It is commonly said that if you lift an object above the earth it gains potential(adsbygoogle = window.adsbygoogle || []).push({});

energy equal to mgh (m=mass, g=gravitational acceleration, h=height), suggesting

that the potential energy is in the lifted mass.

This cannot be. Consider the case of two perfectly rigid spheres, isolated in space, and touching one another, held together only by gravity.

Imagine an outside source provides the energy to lift up one of them and then

insert a rigid, weightless rod between them to prevent them from falling together.

The situation is symmetrical.

If the potential energy is in the spheres and only in the spheres, then it must be

divided equally between them, not concentrated in the smaller, because there is no

smaller one.

One answer I have seen is that the potential energy is in the "field" (or system or configuration), but where in the field is it?

Is it at the midpoint between the two spheres? Is it distributed throughout the

field? And if so, how is it distributed?

The potential energy must be somewhere, or we have energy that is not contributing to the gravitational field, don't we?

I don't see how GR gets rid of the problem, although it would use a different

vocabulary. There should be some additional curvature of spacetime due to the "potential curvature" of spacetime that was created by the lifting, right?

Or is there no potential curvature, just curvature immediately realized as the lifting is done?

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# A Where is potential curvature stored in GR?

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