From: hees@itp.uni-frankfurt.de   
      
   The misconception is on your side, not Einstein's ;-).   
      
   An inertial frame of reference is operationally defined by Newton's Lex   
   II: A body moves uniformly (or stays at rest) if it does not interact   
   with anything.   
      
   The mathematical version of the equivalence principle in GR is that   
   spacetime is described by a torsion-free pseudo-Riemannian (Lorentzian)   
   manifold. An inertial frame can only be local, i.e., you can choose at   
   any given spacetime point a Galilean local reference frame. Physically   
   such a frame is realized by a point-like body in free fall, i.e., by a   
   body on which only gravitational forces are acting and (non-rotating,   
   i.e., Fermi-Walker transported) tetrads along its world line.   
      
   True gravitational fields always show up in terms of tidal forces, and   
   any extended test body is thus not force-free. To which extent you can   
   neglect these forces depends on the extension of this test body. It's   
   only "force-free" as long as its extensions is smaller than the   
   curvature radius of space time at the reference point of your   
   free-falling non-rotating reference frame.   
      
   On 13/06/2024 10:29, Luigi Fortunati wrote:   
   > Hendrik van Hees il 11/06/2024 10:46:14 ha scritto:   
   >>> The first is that the accelerometer measures accelerations (and instead   
   >>> it only measures forces) and the second is that free fall is an inertial   
   >>> reference system despite its very evident mutual acceleration towards   
   >>> the other body (also) in free fall.   
   >> I don't know, what's evident in your misconception. By definition bodies   
   >> which move without any interactions except the gravitational interaction   
   >> are by definition in free fall, and according to the equivalence   
   >> principle such bodies define a LOCAL (!!!!) inertial reference frame.   
   >   
   > The inertial reference frame is one where no forces act.   
   >   
   > In free fall, tidal forces act and, therefore, you and Einstein are   
   > wrong when you say that free fall is an inertial reference (whether   
   > local or non-local).   
   >   
   > Luigi Fortunati   
      
   --   
   Hendrik van Hees   
   Goethe University (Institute for Theoretical Physics)   
   D-60438 Frankfurt am Main   
   http://itp.uni-frankfurt.de/~hees/   
      
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