From: mlfasf@comcast.net   
      
   Tom, you've badly misunderstood what I'm doing.   
      
   Start with the gravitational scenario, with no acceleration and no   
   motion at all.  Imagine that there is a high-rise building, with many   
   floors.  A clock and the "AO" (whose "viewpoint" we are seeking) is   
   located on the first floor.   A clock and an attending HF is on each of   
   the higher floors. The distance between the AO and each of the HF's is   
   constant.  They are all motionless and unaccelerated.   
      
   There is initially no gravitational field. And initially all of the   
   clocks are synchronized and ticking at the same rate.  So initially, the   
   rate ratio R, for each HF's clock, is just equal to 1.0.   
      
   But at some instant (say, t = 0), there suddenly appears a constant and   
   uniform gravitational field, of strength "g", directed downwards, and   
   acting over the entire length of the building.  Each person suddenly   
   feels exactly the same force per unit mass, trying to pull them   
   downwards against the floor.  (But they don't move, because they were   
   already tethered in that position).  They could be constantly standing   
   on a bathroom scale, displaying their weight.   
      
   The gravitational time dilation equation says that, according to the AO,   
   each HF's clock suddenly starts ticking faster than the AO's clock, by   
   the rate ratio   
      
      R(t)  =  [ 1 +  L  g  sech^2 (g t) ],   
      
   where "L" is the distance between the AO and that particular HF.  And,   
   according to the AO, the change in age (AC) of each HF (relative to his   
   age when the field suddenly appeared), is   
      
      AC(tau)  =  integral, from zero to tau, of { R(t) dt }   
      
                      =  tau  +  L tanh( g tau ).   
      
   So that's the outcome of the gravitational scenario.   
      
   We now use the equivalence principle (EP) to convert the above   
   gravitational scenario to the EQUIVALENT scenario with the constant and   
   uniform GRAVITATIONAL FIELD acting on the AO and each HF replaced by a   
   constant and uniform ACCELERATION acting on the AO and each HF.   
   Everything else stays exactly the same, except the gravitational field   
   is replaced by an acceleration.   
      
   Just as in the gravitational scenario, each person suddenly feels   
   exactly the same force per unit mass, trying to pull them against the   
   floor.  (But they don't move, because they were already tethered in that   
   position).  They could be constantly standing on a bathroom scale,   
   displaying their weight.  That serves as an accelerometer.   
      
   The equivalence principle says that EVERYTHING stays the same as in the   
   gravitational scenario, except that the parameter "g" just gets replaced   
   by the parameter "A" in the equations, with each having the same   
   numerical value.  So we still have the same equation for R and for AC as   
   we had above, with "g" replaced by "A", with equal numerical values.   
   The fact that "L" and "g" don't vary with time in the gravitational   
   scenario means that "L" and "A" don't vary with time in the acceleration   
   scenario either.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)