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The way I understood general relativity is that there is no force of gravity but instead all object just move forward but the space they move through is distorted and that's why their trajectory seems to be different than a straight line. Now here is the question, if an object is not moving at all, i.e. it has no speed, does that mean that even though space is curved around them there is no speed to move the object towards the larger object?

Warix3
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  • If an object has 'no speed' then it can't be freely falling in a curved spacetime. (I.e. there's some external non-gravitational force on it). – Eletie Nov 29 '20 at 18:30
  • You are always moving within spacetime. Your scenario is not possible. – m4r35n357 Nov 29 '20 at 18:34
  • I understand that you are always moving through time but how are you always moving through space? @m4r35n357 – Warix3 Nov 29 '20 at 18:36
  • Time and space should be treated on equal footing, so that one talks about paths (worldlines) through spacetime as a whole – Eletie Nov 29 '20 at 18:37
  • So if an object moves through time that automatically makes it move through space too? How does that work? @Eletie – Warix3 Nov 29 '20 at 18:39
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    Lets consider an object initially at rest. You can think of all objects as moving through spacetime itself. In a completely flat spacetime, taking the shortest path through spacetime will result in not moving spatially but only moving through time. In a curved geometry however, that shortest path through spacetime (along geodesics) does move through space too. So when dropping an object on Earth it accelerates towards the Earth, because it's following a geodesic. (see link) – Eletie Nov 29 '20 at 19:08
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    @Warix3 so no matter what geometry we have, objects (under no other forces) follow geodesics through spacetime. For flat spacetime (no curvature/gravity), this geodesic moves through spacetime in such a way that the spatial location doesn't change (but of course it moves forward in time). For the curved spacetime (i.e. gravity), the geodesic causes the object to change spatial locations as well as moving forward through time. It's this moving through space along the geodesic that can be equated with acceleration. Hope this helps? – Eletie Nov 29 '20 at 19:16
  • @Eletie Thanks that helps, I understand now that objects will move under influence of gravity even if they have no initial speed. But I still can't intuitively understand why that exactly happens. "In a curved geometry however, that shortest path through spacetime (along geodesics) does move through space too" Is there a visual example of this and how it works? – Warix3 Nov 29 '20 at 19:34
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    @Warix3 I'm glad! And I'd agree, it definitely isn't intuitive when thinking about everyday things. The easiest way to see this is all is through the maths. I'm afraid I don't have a visual (you could simply try Youtube lectures). I think the thing to try and understand first is the properties of spacetime, even in flat Minkowski space (that objects always move through spacetime). – Eletie Nov 29 '20 at 19:47

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If an object is initially static from a larger object (assuming they have the same density), it will follow the geodesics in space-TIME. So the answer is yes because space-time is curved by the second object. This is why when you drop an object, it falls down to earth.

Jeanbaptiste Roux
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  • Does that mean the object with no speed would be affected by the gravity of the larger object and move towards it? – Warix3 Nov 29 '20 at 18:37
  • In the referential of the larger object, the first one will progressively acquire speed, though initially, it did not have any. – Jeanbaptiste Roux Nov 29 '20 at 18:53