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According to general relativity, mass and energy cause the curvature of space. To have perfectly flat space, there must be a completely empty vacuum state with no mass or energy.

Theoretically, is it possible to create perfectly flat space, even locally, by precisely arranging mass and energy in the universe?

I am not a physics major nor have I studied physics in depth; I am an ordinary person.

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    $\begingroup$ I don't see why it can't - presumably you just need to move the mass very far away, or arrange it in a spherically symmetric manner. $\endgroup$
    – Allure
    Commented Jun 13 at 2:43
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    $\begingroup$ Presumably you mean spacetime and not space; the latter can be defined to be whatever is convenient and can often be made flat even if spacetime is curved. $\endgroup$
    – Sten
    Commented Jun 13 at 2:50
  • $\begingroup$ I feel that somebody should reference the Rick and Morty episode "Morty's Mind-Blowers" here, and apparently I'm just the guy to do it. $\endgroup$ Commented Jun 13 at 16:33

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In principle, you would have flat spacetime in the hollow center of a spherically symmetric mass/energy distribution. So you could imagine rearranging the contents of the Universe into such a configuration.

However, most of the energy content of the Universe is dark energy. We are not sure that it even makes sense to talk about moving dark energy from one place to another. If dark energy is uniformly distributed everywhere, as in the simplest models, then it induces spacetime curvature everywhere, which you will never be able to remove or compensate.

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  • $\begingroup$ It is not that clear how "theoretical" the OP wants the answer to be. But in case he meant whether a universe could exist that is flat, as far as we know there is nothing inconsistent about a vanishing cosmological constant. We just happen to have a (very small) positive one. $\endgroup$
    – Kvothe
    Commented Jun 13 at 12:50
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No, since you're not going to be able to evacuate the vacuum energy. Thus you cannot get a perfectly flat space theoretically. However, at most humanly probeable scales today, it would appear flat.

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