From: hees@itp.uni-frankfurt.de   
      
   On 11/06/2024 09:05, Luigi Fortunati wrote:   
   > Hendrik van Hees il 10/06/2024 14:10:37 ha scritto:   
   >> Or to put it simpler. In a local inertial reference frame, realized by a   
   point-like non-rotating body in free fall, you observe (e.g., by using   
   pointlike test particles) only the "true gravitational forces", i.e., the   
   tidal forces.   
   >>   
   >> If you sit on the surface of a planet, you are not in free fall, because   
   there are (electromagnetic) forces keeping you there.   
   >>   
   >> That's why the accelerometer of your smart phone at rest on Earth shows an   
   acceleration of 9.81 m/s^2, because it measures accelerations relative to a   
   local inertial frame of reference! See, e.g.,   
   >   
   > Your reasoning is based on two preconceptions.   
   These are preconceptions well tested with high precision for centuries.   
   Physics is an empirical science, and theories are built based on precise   
   quantitative observations of nature.   
   >   
   > 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.   
   According to GR there are NO GLOBAL inertial frames as there are in   
   Newtonian mechanics and special-relativistic physics. Pointlike test   
   particles move on geodesics of spacetime, determined by the   
   energy-momentum-stress distributions due to the presence of other   
   bodies, if there are no other forces than gravity, i.e., they are not   
   accelerated. Geodesics here refer of course to spacetime not to   
   trajectories in "position space" of some arbitrary observer. E.g., the   
   motion of the planets around the Sun are such geodesics in spacetime for   
   an observer resting far away from the Sun (whose spacetime is locally   
   approximately described by special-relativistic, flat Minkowski   
   spacetime) the spatial trajectories are of course very close to Kepler   
   ellipses.   
   >   
   > 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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