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My understanding is, that according to GR, an apple falls to the ground not because it is being pulled but because it follows the curvature of space, caused by the mass of the Earth. My question is - Why should it follow that curve instead of remaining where it is? Apparently, it is already in motion in Space-Time, with Zero velocity in space and a velocity of C in time? If that be so, what causes it to start moving in space, with a corresponding reduction in time? Is Gravity not a force? What about electricity, magnetism and the strong and weak nuclear forces?

Richnz00
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    This video is helpful https://www.youtube.com/watch?v=DdC0QN6f3G4 . Possible duplicates: http://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity?rq=1 http://physics.stackexchange.com/questions/222390/how-does-curved-space-explain-gravitational-attraction?noredirect=1&lq=1 http://physics.stackexchange.com/questions/243317/how-does-gravity-truly-work?noredirect=1&lq=1 –  Dec 17 '16 at 00:38
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    This question does not show any research effort. – Alfred Centauri Dec 17 '16 at 02:58
  • @NeuroFuzzy - yes that youtube video explains it. Thanks – Richnz00 Dec 17 '16 at 03:45

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You ask very profound questions, that I try to answer briefly here, but for a full discussion I would recommend you a good textbook in GR - for instance Carroll's Spacetime and geometry gives a good explanation of the foundations.

In GR objects do not "fall" and there is no force that pulls objects. First keystone of GR: mass(/energy) curves the spacetime in a manner that it is not easy to visualize (maybe impossible in a proper way). Second keystone: objects in their motions follow geodesics.

Geodesics are, roughly speaking, the paths that minimize the distance between points. So the presence of the Earth curves spacetime in such a way that if you pick a point (say, the apple) at some distance from the center or the Earth, the geodesic is a straight line connecting the apple to the center of the planet, hence the motion.

The path that you describe (zero spatial velocity and $c$ time velocity) is not a geodesic for the spacetime deformed by the presence of the Earth, that is why theapple does not follow that motion.

In this sense gravity is not a force: there is no field like in the case of electromagnetism (or weak or strong forces, but these involves other subtleties). In the case of electromagnetism the presence of the charged particle induces a field that can be "seen" by other particles. We say that the particles that are subjected to the field are charged with respect to that field. The particles feel the field because they feel a force connected to it, in the case of EM it is Lorentz force.

  • yoric thanks for your answer. You say "objects in their motion follow geodisics". But what causes to apple to start moving at the moment it breaks from the branch? – Richnz00 Dec 17 '16 at 01:14
  • @Richnz00, think about it this way. Before the apple falls, what keeps it in a "geosyncronous orbit" at such a low altitude? – The Photon Dec 17 '16 at 03:15
  • @The Photon - What keeps it in a geosynchronous orbit? A force? The "force" the stem exerts on the apple at the point of attachment? If this is true and a force mediates to keep it in geosynchronous orbit, the removal of the "force" would cause it to move in the Newtonian way as it would now be subject to another force (Newton's first law). What causes it to move according to GR? The release of the preventing force? I think that would be the one. Which leads to the question - what is acceleration? How is it related to force? – Richnz00 Dec 17 '16 at 03:40
  • Before falling the apple is in orbit because there is the force of the tree that keeps it still. When the link cease to exist, the apple is an isolated system and therefore (II postulate of GR) it starts moving in a geodesic ('free fall': free since there is no force acting on it). Yes it looks like if there were a force pulling it down -- indeed this description has survived for more than 300 years and it is still accurate in many energy regimes. The low energy limit of GR looks like there were a force (Newton's). –  Dec 17 '16 at 11:27
  • Hi yoric, many thanks for your reply. I appreciate you guys taking the time to explain the concepts from where mine possibly go wrong. That Youtube link NeuroFuzzy gave was very helpful. Here's the thing I am struggling with - when the apple is attached to the tree all of you agree there is a force holding it there, which is acting opposite to the geodisic, which is apparantly pointing straight to the centre of the Earth – Richnz00 Dec 17 '16 at 20:25
  • Hi yoric,- when the apple is attached to the tree all of you agree there is a force holding it there, which is acting opposite to the geodisic, which is apparently pointing straight to the centre of the Earth. Since the apple does not move towards it, there must be an equal and opposite force acting in the opposite direction. What is the nature of the 2 forces? Is the central force centripetal? If so what is the force exerted by the tree? What happens to the central force? – Richnz00 Dec 17 '16 at 20:35
  • I stress the fact that there is no gravitational force in GR (even though is looks like a force in low energy limit). When the apple ceases to be connected to the tree it is an isolated object; isolated objects move along geodesics. When the constraint that keeps the apple tied to the tree ceases to exist, the apple start to freely falling, i.e. it is in geodesic motion. The geodesic for those particular initial conditions (object standing still at distance h from the center of the earth at t=0) is a radial motion. –  Dec 17 '16 at 20:42
  • When the apple is connected to the tree it is not an isolated object hence it is not in geodesic motion. Note that the equation of motion is NOT F=ma, but there are much more complicated terms involving the constraint and the geometry of spacetime. However I invite you to read Carroll's Spacetime and geometry (the first chapters) - there are also his notes that then became the book available in his website for free. –  Dec 17 '16 at 20:46