Kavli Affiliate: Craig Hogan
| First 5 Authors: Craig Hogan, Ohkyung Kwon, Nathaniel Selub, ,
| Summary:
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 $ctaull R$ should depend only on
$tau$, 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 $Theta$,
$langledeltatau^2rangle_Thetasimeqtau:!t_psimTheta R:!t_P/c$, and
angular power spectrum $C_ellsim (R:!l_P)/ell^3$ at $ellgg1$. 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 $ell$. The high $ell$ scaling is contrasted with that
predicted in some other quantum models, which differ by one power of angular
wavenumber $ell$ and are shown to predict excessive blurring of images from
distant sources.
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