From: fortunati.luigi@gmail.com   
      
   Stefan Ram venerd=EC 09/09/2022 alle ore 08:30:00 ha scritto:   
   >   I currently can't go on websites, but maybe what is intended   
   >   is this: a particle is placed on a geodesic compatible with   
   >   that particle. The particle now can move on the geodesic,   
   >   but how does it know in which direction as the geodesic has   
   >   no preferred direction?   
   >   
   >   The answer might be: While a geodesic has no preferred   
   >   direction, the time coordinate has.   
      
   The time coordinate is part of the geodesic.   
      
   If the time coordinate has a preferred direction, the geodesic also has   
   a preferred direction.   
      
   [[Mod. note --   
   A useful mental model for a geodesic at a point is motion on the surface   
   of the Earth.  That is, starting at some specified point, we can move   
   in a specified compass direction (e.g., you might start out moving due   
   west).  If, once moving, we don't turn left and you don't turn right,   
   our motion will be along a geodesic on the Earth's surface.   
      
   Thinking of our starting point again, you could have started moving   
   in any direction (e.g., instead of bearing 090 degrees = due west, we   
   could have chosen any other compass bearing).  So there are a whole   
   (infinite) family of possible geodesics passing through that starting   
   point (one for each possible compass bearing).   
      
   If I understand you correctly, you're asking "once a particle is moving,   
   how does it know to continue moving in that direction?".  The answer is   
   basically conservation of momentum: unless there is some external force   
   pushing on the particle, it's going to continue moving in the *same*   
   direction it was already moving in.   
      
   In terms of geodesics in relativity (the original context of your question),   
   it's essential to realise that (as others have noted) the trajectoris of   
   free particles are geodesics in *spacetime*, not geodesics in *space*.   
   That means the most useful particle velocity to think about is the   
   4-velocity, which is *never* zero (you're always moving forward in time),   
   and corresponding momentum is the 4-momentum, which is also never zero.   
   (Recall that in relativity, even a zero-rest-mass particle like a photon   
   still has a nonzero momentum so long as it carries nonzero energy.)   
   -- jt]]   
      
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