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General relativity explains that gravity is the curving of spacetime by massive objects. This makes sense, like when I throw a ball, it follows the curve of spacetime, which is towards the center of the earth.

But what I’m struggling to understand is if something has no acceleration, why does it still fall towards earth? If gravity is just matter traveling through curved spacetime, then wouldn’t something with no acceleration just act like it’s in outer space (just floating)?

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  • $\begingroup$ It’s not a proper answer but I once heard an argument that maybe already helps: everything is moving all the time through space-time because we are moving through time even when we are not moving through space. $\endgroup$
    – Hartmut Braun
    Apr 11, 2022 at 4:45
  • $\begingroup$ Maybe this video helps. It doesn’t answer your actual question but it explains the “moving through spacetime“ aspect: youtu.be/A2JCoIGyGxc $\endgroup$
    – Hartmut Braun
    Apr 11, 2022 at 5:02
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    $\begingroup$ I’m voting to close this question because there is only incidental astrophysical relevance, and this question already has a good answer on Physics Please go and see physics.stackexchange.com/questions/90592/… to understand how the problems with the rubber sheet model of GR. And this comic xkcd.com/895 for the difficulty in talking about General Relativity in any terms. $\endgroup$
    – James K
    Apr 11, 2022 at 7:19
  • $\begingroup$ For a bit more maths, physics.stackexchange.com/questions/47379/… shows how to calculate the weight of an object using GR. $\endgroup$
    – James K
    Apr 11, 2022 at 8:29
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    $\begingroup$ This is an excellent question. But you won't get any satisfying answer to it, unfortunately. You'll mainly be told, in ways both direct and indirect, that time is somehow the accelerant. Time though is of course not a thing; it can't move anything. And so, we're really left in a weird position here. $\endgroup$
    – White Prime
    Apr 12, 2022 at 0:08

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If gravity is just matter traveling through curved spacetime, then wouldn’t something with no acceleration just act like it’s in outer space (just floating)?

You have already answered your question, yes gravity is an effect of Spacetime curvature, it is the curvature of both space and time component that fully explains gravity. For a bit more understanding, remember that everything that has mass (or energy) curves spacetime, the time is the thing that causes acceleration, see the answers to this question to get a clear view on time dilation. For a more intuitive understanding consider the following graphs: enter image description here

In the above graph where there is not curvature of spacetime and you are at rest, the axis of both time and space/ distance will be perpendicular, So if your are at rest, you will be staying at rest according to Newton's first law.

Now if there is a curvature in spacetime, there time dilation takes place, which will change the angle between your time axis and your space axis, this will give: enter image description here

Now, you are not moving and not external force is acting on you, but since the angle between your time axis and space axis s changed, you will see that while you move in time you also move through space, this is the concept of gravitational acceleration according to general relativity. And the graph I showed here does not show you the acceleration, to see acceleration, just see that the angle between the two axis changes at every instant, which will give you a curved graph.

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