Correct me if I'm wrong, but if you have a proton that is in superposition, you don't know where exactly it is; it is everywhere but with different probability. Couldn't you measure the gravity field it creates? And if you could, you would know where it is and it wouldn't be in superposition. I'm new to superposition but this keeps confusing me.
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I think the title and the question are a bit conflicted. In the example you’re considering, it wasn’t gravity that collapsed a superposition— it was your measurement of the particle’s state via a measurement of the gravitational field it was generating that would collapse the superposition. Such a measurement, if sufficiently precise, could cause a collapse. But this isn’t special to gravity, you could measure the coulomb field of a charged particle in a superposition of position states and obtain the same result.
The distinction between “the field collapsing the state” and “the measurement collapsing the state” is that if you don’t bother measuring the gravitating states in question, then a collapse won’t transpire. There’s nothing wrong with simply plugging a gravitational potential term $V(X)$ into the Hamiltonian, H(X,P), and evolving the state forward in time unitarily.
But this doesn’t mean that gravitational (or even electromagnetic) interactions between particles cannot themselves produce over time a loss of coherence between multiple interacting states. For a really brilliant demonstration of this happening in a gedankenexperiment I refer to this paper by Alessio Belenchia, Robert M. Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer.
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