We know from the answer to previous questions that gravity contracts length and the length contraction only happens vertically, that is towards the centre of mass.
If we think of an object at a distance d from a mass this is a length and we know that this should be contracted by the mass' gravity. Now d is smaller and the gravity would contract the distance again. Could this be viewed as a simple explanation for gravity as an attracitve force?
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Qmechanic
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Derek Seabrooke
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No, this is not a good way to explain why spacetime curvature leads to a gravitational acceleration. The gravitational acceleration exists only because the falling object is moving in spacetime so it is moving over a curved (four dimensional) surface and its trajectory curves because only because it is moving.
if you consider the common analogy of an ant walking on the surface of an apple, it accelerates (i.e. its path curves) only when it is moving. If it halts it stays where it is and doesn't accelerate anywhere. Likewise if you could halt in spacetime you wouldn't accelerate either - even if you were near a black hole. The problem is that you are always moving in spacetime because even if you are stationary in space you are moving in time, and it's this motion through time that causes the displacement in space. For the gory details see my answer to How does "curved space" explain gravitational attraction?, though this is only for the determined!
The change in the radial coordinate with distance plays a role, but it alone cannot explain gravitational acceleration as it would not cause a gravitational attraction without the additional element of motion through spacetime.
John Rennie
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