2012/04/25 by Craig J. Hogan, Hogan, Craig J. · 1 citation
Decision Sciences · Engineering · Mathematics · #Diverse Scientific and Engineering Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Probabilistic and Robust Engineering Design #Quantum Physics (quant-ph) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1204.5948
openalex publication_date 2012/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓP in place of Planck's constant ℏ. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by ⟨ Δθ2⟩ = ℓP/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 ℓP= lP/√(4π), where lP≡ √(ℏ G/c3) 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 ⟨ Δθ2⟩ on timescale τ≈ 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.