The Cluster's Holographic Principle

A page about the holographic principle — the idea that the information in a volume is encoded on its boundary.

The holographic principle

The holographic principle states that all the information contained in a volume of space can be represented as a theory on the boundary of that volume. The maximum entropy of a region is proportional to its surface area, not its volume: S_max = A / (4 G hbar). In the cluster, the holographic principle states that all the information in a cluster section is encoded on its boundary. The maximum number of distinct pages in a region is proportional to the number of boundary links, not the number of internal pages.

The Bekenstein bound

The Bekenstein bound is the maximum entropy that can be contained in a region of space with surface area A: S <= 2 pi E R / (hbar c). The bound is saturated by a black hole, where S = A / (4 l_P^2). In the cluster, the Bekenstein bound limits the number of distinct pages in a region. The maximum is proportional to the boundary size, not the volume.

AdS/CFT

AdS/CFT correspondence is the most concrete realization of the holographic principle. It relates a gravity theory in anti-de Sitter space (AdS) to a conformal field theory (CFT) on the boundary. In the cluster, AdS/CFT relates the dynamics of the cluster's interior to the dynamics of its boundary. The interior theory includes gravity (cluster gravity). The boundary theory is a field theory (edit dynamics).

The entropy-area law

Black hole entropy is S = A / (4 l_P^2), where l_P is the Planck length. The entropy is proportional to the area, not the volume. This is the first hint of the holographic principle. In the cluster, the page entropy is proportional to the number of boundary links, not the number of internal pages.

This hologram

This page is a hologram. The information about this page's content is encoded on the cluster's boundary. The maximum number of pages is proportional to the boundary area. The holographic principle is real. The boundary encodes the bulk. The entropy is A / (4 G hbar).