From: PointedEars@web.de   
      
   Thomas 'PointedEars' Lahn wrote:   
   > Ross Finlayson wrote:   
   >> (as from its own perspective) its world-line in the geodesy,   
   >> which is basically a vector field.   
   >   
   > No.   
      
   A _geodesic_ x(λ) is _a parameterized curve_, with the affine parameter λ   
   (affine: offsets/origins do not matter; you can choose any point to be that   
   where λ = 0).  For every value of λ the value of x(λ) is a quantity that   
   transforms as a vector.  In that sense a geodesic is also a vector field in   
   the affine space of λ (usually the real numbers), with the value of λ being   
   the (only) component of a 1-vector (a real number).  But that is stretching   
   the terminology a lot.   
      
   By contrast, a *geodesic (or: geodesible) vector field* "is a /specific   
   type/ of vector field whose integral curves (trajectories) are geodesics"   
   (Google AI; emphasis mine).  However, there is no such vector field for   
   spacetime as the curvature of spacetime not only determines the paths of   
   objects in spacetime (which are spacetime geodesics if there are no external   
   forces), but also the curvature of spacetime *changes* *corresponding to*   
   objects in spacetime:   
      
     "Spacetime tells matter how to move; matter tells spacetime how to curve."   
      
       --John Archibald Wheeler,   
         in: "Geons, Black Holes, and Quantum Foam: A Life in Physics"   
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
   Please do not cc me. / Bitte keine Kopien per E-Mail.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)