From: tjroberts137@sbcglobal.net   
      
   On 5/2/22 3:37 AM, Luigi Fortunati wrote:   
   > Newton says that the reference of the center of the Earth is inertial   
   > and those of the 2 free-falling elevators from the north and south   
   > poles are accelerated.   
   >   
   > Instead, Einstein argues that all three motions are inertial.   
      
   No. GR says that the three are LOCALLY inertial. You cannot omit   
   "locally", and that is the crux of your confusion.   
      
   > If one of the two is right, the other is wrong: it is obvious.   
      
   Not true, because they are really saying different things, in different   
   contexts. Both are true within their respective contexts. But your   
   imprecise and ambiguous language hides that.   
      
   > How can we determine who is right and who is wrong?   
      
   By making precise, unambiguous statements. Binary logic applied to   
   ambiguous statements is useless, as is logic applied to statements   
   belonging to different contexts.   
      
   Statements containing ambiguous words like "acceleration" can be   
   ambiguous: neither true nor false. Correct statements must avoid all   
   such words, and be precise enough to be adjudged true.   
      
   "Proper acceleration" and "coordinate acceleration" are precise enough   
   here, while unqualified "acceleration" is not. Newtonian mechanics does   
   not have the concept of proper acceleration; GR introduced it to avoid   
   the ambiguity that is confusing you.   
      
   > In my opinion, a good way to judge is the following. [... useless   
   > method using speeds]   
      
   The correct way is to distinguish proper acceleration from coordinate   
   acceleration (which you failed to do).   
      
   The proper acceleration of a (pointlike) object is its acceleration   
   relative to its instantaneously co-moving locally inertial frame; it is   
   invariant (independent of coordinates -- all observers agree on its   
   value), while coordinate accelerations are not invariant. This is true   
   independent of whether the object is in freefall (zero proper   
   acceleration), or not (nonzero proper acceleration).   
      
   In the first paragraph quoted above, objects at rest in the center of   
   the earth and at rest in each elevator have zero proper accelerations.   
   When one uses the coordinates of their locally-inertial frame, each has   
   zero coordinate acceleration. When one uses the coordinates of one of   
   those frames to describe an object at rest in a different one, the   
   coordinate acceleration is nonzero.   
      
       (In general, the coordinates of a locally inertial frame   
        might not be valid far away -- they are LOCAL.)   
      
   Bottom line: complicated and subtle subjects like modern physics require   
   precision in thought and word. You need to make more precise statements   
   that are not ambiguous.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)