From: tjroberts137@sbcglobal.net   
      
   On 4/25/22 2:41 AM, Mike Fontenot wrote:   
   > On 4/21/22 12:21 AM, Mike Fontenot wrote:   
   >> On 4/20/22 11:57 AM, Tom Roberts wrote:   
   >>> But a calculation shows that in SR, helper friends (HFs) with   
   >>> proper accelerations equal to that of the accelerated observer   
   >>> (AO), do NOT remain at constant proper distance from the AO,   
   >>> contrary to your claim.   
   >   
   > In Tom Roberts' scenario (which is the "Bell Paradox" scenario), the   
   > perpetually-inertial observers correctly conclude that, according to   
   > their inertial frame, the accelerating people are all accelerating at   
   > the same constant rate (and therefore that their separations are all   
   > equal and constant).   
      
   You need to read more carefully. In the paragraph you quoted above, I   
   specifically said "proper distance" -- and earlier in that post I   
   clarified that this means the distance measured in the AO's   
   instantaneously co-moving inertial frame (ICIF). That is NOT "according   
   to their inertial frame", it is according to the AO's ICIF (which   
   obviously changes over time as the AO is accelerating).   
      
   > The accelerating people do NOT agree with them.   
      
   You claim the accelerating people measure proper distance, so they MUST   
   agree with ANYBODY who also measures (or calculates) proper distance.   
   After all, the (pairwise) proper distances are each unique and invariant   
   (at any given point along the AO's worldline).   
      
   > The perpetually-inertial observers are certainly entitled to set up   
   > that scenario, but that is a scenario that I have NO interest in at   
   > all.   
      
   And it is NOT what I was discussing. You misread what I wrote.   
      
   > The scenario that I am interested in, is the scenario where it is   
   > the accelerated people who correctly conclude that their   
   > accelerations are all equal, and that their separations are all   
   > constant.   
      
   You may be "interested" in such a scenario, but it is inconsistent with   
   relativity -- equal (proper) accelerations do NOT yield Born rigid   
   motion (in which all pairwise proper distances remain constant).   
      
   There are two choices:   
        A) all have equal proper accelerations, in which case their   
           pairwise proper distances are changing.   
   or:   
        B) All pairwise proper distances are constant, in which case   
           "lower" people have larger proper accelerations than   
           "higher" people (here "lower" people are behind "higher"   
           people along the direction of acceleration).   
      
   This is directly related to the Bell spaceship paradox. The fact that   
   you don't realize that is a major part of your misunderstanding.   
      
   > In that scenario, perpetually-inertial observers do NOT agree with   
   > them.   
      
   When the perpetually-inertial people make measurements and compute the   
   proper distances, they MUST agree with the accelerated people (who do   
   the same). Because such (pairwise) proper distances are each unique and   
   invariant (at any given point along the AO's worldline).   
      
   > [... further discussion based on the above error]   
      
   I give up. You keep repeating the same errors without reading what I   
   write, so there's no point in continuing. Goodbye. (I'm surprised the   
   moderators have let it go this long.)   
      
   Tom Roberts   
      
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