The solution to this is almost certainly "moving the wormhole takes energy and solves this 'paradox'". The mass-energy of the wormhole could be from gravitational field energy, for example.

How much energy? The wormhole doesn't have an inherent mass, so how much energy does it take? After all you can put an arbitrary amount of mass through it.

You're looking at it the wrong way. If you can extract energy from dropping the rock through the wormhole, it takes energy to pull the rock away from the wormhole (and, by symmetry, it takes that much energy to move the wormhole away from the rock).

I would guess that that would depend on the situation.

I would think that whatever method you have of moving a mouth of the wormhole, would have some interactions with the masses providing the gravitation.

Also, I'm not 100% sure that a wormhole would not have something like an inherent mass, because iirc there are solutions where a black hole mass is entirely because of the way spacetime is set up, without any particles needed? I'm not sure about that, but I think that is what I read..

I'm kind of lost by your contruction. Is the something we drop the same as the object we "lift"? What does it mean to lift the object? Try removing the pronouns, and being more specific with your steps.

Is this a thought experiment you came up with on your own, or do you have a paper you're citing? If the latter, do you have a link?

> Try removing the pronouns, and being more specific with your steps.

That would be even worse. Let the strong gravitational force of the Earth go through a wormhole located on a small platform in deep space, and drop a rock near the wormhole (not through the wormhole).

Then move the wormhole (and the gravitational force) elsewhere, lift the rock off the platform, and bring the wormhole back.

Your thought experiment clearly implies energy is spent moving the wormhole. That would be the energy needed to spend to move your example rock.