From: tjroberts137@sbcglobal.net   
      
   On 9/22/17 9/22/17   12:42 AM, Luigi Fortunati wrote:   
   > Tom Roberts giovedà 21/09/2017 alle ore 15:53:32 ha scritto:   
   >>> Newton claims that gravity is a force, Einstein denies it: for him it is   
   >>> not a force (it is something else).   
   >>   
   >> Yes, in GR gravity is an aspect of the geometry of spacetime -- it can   
   >> masquerade as a fictitious "force", like "centrifugal and Coriolis force",   
   >>  due to choice of coordinates.   
   >   
   > How can a different choice of coordinates have some influence on the   
   > "measurement" of a force?   
      
   For a real force, coordinates don't matter. But for a "fictitious force"   
   that is explicitly coordinate dependent, they do. That's why I put   
   "gravitational force", "centrifugal force", and "Coriolis force" in   
   quotes -- they aren't really forces at all, it's just that their   
   historical names contain the word inappropriately. They are really   
   FUDGES that permit one to act as if accelerated coordinates were   
   inertial, so Newton's laws are valid in them.   
      
   With the hindsight of GR, we understand why Newton thought there was a   
   "force of gravity" -- he was unknowingly using coordinates that were   
   themselves accelerated, and attributed the acceleration of free objects   
   relative to them to a "force". In retrospect, those free objects were   
   moving inertially, and the coordinates were accelerated.   
      
   > Force is the one exercised in its "point of application" and is   
   unique. But neither "gravity" nor "centrifugal force" nor "Coriolis   
   force" have any "POINT of application" -- they all apply equally to all   
   points of an object.   
      
   	Real forces, in the sense of "a push or a pull", do indeed have   
   	a point of application. (Electrical and magnetic forces have   
   	a point of application at each charged particle.)   
      
   > If the bleacher exerts a force of 600 N on the scaffolding (and vice versa),   
   > that force is always equal to 600 N for everyone!   
      
   Sure.   
      
   But a freefalling ball above them feels no force at all (neglecting   
   air). The forces on scaffolding and bleachers are real, contact forces,   
   which are diverting the bleachers from their inertial path (which would   
   of course be falling downward).   
      
   > Otherwise tell me in what other reference system the bleacher could exert on   
   > the scaffold a force other than 600 N or even nothing.   
      
   You are using the wrong situation -- real forces like that are not   
   coordinate dependent. Look at the freefalling ball above the bleachers,   
   neglecting air -- it feels no force. It is accelerating relative to   
   coordinates fixed to the ground simply because the latter are   
   accelerating.   
      
   	Consider a baseball thrown straight up and in the air for 4   
   	seconds: it goes up ~ 64 feet and comes back down. Using   
   	coordinates fixed to the earth, its trajectory through   
   	spacetime extends for 744,000 miles along the time   
   	coordinate and 64 feet in space -- very nearly a straight   
   	line, because near earth the curvature of the manifold is   
   	quite small. (metric: 1,200,000 km and 20 meters.)   
      
   General Relativity is a whole new way of looking at the world, compared   
   to Newtonian mechanics. A newsgroup like this is not a good place to   
   learn it -- get a good textbook.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)