From: helbig@asclothestro.multivax.de   
      
   In article ,   
   ram@zedat.fu-berlin.de (Stefan Ram) writes:   
      
   >   If you put the same two test bodies into an elevator that is   
   >   falling freely, one on the floor of the elevator and the   
   >   other one into the air one meter above the first one,   
   >   their distance will /not/ decrease because the force of the   
   >   Earth's surface and thus the squeezing force is missing here.   
      
   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.   
      
      
   [[Mod. note -- To add to what Stefan and Phillip wrote:   
      
   One might ask how tidal forces are distinguished from "non-tidal" ones   
   like those that define the Newtonian "little g".  The answer is to write   
   the coordinate positions of test bodies as power series in time and space;   
   tidal forces enter at higher order than "little g" forces.   
      
   That is, in a Newtonian reference frame (which need not be inertial),   
   we can write the position of a test body (in 1 dimension for simplicity)   
   as a power series in time (taking $t=0$ to be a nearby "reference time")   
     $x(t) = x_0 + x_1 t + (1/2!) x_2 t^2 + (1/3!) x_3 t^3 + ...$   
   Then $x_0$ and $x_1$ tell us the position & velocity of our test particle   
   (with respect to our coordinate system), i.e., they are specific to that   
   test particle.  $x_2$, in contrast, tells us the Newtonian "little g"   
   (with respect to our coordinate system) near $t=0$,$x=0$.  In Newtonian   
   mechanics $x_2$ is the same for all test particles near $t=0$,$x=0$; this   
   is called the "universality of free fall".  It's because $x_2$ is the   
   *same* for all test particles (near $t=0$,$x=0$) that we can say that the   
   distance between two different test particles won't change (given suitable   
   initial positions/velocities).   
      
   $x_3$ and higher coefficients describe the tidal field which Phillip   
   referred to.   
      
   So, when we say "in the limit of an arbitrarily small elevator", what   
   we really mean is "ignoring $x_3$ and higher terms in the power series.   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)