From: tjroberts137@sbcglobal.net   
      
   On 4/21/22 2:24 AM, Luigi Fortunati wrote:   
   > Richard Livingston marted=EC 19/04/2022 alle ore 15:28:38 ha   
   > scritto:   
   >> With respect to this inertial frame it is the earth that is   
   >> accelerating upward.   
   >   
   > This is incomprehensible.   
      
   Not really. But one must be thinking in terms of General Relativity   
   (GR), not Newtonian mechanics (NM).   
      
   > Acceleration occurs in the presence of a force (F=ma).   
      
   But there quite clearly is a force: for an object sitting at rest on the   
   surface of the earth, there is an upward force on it, which we call   
   "weight".   
      
   > This force justifies the downward acceleration of the elevator but   
   > could never justify the acceleration of the entire earth mass   
   > upward!   
      
   You need more precision in your thoughts and words. "Acceleration" by   
   itself is insufficiently defined -- use either "proper acceleration" or   
   specify a (locally) inertial frame relative to which it is measured.   
   "The entire earth mass" is likewise ill defined -- consider just a small   
   portion of its surface. A small object at rest on earth's surface has a   
   proper acceleration of 9.8 m/s^2 (directed upward); in GR this is in   
   response to the (upward) force exerted on the object by the earth's surface.   
      
       [In physics, "proper" means "relative to the instantaneously   
        co-moving inertial frame of the object in question".]   
      
   In NM, near the surface of the earth, we generally use coordinates in   
   which that surface is at rest. This hides the underlying issue -- these   
   coordinates hide the force that the surface exerts on such objects. NM   
   then adds a gravitational force to cancel the force the surface exerts,   
   yielding net zero force -- this is CLEARLY WRONG as we humans can feel   
   the force from the surface on our bodies, and it is clearly not zero. GR   
   corrects this conceptual error:   
      
   In GR, near the surface of the earth, locally inertial frames are all   
   accelerating downward at 9.8 m/s^2, so an object at rest on the surface   
   is accelerating (upward) relative to them -- responding to the force   
   that the surface exerts on such objects.   
      
   Tom Roberts   
      
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