I understand why a released object moves as it does once it has started moving, and why all objects fall at the same speed, removing other effects. But I don't see why the curvature of space would make it start to move in the first place, thank you.
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In the weak field limit (which applies near a planet) curvature of space is so small that its effect can be ignored completely; gravity is explained by looking only at time. We know that clocks on GPS satellites do not keep time with identical clocks on Earth, and we also know that energy is the time component of a 4-vector. It follows that energy is changed when an object moves up or down. We measure the energy change directly, as light is redshifted when it goes upwards, and we can calculate that the change is equivalent to potential energy in Newtonian gravity. The apparent force of gravity is minus the gradient of potential energy, so that the apparent change in the rate of clocks with height is directly responsible for the apparent force of gravity.
Charles Francis
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