From: richalivingston@gmail.com   
      
   On Monday, December 18, 2023 at 2:14:47 AM UTC-6, Luigi Fortunati wrote:   
   > Luigi Fortunati il 17/12/2023 09:29:50 ha scritto:   
   ...   
   > By gravity I mean the Newtonian force F directly proportional to the product   
   of the masses m1 and m2 and inversely proportional to the square of their   
   distance.   
   ...   
   > Does all this exclude that, in classical mechanics, gravity is a fundamental   
   force and, therefore, is necessarily a vector?   
   ...   
   > If there are many directions in the GR, why does the elastic sheet sink   
   *always and only* downwards, i.e. towards a single direction?   
   >   
   > Luigi Fortunati   
      
   As mentioned by the moderator, our current understanding of gravity is   
   considerably more complex and subtle than Newton's concept.  Experimental   
   evidence has confirmed all this.  In particular, thinking of gravity only as a   
   force is missing some    
   important phenomena.   
      
   The current understanding is that space time is not Euclidean everywhere, but   
   can be curved in various ways.  The geometry of space-time is described by the   
   metric tensor, which is a 4x4 tensor with 10 unique parameters.  The ways that   
   space-time can be    
   distorted is more complex than can be described by a simple vector.  However,   
   with the metric  tensor one can calculate how objects move from point to point   
   via the covariant derivative.  This is an extension of the ordinary derivative   
   to a non-Euclidean    
   space-time.  One of these derivatives can calculate what we commonly   
   experience as the "force of gravity", and that is a vector with direction and   
   magnitude.  But that is only one of several gravitational effects that we now   
   understand.   
      
   To put that more clearly, gravity is not just an attractive force.  There are   
   a multitude of effects we now understand to be due to gravity.   
      
   In general relativity gravity can manifest in ways other than a simple   
   attractive force.  The gravitational red shift is one.  Actually, what we   
   regard as a "force" is due to the variation in this red shift with radial   
   position.  Geometrically, there is    
   a curvature of the time metric, g_00, in the radial direction.  But GR also   
   shows that the radial metric varies in the radial direction.  This is a   
   different kind of curvature and it does not result in a "force", but it does   
   affect the paths that free    
   objects follow.  As an example. if you could somehow turn off the g_00   
   curvature (i.e. make g_00 = 1 everywhere), then objects could orbit a black   
   hole at the event horizon at any speed without falling in, and without   
   experiencing anything you would     
   call a force.  That is, an object in a circular orbit will behave as if it is   
   going in a straight line, which geometrically it is, even though it returns to   
   the same place every orbit.  This is not a force, yet it is a gravitational   
   effect.   
      
   Rich L.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)