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So I know that in general relativity, superposition cannot be true. However, since string theory supposedly connects quantum mechanics and gravity, how does it relate superposition and gravity?

Jungwoon Song
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  • "Superposition" is not usually the issue in merging GR and quantum mechanics, so I'm a bit lost what you expect as an answer to this question. See https://physics.stackexchange.com/q/387/50583 for a discussion of the actual issues. – ACuriousMind May 26 '22 at 16:39

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Theories that allow for superpositions of space being curved in different ways have all of their inconsistencies show up at high energies. The new degrees of freedom which come to the rescue in string theory become less important at low energies thereby leading to a theory which looks like a supersymmetric analogue of general relativity. A large research area focuses on building models where the same can be said about ordinary general relativity.

The situation should be morally similar to Fermi's theory of beta decay. Even though it was useful for many things, it could not be formally reconciled with the idea of superpositions due to a UV catastrophe. This changed with the discovery of the W boson leading to a much nicer theory whose IR behaviour still matched that of Fermi.

Connor Behan
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  • I'm curious, in which theories do we have an analog of superposition in the curvature? – Charlie May 26 '22 at 16:56
  • That's just synonymous with quantum gravity right? When you promote the metric to an operator, the Hilbert space on which it acts includes more than just its eigenstates. This was not emphasized in early attempts which mostly considered graviton scattering amplitudes instead of taking coherent states of gravitons. – Connor Behan May 26 '22 at 17:11
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So I know that in general relativity, superposition cannot be true.

General Relativity is a classical theory, and is not quantized yet, its quantization is a matter of current research, and string theories are part of this research.

However, since string theory supposedly connects quantum mechanics and gravity, how does it relate superposition and gravity?

String theories are quantum mechanical theories and all the concepts of quantum mechanics are within those models.If a string theory is successful in modeling the data and observations it will be also including a quantization of general relativity, which will follow the rules of superposition in quantum mechanics.

anna v
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Unlike what you may hear in many places, we have a perfectly good theory of quantum gravity: you just treat general relativity as a quantum field theory! Now, it's true that the result is non-renormalizable. But that just means that it only gives useful predictions below a certain energy scale $\Lambda$, or for distance scales longer than some length $\Lambda^{-1}\sim \sqrt{\hbar G_N}$. We call this an "effective theory".

That theory deals perfectly well with superposition. The result is much the same as any other quantum theory: the dynamical variables can be in a superposition of different states. In gravity, the dynamics describes the geometry of spacetime. So spacetime can be in a superposition of different geometries!

String theory is more complete (it gives predictions even at the very short distances where the above description fails), but for the purposes of this question all you need to know is that at long distances or low energies it gives the quantum theory of GR described above. So in string theory too, spacetime can be in a state with a superposition of different geometries.

Holographer
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