Holograms in our world
Raphael Bousso, Geoff Penington
Abstract
In $\mathrm{AdS}/\mathrm{CFT}$, the entanglement wedge $\mathrm{EW}(B)$ is the portion of the bulk geometry that can be reconstructed from a boundary region $B$; in other words, $\mathrm{EW}(B)$ is the hologram of $B$. We extend this notion to arbitrary spacetimes. Given any gravitating region $a$, we define a max- and a min-entanglement wedge, ${e}_{\mathrm{max}}(a)$ and ${e}_{\mathrm{min}}(a)$, such that ${e}_{\mathrm{min}}(a)\ensuremath{\supset}{e}_{\mathrm{max}}(a)\ensuremath{\supset}a$. Unlike their analogs in $\mathrm{AdS}/\mathrm{CFT}$, these two spacetime regions can already differ at the classical level, when the generalized entropy is approximated by the area. All information outside $a$ in ${e}_{\mathrm{max}}(a)$ can flow inwards towards $a$, through quantum channels whose capacity is controlled by the areas of intermediate homology surfaces. In contrast, all information outside ${e}_{\mathrm{min}}(a)$ can flow outwards. The generalized entropies of appropriate entanglement wedges obey strong subadditivity, suggesting that they represent the von Neumann entropies of ordinary quantum systems. The entanglement wedges of suitably independent regions satisfy a no-cloning relation. This suggests that it may be possible for an observer in $a$ to summon information from spacelike related points in ${e}_{\mathrm{max}}(a)$, using resources that transcend the semiclassical description of $a$.