From: tjroberts137@sbcglobal.net   
      
   On 4/17/22 3:03 AM, Mike Fontenot wrote:   
   > On 4/16/22 12:57 AM, Tom Roberts wrote:   
   >> Bottom line: the POE applies ONLY in regions of spacetime that are   
   >> small enough that any curvature is negligible (compared to   
   >> measurement accuracies). For the case you have in mind, with   
   >> helper friends ("people") near a distant friend while the   
   >> accelerated observer ("AO") roams the universe, those people span   
   >> an enormous spatial region, over a very long time.   
   >   
   > The theory of special relativity places no limits AT ALL on the   
   > extent of spacetime.  THAT is the domain of my scenario with   
   > acceleration.   
      
   Sure. But you attempt to argue by "equivalence" to a situation in which   
   a uniform gravitational field is present -- that is NOT Special   
   Relativity, and that "equivalence" is NOT valid, as I explained earlier.   
      
   Specifically: in flat spacetime for helper friends with equal proper   
   accelerations, you claim that the pairwise distances [#] between helper   
   friends are constant, because they are constant in the uniform-gravity   
   spacetime you think is "equivalent". Your argument is invalid because   
   the physical situations aren't actually equivalent -- the region   
   involved is too large for the Principle of Equivalence to apply; for   
   your case in flat spacetime those pairwise distances [#] are not   
   constant, as one can explicitly calculate.   
      
       [#] Pairwise distances are measured in the instantaneously   
       co-moving inertial frame of the accelerating observer (AO).   
      
   [This is getting tedious and overly repetitive. Unless you come up with   
   something new, I won't continue.]   
      
   Tom Roberts   
      
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