Angular spectrum of quantum fluctuations in causal structure

Kavli Affiliate: Craig Hogan

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| 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 $ctau$ should depend only on
$tau$, with a normalization set by the Planck time $t_P$, and not on $R$, or
on any larger system in which it may be embedded. This principle leads to
universal scaling for variance on angular scale $Theta$ , $langledeltatau^2
rangle_Theta simeq tau t_psim Theta R t_P/c$, and angular power spectrum
$C_ellsim (Rl_P)/ell^3$ at $ell gg 1$. This spectrum is demonstrated
explicitly in a relational model of holographic noise based on causally
coherent virtual null gravitational shocks, which is valid at all $ell.$ The
high $ell$ scaling is contrasted with that predicted in some 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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