  A model quantum system is proposed to describe position states of a massive
body in flat space on large scales, excluding all standard quantum and
gravitational degrees of freedom. The model is based on standard quantum spin
commutators, with operators interpreted as positions instead of spin, and a
Planck-scale length $\ell_P$ in place of Planck's constant $\hbar$. The algebra
is used to derive a new quantum geometrical uncertainty in direction, with
variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation
$L$, that dominates over standard quantum position uncertainty for bodies
greater than the Planck mass. The system is discrete and holographic, and
agrees with gravitational entropy if the commutator coefficient takes the exact
value $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes
the standard Planck length. A physical interpretation is proposed that connects
the operators with properties of classical position in the macroscopic limit:
Approximate locality and causality emerge in macroscopic systems if position
states of multiple bodies are entangled by proximity. This interpretation
predicts coherent directional fluctuations with variance $\langle \Delta
\theta^2\rangle $ on timescale $\tau \approx L/c$ that lead to precisely
predictable correlations in signals between adjacent interferometers. It is
argued that such a signal could provide compelling evidence of Planck scale
quantum geometry, even in the absence of a complete dynamical or fundamental
theory.
