From: mlfasf@comcast.net   
      
   On 3/15/22 7:55 AM, Richard Livingston wrote:   
   >   
   > Keep in mind that when the moving twin stops, both twins will agree   
   > on how far apart they are.  During the deceleration the moving twin   
   > will observe the apparent expansion of the universe along the axis   
   > of travel, and what while moving appeared to be 3.464 light years   
   > will expand to 6.928 light years.   
   >   
      
   That's true.  But of the two effects (spatial and temporal), I think   
   what special relativity has to say about time is more interesting than   
   what it says about space (and distance).   
      
   The best example of that is the case of "negative ageing": if the   
   distant traveling twin (he) suddenly accelerates in the direction AWAY   
   from the home twin (her), he will conclude that she suddenly gets   
   YOUNGER during his velocity change.  That result drives a lot of people   
   (including many physicists) crazy!  Some physicists maintain that the   
   conclusions of the traveler during those occurrences must be ruled   
   inadmissible.  But the negative ageing can't logically be ignored, or   
   disallowed, for the following reason:  the traveler can do two   
   back-to-back instantaneous velocity reversals, which, taken together,   
   just cancel out.  So we can't allow one of those velocity reversals, but   
   disallow the other.   
      
   For example, take the case where he is originally moving away from her   
   at speed   
      
      v  =  V1  =  +V,   
      
   where V is some positive number.  And let L be their distance apart   
   (according to her) at some instant.  Then, at that instant, he suddenly   
   changes his velocity to   
      
      v  =  V2  =  -V.   
      
   So   
      
      delta_v_1  =  V2  -  V1  =  (-V)  -  V  =  - 2 * V.   
      
   And   
      
   delta_age_1 =  -L  *  delta_v_1  =  -L  *  (-2 * V)  =  2 * L * V.   
      
   So he concludes that her age has instantaneously increased by (2 * L * V).   
      
   But suppose he IMMEDIATELY decides to reverse course again.  He will   
   then conclude that her age has instantaneously DECREASED by (2 * L * V).   
     I.e.,   
      
      delta_v_2  =  V  -  (-V)  =  V + V  =  2 * V.   
      
   and   
      
   delta_age_2 =  -L  *  delta_v_2  =  -L  *  (2 * V)  =  -2 * L * V.   
      
   So he concludes that her age has instantaneously decreased by (2 * L * V).   
      
   So that gets her age (according to him) right back to where it was   
   before he did any accelerating ... everything is as if he had done NO   
   accelerating at all.  But that means that we CANNOT say that   
   instantaneous age INCREASES are OK, but that instantaneous age DECREASES   
   are NOT OK.  You can't allow one but disallow the other.   
      
      
   And Richard Livingston continues:   
      
   > Something to keep in mind is that neither twin can see the other at   
   > what each considers "now".  They only see the other on their own   
   > past light cone.  So while the moving twin is stopping, he will NOT   
   > see his twin back on earth suddenly aging.  This is because what   
   > he sees is not the instantaneous state of the earth, but an image   
   > conveyed by light.  Instead he will see her as she was about 6.928   
   > years earlier.  Thus what he sees is a much younger twin, only   
   > about a year older than when he left earth.  It is on the trip back   
   > to earth that he sees her age rapidly as  he passes the light   
   > traveling outbound from earth.   
   >   
      
   That's all true.  But I am not interested in what TV images he receives   
   from her ... those just tell him what she looked like in the past, and   
   how old she was in the past.  Instead, I am interested in what he   
   DEDUCES about her CURRENT age at any given instant in his life, using   
   the laws of special relativity.  I.e., I'm interested in his "NOW"   
   instant ... what does he say her age is "RIGHT NOW", at some instant in   
   his life.  I'm purely interested in what he says about "simultaneity at   
   a distance".   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)