From: mlfasf@comcast.net   
      
   On 4/2/18 3:21 PM, Michael Cole wrote:   
   > Well, personally I see no problem in saying that two comoving observers   
   > see each other's clock as running slower.   
      
   True for co-moving INERTIAL observers.   
      
   >The usual twin paradox is a   
   > different situation.  The two clocks are reunited and hence one (or   
   > both) clocks have to turn around and undergo acceleration.  Actually,   
   > though, I think it is misleading to layman to talk about acceleration.   
   > One can simply idealize the acceleration as instantaneous.   
      
   Either way, it's acceleration.  In the instantaneous velocity-change   
   case, the acceleration is a Dirac delta function ... zero everywhere   
   except at the single instant of the turnaround, and infinite there, but   
   such that "the area under the curve" (i.e., the integral of the delta   
   function) is finite.   
      
   >Suppose I stay at home while my twin hops   
   > into her rocket ship and does a round trip to Alpha Centauri and back at   
   > relativistic speed.  Then there are THREE inertial frames involved.   
      
   There are only two frames of importance.  Each twin is entitled to their   
   own single frame for the entire scenario, in which they are perpetually   
   located at the spatial origin.  The home twin's frame is an inertial   
   frame.  The traveler's frame is NOT an inertial frame, because he   
   accelerates at least once during the trip: at the turnaround.  There can   
   be portions of the traveler's life (when he is not accelerating) for   
   which his frame is identical with a co-moving inertial frame.  But it is   
   a mistake to say that the traveler does not have a single frame ... it   
   is a perfectly good frame that is not perpetually inertial.   
      
   According to the traveler's single non-inertial frame, the home twin   
   ages by a large amount during the turnaround.  THAT is the resolution of   
   the twin "paradox":  THAT is how the traveler (he) can understand how   
   the home twin (she) can be the older one when they are reunited, even   
   though she ages more slowly than he does during the portions of his trip   
   when he is not accelerating.  (And for the simple case of an   
   instantaneous turnaround, the home twin INSTANTANEOUSLY ages by a large   
   amount during the turnaround).   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)