From: fortunati.luigi@gmail.com   
      
   Richard Livingston giovedì 28/04/2022 alle ore 09:05:51 ha scritto:   
   > You need to be more precise about what frame you are talking about.   
   > The center of gravity of the earth is in free fall (around the sun)...   
      
   The center of gravity of the elevator is also in free fall around the   
   sun.   
      
   And both (Earth and elevator) are in free fall also with respect to   
   Jupiter,   
   Mars and all the other planets.   
      
   We want to talk only about the Earth and the elevator without third   
   party   
   inconveniences which, moreover, act on both and not on just one?   
      
   And therefore, in ALL references the free-fall elevator does not move   
   at random   
    but accelerates exactly in the direction that goes towards the center   
   of the Earth.   
      
   In ALL references the free-falling Earth does not move haphazardly but   
   accelerates   
   exactly in the direction that goes towards the center of the elevator.   
      
   They are two opposite free falls where the center of gravity of each   
   mass goes exactly towards the center of gravity of the other mass.   
      
   The surface of the Earth has nothing to do with it just as the surface   
   of the elevator has nothing to do with it.   
      
   The interaction is between two masses (whose centers of gravity tend   
   to approach each other) and not between two surfaces.   
      
   [[Mod. note -- The fundamental difference between the elevator and   
   the Earth is that the Earth is a self-gravitating system -- different   
   parts of the Earth have a non-trivial gravitational interaction with   
   each other.  That means that (a) an inertial reference frame (IRF)   
   on one side of the Earth (right next to the elevator), (b) an IRF at   
   the center of mass of the Earth, and (c) an IRF on the other side of   
   the Earth, are three DISTINCT IRFs.   
      
   As measured with respect to IRF (a), the free-falling elevator is   
   unaccelerated (stationary or moving uniformly).   
      
   If we were to try to extend the Earth-center-of-mass IRF (b) to cover   
   the entire Earth and its immediate neighbourhood, we'd find that with   
   respect to the extended IRF (b), IRF (a) and the free-falling elevator   
   are both accelerating at 1 g in the (vector) direction from the elevator   
   towards the center of the Earth, while IRF (c) is accelerating at 1 g   
   in the (vector) direction from the center of the Earth towards the   
   elevator.   
      
   As Richard Livingston said in a previous article in this thread,   
   > Each of these inertial frames will see the other as accelerating.   
   > That doesn't mean either of these frame are not inertial.  The property   
   > of being an inertial frame is a local thing.   
      
   So, one reasonable answer to the question you asked in a previous posting   
   in this thread,   
   > And why is the Earth in free fall (relative to the elevator) NOT an   
   > inertial reference frame?   
   is that the center of mass of the Earth (and its corresponding IRF (b))   
   *is* in free-fall with respect to the elevator.  But no part of the Earth's   
   surface is in free-fall (it's all supported in a non-free-fall state by   
   the solid body of the Earth).   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)