  Recently, interest has increased in the entanglement of remote quantum
particles through the Newtonian gravitational interaction, both from a
fundamental perspective and as a test case for the quantization of gravity.
Likewise, post-Newtonian gravitational effects in composite nonrelativistic
quantum systems have been discussed, where the internal energy contributes to
the mass, promoting the mass to a Hilbert space operator. Employing a modified
version of a previously considered thought experiment, it can be shown that
both concepts, when combined, result in inconsistencies, reinforcing the
arguments for the necessity of a rigorous derivation of the nonrelativistic
limit of gravitating quantum matter from first principles.
