Kavli Affiliate: Craig J. Hogan

| First 5 Authors: Craig J. Hogan, , , ,

| Summary:

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 $langle Delta theta^2rangle = ell_P/L$ 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 $ell_P= l_P/sqrt{4pi}$, where $l_Pequiv sqrt{hbar G/c^3}$ 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^2rangle $ 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.

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