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The Bousso bound captures a fundamental relation between quantum information and the geometry of space and time. It appears to be an imprint of a unified theory that combines quantum mechanics with Einstein's general relativity. [1] The study of black hole thermodynamics and the information paradox led to the idea of the holographic principle: the entropy of matter and radiation in a spatial region cannot exceed the Bekenstein–Hawking entropy of the boundary of the region, which is proportional to the boundary area. However, this "spacelike" entropy bound fails in cosmology; for example, it does not hold true in our universe. [2]
Raphael Bousso showed that the spacelike entropy bound is violated more broadly in many dynamical settings. For example, the entropy of a collapsing star, once inside a black hole, will eventually exceed its surface area. [3] Due to relativistic length contraction, even ordinary thermodynamic systems can be enclosed in an arbitrarily small area. [1]
To preserve the holographic principle, Bousso proposed a different law, which does not follow from black hole physics: the covariant entropy bound [3] or Bousso bound. [4] [5] 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 at a moment of time in Minkowski space, then there are two lightsheets, generated by the past or future directed light-rays emitted towards the interior of the sphere at that time. If B is a sphere surrounding a large region in an expanding universe (an anti-trapped sphere), then there are again two light-sheets that can be considered. Both are directed towards the past, to the interior or the exterior. If B is a trapped surface, such as the surface of a star in its final stages of gravitational collapse, then the lightsheets are directed to the future.
The Bousso bound evades all known counterexamples to the spacelike bound. [1] [3] It was proven to hold when the entropy is approximately a local current, under weak assumptions. [4] [5] [6] In weakly gravitating settings, the Bousso bound implies the Bekenstein bound [7] and admits a formulation that can be proven to hold in any relativistic quantum field theory. [8] The lightsheet construction can be inverted to construct holographic screens for arbitrary spacetimes. [9]
A more recent proposal, the quantum focusing conjecture, [10] implies the original Bousso bound and so can be viewed as a stronger version of it. In the limit where gravity is negligible, the quantum focusing conjecture predicts the quantum null energy condition, [11] which relates the local energy density to a derivative of the entropy. This relation was later proven to hold in any relativistic quantum field theory, such as the Standard Model. [11] [12] [13] [14]
The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region – such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string theoretic interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Susskind said, "The three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978, that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence.
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In physics, the Bekenstein bound is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite.
Christopher T. Hill is an American theoretical physicist at the Fermi National Accelerator Laboratory who did undergraduate work in physics at M.I.T., and graduate work at Caltech. Hill's Ph.D. thesis, "Higgs Scalars and the Nonleptonic Weak Interactions" (1977) contains one of the first detailed discussions of the two-Higgs-doublet model and its impact upon weak interactions. His work mainly focuses on new physics that can be probed in laboratory experiments or cosmology.
Subir Sachdev is Herchel Smith Professor of Physics at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018, and was elected Foreign Member of the Royal Society ForMemRS in 2023. He was a co-editor of the Annual Review of Condensed Matter Physics 2017–2019, and is Editor-in-Chief of Reports on Progress in Physics 2022-.
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Raphael Bousso is a theoretical physicist and cosmologist. He is a professor at the Berkeley Center for Theoretical Physics in the Department of Physics, UC Berkeley. He is known for the Bousso bound on the information content of the universe. With Joseph Polchinski, Bousso proposed the string theory landscape as a solution to the cosmological constant problem.
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A black hole firewall is a hypothetical phenomenon where an observer falling into a black hole encounters high-energy quanta at the event horizon. The "firewall" phenomenon was proposed in 2012 by physicists Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully as a possible solution to an apparent inconsistency in black hole complementarity. The proposal is sometimes referred to as the AMPS firewall, an acronym for the names of the authors of the 2012 paper. The potential inconsistency pointed out by AMPS had been pointed out earlier by Samir Mathur who used the argument in favour of the fuzzball proposal. The use of a firewall to resolve this inconsistency remains controversial, with physicists divided as to the solution to the paradox.
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Veronika E. Hubeny is an American physicist and academic who specialises in string theory and quantum gravity. Since 2015, she has been a professor in the Department of Physics of University of California, Davis. Previously, Hubeny was Professor of Physics at Durham University, where she had worked from 2005 to 2015. From January to April 2014, she was a member of the Institute for Advanced Study in Princeton, New Jersey. In 2019, she was selected as a fellow of the International Society on General Relativity and Gravitation.
A. W. Peet is a professor of physics at the University of Toronto. Peet's research interests include string theory as a quantum theory of gravity, quantum field theory and applications of string theory to black holes, gauge theories, cosmology, and the correspondence between anti-de Sitter space and conformal field theories.
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