Bousso's holographic bound

Lore & Background

Raphael Bousso showed that the spacelike entropy bound is violated in many dynamical settings, such as when the entropy of a collapsing star inside a black hole exceeds its surface area, and due to relativistic length contraction, ordinary thermodynamic systems can be enclosed in an arbitrarily small area. To preserve the holographic principle, Bousso proposed a different law: the covariant entropy bound, or Bousso bound, which does not follow from black hole physics. Its central geometric object is a lightsheet, defined as a region traced out by non-expanding light-rays emitted orthogonally from an arbitrary surface B. For example, if B is a sphere in Minkowski space, there are two lightsheets generated by past or future directed light-rays towards the interior. If B is an anti-trapped sphere in an expanding universe, both lightsheets are directed towards the past. If B is a trapped surface, such as a collapsing star's surface, the lightsheets are directed to the future.

Reader's Guide

The Bousso bound evades all known counterexamples to the spacelike bound and was proven to hold when entropy is approximately a local current under weak assumptions. In weakly gravitating settings, it implies the Bekenstein bound and admits a formulation provable in any relativistic quantum field theory. The lightsheet construction can be inverted to construct holographic screens for arbitrary spacetimes. A more recent proposal, the quantum focusing conjecture, implies the original Bousso bound and can be viewed as a stronger version. In the limit where gravity is negligible, the quantum focusing conjecture predicts the quantum null energy condition, which relates local energy density to a derivative of entropy, later proven to hold in any relativistic quantum field theory such as the Standard Model. The Bousso bound thus serves as a foundational element in the study of quantum gravity and holography.

Did You Know?

• The Bousso bound captures a fundamental relation between quantum information and the geometry of space and time.
• The spacelike entropy bound fails in cosmology; for example, it does not hold true in our universe.
• The Fischler–Susskind holographic bound failed in certain situations such as closed or collapsing cosmologies and was generalized by Bousso into the covariant entropy bound.