Angular spectrum of quantum fluctuations in causal structure

• URL: http://arxiv.org/abs/2303.06563v2
• Date: Sun, 12 May 2024 22:00:05 GMT
• Title: Angular spectrum of quantum fluctuations in causal structure
• Abstract summary: Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds. The small-angle spectrum of displacement is derived from a form of scale invariance. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $c\tau\ll R$ 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 $\Theta$, $\langle\delta\tau^2\rangle_\Theta\simeq\tau\:\!t_p\sim\Theta R\:\!t_P/c$, and angular power spectrum $C_\ell\sim (R\:\!l_P)/\ell^3$ at $\ell\gg1$. 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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