  Recently there has been a great deal of interest in tabletop experiments
intended to exhibit the quantum nature of gravity by demonstrating that it can
induce entanglement. We argue that these experiments also provide new
information about the interpretation of quantum mechanics: under appropriate
assumptions, $\psi$-complete interpretations will generally predict that these
experiments will have a positive result, $\psi$-nonphysical interpretations
predict that these experiments will not have a positive result, and for
$\psi$-supplemented models there may be arguments for either outcome. We
suggest that a positive outcome to these experimenst would rule out a class of
quantum gravity models that we refer to as $\psi$-incomplete quantum gravity
(PIQG) - i.e. models of the interaction between quantum mechanics and gravity
in which gravity is coupled to non-quantum beables rather than quantum beables.
We review some existing PIQG models and consider what more needs to be done to
make these sorts of approaches more appealing, and finally we discuss a
cosmological phenomenon which could be regarded as providing evidence for PIQG
models.
