When two masses occupy spatial superpositions, their branch-dependent Newtonian gravitational potential energy produces relative phases. If those phases cannot be separated into one phase for each mass, the interaction turns an initial product state into an entangled state.
The Bose--Marletto--Vedral experiment proposes placing two nearby masses in spatial superpositions and detecting the entanglement generated by their branch-dependent gravitational phases. Under locality assumptions and in the absence of other interactions, an entangling mediator must possess incompatible observables rather than behave as a single classical local variable.
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