Modular Fluctuations from Shockwave Geometries

TL;DR

This paper shows that modular fluctuations in Minkowski space, which obey an area law, can be physically explained by shockwaves generated from vacuum fluctuations, linking quantum field theory and spacetime geometry.

Contribution

It demonstrates that modular fluctuations and their area law in Minkowski space can be derived from shockwaves caused by vacuum fluctuations, connecting quantum and geometric aspects.

Findings

Modular fluctuations follow an area law in Minkowski space.

Shockwaves from vacuum fluctuations reproduce the modular area law.

Vacuum fluctuations are constrained by light-ray operator commutation relations.

Abstract

Modular fluctuations have previously been shown to obey an area law $\langle \Delta K^2 \rangle = \langle K \rangle = {A}/{4 G_N}$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d-$dimensionsal Minkowski space, can be reproduced from shockwaves arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in light-ray operators, of the same form postulated by 't Hooft in the context of black hole horizons.