From: mlfasf@comcast.net   
      
   On 4/18/22 9:46 AM, Tom Roberts wrote:   
   > Your argument is invalid because   
   > the physical situations aren't actually equivalent -- the region   
   > involved is too large for the Principle of Equivalence to apply   
      
   The equivalence principle has no restrictions on the size of the region   
   in which it is valid.   
      
   [[Mod. note -- The EP applies if and only if we neglect tidal effects,   
   i.e., if tidal effects are "small".  But the size of tidal effects grows   
   with the distance, so saying that tidal effects should be "small" (so   
   that we can apply the EP) is essentially saying that the size of our   
   region should be "small".  So, effectively, the EP only applies in "small"   
   regions, where the precise definition of "small" depends on the curvature   
   of spacetime and your accuracy threshold for how small tidal effects need   
   to be before it's ok to neglect them.   
      
   For example, suppose we're considering some experiment near the Earth's   
   surface, where we're measuring accelerations on the order of 1g.  We might   
   reasonably say that for this experiment, we're willing to apply the EP   
   (i.e., neglect tidal effects) if the tidal accelerations are below 1e-6 g   
   in magnitude, i.e., if the tidal accelerations are < 1 part-per-million   
   of the Earth's Newtonian "little g".  To satisfy that condition requires   
   that our experimental region be (roughly) < 3 meters in diameter.  That   
   is, the tidal change in the Earth's Newtonian "little g" over a vertical   
   distance of 3 meters is about 1 part-per-million.  (In the horizontal   
   direction the change is probably a bit smaller.)  If our experimental   
   region is larger than 3 meters in diameter, the tidal change in "little g"   
   from one part of our apparatus to another part may be > 1 part-per-million,   
   so we can't safely apply the EP across at our 1 part-per-million accuracy   
   threshold.   
   -- jt]]   
      
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