The holographic principle

TLDR

The area of a surface limits the information content of adjacent spacetime, suggesting a holographic principle whose origin in fundamental degrees of freedom and quantum gravity remains to be explained. The authors review the developments leading to the entropy bound and survey successes and challenges in implementing the holographic principle. They discuss the construction of light‑sheets that associate spacetime regions to surfaces, explain how the entropy bound is tested, and demonstrate its validity across many examples. The bound is tested and validated in many examples, revealing a universal relation between geometry and information.

Abstract

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.