From: tjoberts137@sbcglobal.net   
      
   On 5/2/23 7:57 PM, Luigi Fortunati wrote:   
   > [...]   
      
   You have completely missed the essential thing about locally inertial   
   frames in GR: they are APPROXIMATIONS. There exists no perfectly   
   inertial frame anywhere in the universe we inhabit, including here on   
   earth. But this is physics, and measurements are never perfect, they   
   always have a resolution/errorbar. A region of spacetime that is small   
   enough so the deviations from a truly inertial frame are smaller than   
   measurement resolutions can be treated as if it is inertial -- in   
   particular, gravity can be ignored and SR can be applied (which is   
   enormously simpler to use than GR).   
      
   That usually means the locally inertial frame must be in freefall, and   
   small enough so any tidal forces present are smaller than measurement   
   resolutions. But not always:   
      
   For instance, at the LHC the experimental caverns are less than 100   
   meters in any direction. The particles they measure travel with speed   
   indistinguishable from c relative to the lab. So each event has a   
   duration less than 100m/c = 3E-7 seconds. During such an event, a truly   
   inertial frame initially at rest relative to the lab would fall   
   	0.5 g t^2 = 0.5 9.8 (3E-7)^2 = 5E-13 meters   
   Their best detectors have resolution greater than 1E-6 meters, so for   
   each event they can consider the apparatus to be at rest in a locally   
   inertial frame, and use SR in their analysis. They analyze each event   
   separately, because for longer durations (> ~ milliseconds) the   
   difference between a locally inertial frame and their lab cannot be   
   neglected.   
      
        [That estimate uses the first-order contribution from   
         earth's gravity; higher order contributions, such as   
         tidal forces, are considerably smaller and can also   
         be neglected. Ditto for the non-inertial effects of   
         earth's rotation.]   
      
   This is physics, and approximations abound. It is ESSENTIAL to be able   
   to estimate when a given approximation is good enough. In all your   
   discussions of elevators you have never mentioned how accurately   
   measurements are made -- that is essential information for one to   
   determine whether the elevator can be considered to be locally inertial.   
   (The moderator and I have mentioned this, but you have ignored that.)   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
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