  Standard quantum mechanics and gravity are used to estimate the mass and size
of idealized gravitating systems where position states of matter and geometry
become indeterminate. It is proposed that well-known inconsistencies of
standard quantum field theory with general relativity on macroscopic scales can
be reconciled by nonstandard, nonlocal entanglement of field states with
quantum states of geometry. Wave functions of particle world lines are used to
estimate scales of geometrical entanglement and emergent locality. Simple
models of entanglement predict coherent fluctuations in position of massive
bodies, of Planck scale origin, measurable on a laboratory scale, and may
account for the fact that the information density of long lived position states
in Standard Model fields, which is determined by the strong interactions, is
the same as that determined holographically by the cosmological constant.
