > Tom Roberts   
      
     But even the ship's reference is inertial because after the initial   
   acceleration it travels for 5 years with out-of-engine engines.   
      
   [[Mod. note -- The ship's reference frame is inertial during its   
   outbound journey.  Then (after a brief non-inertial period during the   
   turnaround) the ship's reference fame is a DIFFERENT inertial frame   
   during its return journey.   
   -- jt]]   
      
   Luigi.   
      
   --   
   Luigi Fortunati   
      
   Credere e' piu' facile che pensare   
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