From: mlfasf@comcast.net   
      
   On 4/11/22 2:00 AM, (I) Mike Fontenot wrote:   
   >   
   > If I am an accelerating observer, and if I OBSERVE a TV image of the   
   > distant person, that tells me what that distant person looked like a   
   > long time ago.  That's not meaningful to me, because I don't know how to   
   > determine how much she aged while the message was in transit.   
   >   
      
   I need to correct that last sentence.  Observing the TV image of the   
   distant person WOULD be meaningful to me.  ALL observations are   
   meaningful, almost by definition.  But what I was thinking when I made   
   that statement was that, that observation wouldn't help me determine her   
   current age "right now", because I don't know how to determine how much   
   she aged while the message was in transit.   
      
   > But if I'm mutually stationary wrt the array of clocks that I have   
   > previously described, which provides a "NOW" for me extending throughout   
   > space, that DOES give me a meaningful answer to the question of how old   
   > she currently is.  And by "meaningful", I mean that I REALLY believe   
   > that she is currently that age.  The only way I can be wrong about her   
   > current age is if my equation for the rate ratio of the two clocks is   
   > wrong.  I'm confident that it is correct.  I think it IS experimentally   
   > testable.   
   >   
      
   The ability to construct an array of clocks (mutually stationary with   
   the accelerating observer) establishes a "NOW" moment for him, and   
   answers his question about her current age in a way that is fully   
   meaningful.  But that hinges on my equations for the rate ratio R(t) and   
   the ace change AC(t) being correct.   
      
   The rate ratio equation is   
      
        R(t)  =  [ 1 +-  L  A  sech^2 (A t) ],   
      
   where L is the constant distance between him and the given HF, and   
   sech() is the hyperbolic secant (which is the reciprocal of cosh(), the   
   hyperbolic cosine).  The "^2" after the sech indicates the square of the   
   sech.  The "+-" in the above equation means that the second term is   
   ADDED to 1 for the HF's who are LEADING the accelerating observer, and   
   the second term is SUBTRACTED from 1 for the HF's who are TRAILING the   
   accelerating observer.   
      
   The limit of R(t), as "t" goes to zero, is 1 + L A.  The limit of R(t),   
   as "t" goes to infinity, is 1.0  So R(t) starts out at some positive   
   number greater than 1, and then approaches 1.0 as t goes to infinity. So   
   eventually, all the clocks essentially tic at the same rate, but early   
   in the acceleration, the ratio of the tic rates varies significantly   
   with time.   
      
   The current reading of the HF's clock (the "Age Change" or "AC"), when   
   the AO's clock reads "tau", is   
      
      AC(tau)  =  integral, from zero to tau, of { R(t) dt }   
      
                     =  tau  +  L tanh( A tau ).   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)