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I have a question about the electromagnetic field of a quantum superposition. Let me be clear about the context:

In arXiv:gr-qc/0203072v1 is mentioned the following:

"We would like to have, at least in principle, a way to envision a a manner to describe space-time at, say, the atomic scale, whose curvature is associated with a nucleus which is in a state for which the position is not well defined."

In the Kiefer's quantum gravity book is mentioned something similar:

"Since every quantum object carries energy, it generates a gravitational field. A superposition of a quantum object where, for example, it was at two different places would then entail a corresponding superposition of the respective gravitational fields and thus demand a quantum theory of gravity for its description—unless the superposition principle ceases to be valid at that scale."

I agree that we don't have, at least not currently, a way to describe such physical situation, but the question that arises for me is: what is the the electric field of an atomic nucleus in a state for which the position is not well defined?, or more precisely, what is the electric field of an atomic nucleus that is in a quantum superposition where the nucleus is at two differents places?

I still have little knowledge about quantum field theory, so I'd like to know if there is a way to describe such kind of situation in the framework of standard quantum field theory or quantum electrodynamics, and what is the description of this situation given by such framework. I'll appreciate your answers.

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If the nucleus is at position $A$ then classically it will have electric field configuration $E_A$. If the nucleus is at position $B$ then classically it will have electric field configuration $E_B$.

Quantum mechanically, if the nucleus is in a superposition of positions $A$ and $B$ then the electric field will be in a superposition of field configurations $E_A$ and $E_B$. The electric field and nuclear position will be entangled in the sense that if the field is found to be in configuration $E_B$ then the nucleus will be found at positions $B$ and likewise for $A$.

This state of affairs for electrodynamics is not at all controversial. I guess the math for GR is more complicated making the superposition principle controversial for that theory.

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