Abstract
Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: the variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius R at transverse physical separation cτ≪ R should depend only on τ, with a normalization set by the Planck time t_P, and should not depend on R. For measurements on scale R, the principle leads to universal scaling for variance on angular scale Θ, δτ²_Θ≃τt_p∼Θ Rt_P/c, and angular power spectrum C_ℓ∼ (Rl_P)/ℓ³ at ℓ≫1. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all ℓ. The high ℓ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wavenumber ℓ and are shown to predict excessive blurring of images from distant sources.