From: mlfasf@comcast.net   
      
   On 3/4/22 2:04 PM, Phillip Helbig (undress to reply) wrote:   
   > Minor nitpick (the summary is otherwise excellent): in practice, the   
   > distance between the two test bodies in an elevator will INCREASE   
   > because gravity is slightly stronger lower down.  That is an example of   
   > a tidal force.  Similarly, two bodies side-by-side in an elevator will   
   > approach each other.  At rest or in uniform motion in no gravitational   
   > field, neither would happen.  In other words, this form of the   
   > equivalence principle is valid only in the limit of an arbitrarily small   
   > elevator.   
      
   But with a UNIFORM and constant gravitational field (absolutely parallel   
   field lines, and no variation in field strength), the equivalence   
   principle says this is equivalent to two test bodies undergoing the same   
   constant acceleration, with no gravitational field present.   
      
   [[Mod. note -- Note that the gravitational field near the Earth (whether   
   in an elevator or not) isn't uniform.  But over sufficiently small scales   
   we can approximate it as uniform, essentially neglecting higher-order   
   terms in the Taylor series I alluded to in a previous moderator's note.   
      
   Note also that in the context of general relativity, one needs to be   
   careful in invoking the equivalence principle for a *uniform* *constant*   
   gravitational field.  The problem is that such a field is the result of   
   (i.e., implies the presence of) an infinte mass plane, which means that   
   spacetime is *not* asymptotically flat.  That has a number of "interesting"   
   consequences...   
   -- jt]]   
      
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