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Hypothetically, if space could be moved or scaled, what would happen to everything inside?

I'd like to know if an element of momentum could be transferred to objects by contorting space-time.

Other than gravity, what effects does space-time contortion have on mass?

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It seems that what astronomers call gravitational waves are more or less what you are referring to. If it is the case, then these waves have momentum, which they can transfer to objects. It is argued that it might be possible to detect them that way. –  chris Jun 3 at 2:10

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