Jae-Weon Lee
It was recently suggested that quantum mechanics and gravity are not fundamental but emerge from information loss at causal horizons. On the basis of the formalism the holographic principle is also shown to arise naturally from the loss of information about bulk fields observed by an outside observer. As an application, Witten's prescription is derived.
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Lorentzian holographic gravity and the time-energy uncertainty principle
本文基于体理论基态假设与时间-能量不确定性原理，启发式推导了非零质量下洛伦兹经典化全息张量网络的在壳方程，为洛伦兹引力提供了一种基于全息原理和经典化的量子力学时间不确定性新图景。
We show in this pedagogical review that far from being "an apparent law of physics that stands by itself" (R. Bousso, Rev. Mod. Phys. 74 (2002), 825-874), the holographic principle (HP) is a straightforward consequence of the quantum information theory of separable systems. It provides a basis for the theories of measurement, time, and scattering. Principles equivalent to the HP appear in both computer science and the life sciences, suggesting that the HP is not just a fundamental principle of physics, but of all of science.
We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincare group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast a la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the repre…
Spacetime foam, also known as quantum foam, has its origin in quantum fluctuations of spacetime. Arguably it is the source of the holographic principle, which severely limits how densely information can be packed in space. Its physics is also intimately linked to that of black holes and computation. In particular, the same underlying physics is shown to govern the computational power of black hole quantum computers.
A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the entropy inside a region is bounded by the area of the boundary of that region. This principle can be called the kinematical holographic principle. We argue that it can be derived from the dynamical …
F. Scardigli and R. Casadio have considered uncertainty principles which take into account the role of gravity and possible existence of extra spatial dimensions. They have argued that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalization and without extra dimensions. Taking into account the additional inevitable source of uncertainty in distance measurement, which is missed in their approach, we show that the holographic properties of the proposed uncertainty principle is recovered in the mod…
What do simple clocks, simple computers, black holes, space-time foam, and holographic principle have in common? I will show that the physics behind them is inter-related, linking together our concepts of information, gravity, and quantum uncertainty. Thus, the physics that sets the limits to computation and clock precision also yields Hawking radiation of black holes and the holographic principle. Moreover, the latter two strongly imply that space-time undergoes much larger quantum fluctuations than what the folklore suggests --- large enough to be detected with modern gravitational-wave inte…
We reply to the comments by P.Midodashvili about our previous paper [1]. We argue that, contrary to the conclusions in Refs. [2,3], the Generalized Uncertainty Principle proposed by Ng and van Dam in Ref. [4] is compatible with the Holographic Principle in spacetimes with extra dimensions only for a very special (and somehow unrealistic) choice of the relation between the size and mass of the clock.
It is likely that the holographic principle will be a consequence of the would be theory of quantum gravity. Thus, it is interesting to try to go in the opposite direction: can the holographic principle fix the gravitational interaction? It is shown that the classical gravitational interaction is well inside the set of potentials allowed by the holographic principle. Computations clarify which role such a principle could have in lowering the value of the cosmological constant computed in QFT to the observed one.
Extending the holographic program of [1], we derive f(R) gravity and the Maxwell equations from the holographic principle, using time-like holographic screen. We find that to derive the Einstein equations and f(R) gravity in a natural holographic approach, the quasi-static condition is necessary. We also find the surface stress tensor and the surface electric current, surface magnetic current on the holographic screen for f(R) gravity and Maxwell's theory, respectively.
In the three-dimensional anti-de Sitter spacetime/two-dimensional conformal field theory correspondence, we derive the imaginary-time path-integral of a non-relativistic particle in the anti-de Sitter bulk space, which is dual to the ground state, from the holographic principle. This derivation is based on (i) the author's previous argument that the holographic principle asserts that the anti-de Sitter bulk space as a holographic tensor network after classicalization has as many stochastic classicalized spin degrees of freedom as there are sites and (ii) the reinterpretation of the Euclidean a…
We present a fully quantum version of the holographic principle in terms of quantum systems, subsystems, and their interactions. We use the concept of environment induced decoherence to prove this principle. We discuss the conditions under which the standard (semi-classical) holographic principle is obtained from this quantum mechanical version.
Renormalization Group Is the Principle behind the Holographic Entropy Cone
本文证明全息熵不等式可通过纠缠楔子深度关系表达，揭示了重整化群在全息原理中的核心作用。
It is suggested that quantum entanglement emerges from the holographic principle stating that all of the information of a region (bulk bits) can be described by the bits on its boundary surface. There are redundancy and information loss in the bulk bits that lead to the nonlocal correlation among the bulk bits. Quantum field theory overestimates the independent degrees of freedom in the bulk. The maximum entanglement in the universe increases as the size of the cosmic horizon and this could be related with the arrow of time and dark energy.
Starting from a critical analysis of recently reported surprisingly large uncertainties in length and position measurements deduced within the framework of quantum gravity, we embark on an investigation both of the correlation structure of Planck scale fluctuations and the role the holographic hypothesis is possibly playing in this context. While we prove the logical independence of the fluctuation results and the holographic hypothesis (in contrast to some recent statements in that direction) we show that by combining these two topics one can draw quite strong and interesting conclusions abou…
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. Such a spectrum obtained earlier in loop quantum gravity (LQG) does not comply with the holographic bound. This bound fixes the Barbero-Immirzi parameter of LQG, and thus leads to the unique result for the spectrum of horizon area.
Two quantum field theories whose Hilbert spaces do not overlap cannot transmit a signal to one another. From this simple principle, we deduce some highly nontrivial consequences for holographic quantum gravity. These include: (1) certain cosmological bounces are forbidden, (2) generic singularities inside black holes cannot be resolved, and (3) traversable wormholes do not exist. At the classical level, this principle rules out certain types of naked singularities and suggests that new singularity theorems should exist.
A remark on quantum measuring systems and the holographic principle
本文从全息原理出发，论证体空间量子态经典化后，量子测量主体的连续性可作为该原理的基本结果。
We apply the holographic principle during the inflationary stage of our universe. Where necessary, we illustrate the analysis in the case of new and extended inflation which, together, typify generic models of inflation. We find that in the models of extended inflation type, and perhaps of new inflation type also, the holographic principle leads to a lower bound on the density fluctuations.
We propose an infrared cut-off for the holographic density which incorporates among others a constant term, that produces the effect of the cosmological constant, improving the results of previously considered holographic models based on local quantities. The inclusion of constant term is interpreted as a natural first approximation for the infrared cutoff which is associated with the vacuum energy, and the additional terms guarantee an appropriate evolutionary scenario that fits the astrophysical observations. Cosmological constraints on the model have been studied using the observational dat…
We discuss the anthropic principle when applied to the holographic dark energy. We find that if the amplitude of the density fluctution is variable, the holographic dark energy fares better than the cosmological constant. More generally, the anthropic predictions agree better with observation for dark energy with $w_\d=p_\d/ρ_\d$ decreasing over time.
We prove a c-theorem for holographic theories.
In the article we present explicit expressions for quantum fluctuations of spacetime in the case of $(4+n)$-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We also consider quantum fluctuations and their holographic properties in ADD model and estimate the typical size and mass of the clock to be used in precise measurements of spacetime fluctuations. Numerical estimations of phase incoherence of light from extra-galactic sources in ADD model are also presented.
We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the…
In this paper, we will propose a universal relation between the holographic complexity (dual to a volume in AdS) and the holographic entanglement entropy (dual to an area in AdS). We will explicitly demonstrate that our conjuncture hold for all a metric asymptotic to AdS$_3$, and then argue that such a relation should hold in general due to the AdS version of the Cavalieri principle. We will demonstrate that it holds for Janus solution, which have been recently been obtained in type IIB string theory. We will also show that this conjecture holds for a circular disk. This conjecture will be use…
The holographic principle provides a deep insight into quantum gravity and resolves the fine-tuning crisis concerning the cosmological constant. Holographic dark energy introduces new ultra-violet (UV) and infra-red (IR) cutoffs into quantum gravity which are necessarily strongly related. The equation of state for dark energy $ω= p/ρ$ is discussed from the holographic point of view. The phantom option of $ω< -1$ is resurrected, as in an earlier cyclic cosmology. Such a cyclic model can, however, equally use the cosmological constant with $ω= -1$.
These TASI lectures review the Holographic principle. The first lecture describes the puzzle of black hole information loss that led to the idea of Black Hole Complementarity and subsequently to the Holographic Principle itself. The second lecture discusses the holographic entropy bound in general space-times. The final two lectures are devoted to the ADS/CFT duality as a special case of the principle. The presentation is self contained and emphasizes the physical principles. Very little technical knowledge of string theory or supergravity is assumed.
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound, or demands a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of edges in LQG is discussed, with the following conclusion. Only under the assumption of partial distinguishability of the edges, the microca…
This lecture reviews the black hole information paradox and briefly appraises some proposed resolutions in view of developments in string theory. It goes on to give an elementary introduction to the holographic principle.
A closed universe containing pressureless dust, more generally perfect fluid matter with pressure-to-density ratio w in the range (1/3, - 1/3), violates holographic principle applied according to the Fischler-Susskind proposal. We show, first for a class of two-fluid solutions and then for the general multifluid case, that the closed universe will obey the holographic principle if it also contains matter with w < - 1/3, and if the present value of its total density is sufficiently close to the critical density. It is possible that such matter can be realised by some form of `quintessence', muc…
It is shown that the first law of thermodynamics and the holographic principle applied to an arbitrary large cosmic causal horizon naturally demand the zero cosmological constant and non-zero dynamical dark energy in the form of the holographic dark energy. Semiclassical analysis shows that the holographic dark energy has a parameter $d=1$ and an equation of state comparable to current observational data, if the entropy of the horizon saturates the Bekenstein-Hawking bound. This result indicates that quantum field theory should be modified at large scale to explain dark energy. The relations a…
A geometry of space that satisfies the holographic principle
该研究针对传统三维空间无穷多点假设下距离不确定性的两种解释，证明其均不符合全息原理，并论证全息原理成立与三维空间各区域仅含有限个点的陈述逻辑等价。
We present a simple derivation of an upper bound on the average size of the true vacuum bubbles at the end of inflation, in models of extended inflation type. The derivation uses the inequality that the total energy inside a given volume must be less than its linear dimensions. The above bound is the same as that obtained earlier, by applying the holographic principle according to Fischler-Susskind prescription. Such a bound leads to a lower bound on the denisty fluctuations.
Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. Einstein's equations are not modified and no selection principle is applied to their solutions; Mach's principle is realized wholly within Einstein's general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Specification of both boundary and bulk stress tensors uniquely specifies the geometry and thereby the inert…
We discuss some recent results in the quest to implement the holographic principle in asymptotically flat spacetimes. In particular we introduce the key ingredients of the candidate dual theory which lives at null infinity and it is invariant under the asymptotic symmetry group of this class of spacetimes.
We aim to establish the holographic principle as a universal law, rather than a property only of static systems and special space-times. Our covariant formalism yields an upper bound on entropy which applies to both open and closed surfaces, independently of shape or location. It reduces to the Bekenstein bound whenever the latter is expected to hold, but complements it with novel bounds when gravity dominates. In particular, it remains valid in closed FRW cosmologies and in the interior of black holes. We give an explicit construction for obtaining holographic screens in arbitrary space-times…
Holographic Action Principle for $T\bar{T}$-deformation
本文探索全息$T\ar{T}$-形变的作用量原理，提出一种考虑有限截面弯曲能的方案来重现形变Liouville理论的作用量，实现了场论与引力两侧作用量的完美匹配。
In quantum mechanics without application of any superselection rule to the set of the observables, a closed quantum system temporally evolves unitarily, and this Lorentzian regime is characterized by von Neumann entropy of exactly zero. In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to an imaginary-time classical stochastic process with real-valued conditional probability density in t…
After a pedagogical overview of the present status of High-Energy Physics, some problems concerning physics at the Planck scale are formulated, and an introduction is given to a notion that became known as ``the holographic principle" in Planck scale physics, which is arrived at by studying quantum mechanical features of black holes.
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 …
Using the holographic entropy proposal for a closed universe by Verlinde, a bound on equations of state for different stages of the universe is obtained. Further exploring this bound, we find that an inflationary universe naturally emerges in the early universe and today's dark energy is also needed in the quantum cosmological scenario.
We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.
The interacting and holographic dark energy models involve two important quantities. One is the characteristic size of the holographic bound and the other is the coupling term of the interaction between dark energy and dark matter. Rather than fixing either of them, we present a detailed study of theoretical relationships among these quantities and cosmological parameters as well as observational constraints in a very general formalism. In particular, we argue that the ratio of dark matter to dark energy density depends on the choice of these two quantities, thus providing a mechanism to chang…
An holographic f(R) gravity model of dark energy is proposed. The correspondence between the f(R) geometrical effective energy density with the holographic density, allows the reconstruction of the f(R) gravity in flat FRW background in the Einstein frame. The proposed infrared cut-off for the holographic energy density depends on two parameters which are fit using the luminosity versus redshift data, allowing a suitable reconstruction in two representative cases of the EoS parameter: for $ω>-1$ and $ω<-1$.
We examine in details Friedmann-Robertson-Walker models in 2+1 dimensions in order to investigate the cosmic holographic principle suggested by Fischler and Susskind. Our results are rigorously derived differing from the previous one found by Wang and Abdalla. We discuss the erroneous assumptions done in this work. The matter content of the models is composed of a perfect fluid, with a $γ$-law equation of state. We found that closed universes satisfy the holographic principle only for exotic matter with a negative pressure. We also analyze the case of a collapsing flat universe.
A possible discrepancy has been found between the results of a neutron interferometry experiment and Quantum Mechanics. This experiment suggests that the weak equivalence principle is violated at small length scales, which quantum mechanics cannot explain. In this paper, we investigated whether the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR), can explain the violation of the weak equivalence principle at small length scales. We also investigated the consequences of the GUP on the Liou…
We discuss the relationship between holographic entropy bounds and gravitating systems. In order to obtain a holographic energy density, we introduce the Bekenstein-Hawking entropy $S_{\rm BH}$ and its corresponding energy $E_{\rm BH}$ using the Friedman equation. We show that the holographic energy bound proposed by Cohen {\it et al} comes from the Bekenstein-Hawking bound for a weakly gravitating system. Also we find that the holographic energy density with the future event horizon deriving an accelerating universe could be given by vacuum fluctuations of the energy density.
Holography and the Swampland: Constraints on Quantum Gravity from Holographic Principles
本文通过全息原理探讨Swampland猜想，揭示全息一致性条件如何映射到量子引力约束，并论证Swampland界限可能源于更深层的全息一致性条件。
More on quantum measuring systems and the holographic principle
本文基于整合信息理论，研究了经典化全息张量网络欧几里得区制下的量子测量系统结构，揭示了复形的体验水平、因果效应结构的直接纠缠以及最大因果效应转移概率矩阵的共存图景。
We propose a new model of holographic dark energy with an action. It is the first time that one can derive a HDE model from the action principle. The puzzles of causality and circular logic about HDE have been completely solved in this model. The evolution of the universe only depends on the present state of the universe, clearly showing that it obeys the law of causality. Furthermore, the use of future event horizon as a present cut-off is not an input but automatically follows from equations of motion. Interestingly, this new model is very similar to the initial one of Li except a new term w…
We introduce the brane-bulk interaction to discuss a limitation of the cosmological Cardy-Verlinde formula which is useful for the holographic description of brane cosmology. In the presence of the brane-bulk interaction, we cannot find the entropy representation of the first Friedmann equation (the cosmological Cardy-Verlinde formula). In the absence of the interaction, the cosmological Cardy-Verlinde formula is established even for the time-dependent charged AdS background. Hence, if there exists a dynamic exchange of energy between the brane and the bulk (that is, if $\tilde T^t~_y \not=0$)…
The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-'t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond's holographic screen, measured in Planck units. The most convincing argument for this principle is…
It is believed that a primary principle of the theory of quantum gravity is the Holographic Principle according to which a physical system can be described only by degrees of freedom living on its boundary. The generalized covariant formulation of the principle considers the entropy content on truncated light-sheets: light-like hypersurfaces of non-positive expansion orthogonally generated from a boundary. When we construct the truncated light-sheets for cosmological observers we find a general expression for the minimum cosmic time interval from the apparent horizon to verify the holographic …
We present strong arguments that the deep structure of the quantum vacuum contains a web of microscopic wormholes or short-cuts. We develop the concept of wormhole spaces and show that this web of wormholes generate a peculiar array of long-range correlations in the patterns of vacuum fluctuations on the Planck scale. We conclude that this translocal structure represents the common cause for both the BH-entropy-area law, the more general holographic principle and the entanglement phenomena in quantum theory. In so far our approach exhibits a common structure which underlies both gravity and qu…
String cosmology is revisited from cosmological viewpoint of holographic principle put forward by `t Hooft, and by Fischler and Susskind. It is shown that the holography requires existence of a `graceful exit' mechanism, which renders the Universe nonsingular by connecting pre- and post-big bang phases smoothly. It is proven that flat Universe is consistent with the holography only if it starts with an absolutely cold and vacuous state. Particle entropy produced during the `graceful exit' apparently saturates the holography bound. Open Universe can always satisfy the holography no matter what …
A scenario is proposed in which the matter-antimatter asymmetry behaves like a seed for the inflationary phase of the universe. The mechanism which makes this scenario plausible is the holographic principle: this scheme is supported by a good prediction of the number of e-folds. It seems that such a mechanism can only work in the presence of a Hagedorn-like phase transition. The issue of the "graceful exit" can also be naturally accounted for.
The notion of a holographic entropy cone has recently been introduced and it has been proven that this cone is polyhedral. However, the original definition was fully geometric and did not strictly require a holographic duality. We introduce a new definition of the cone, insisting that the geometries used for its construction should be dual to states of a CFT. As a result, the polyhedrality of this holographic cone does not immediately follow. A numerical evaluation of the Euclidean action for the geometries that realize extremal rays of the original cone indicates that these are subdominant bu…
A new conception is proposed in Ref.\cite{Verlinde:2010hp,Padmanabhan:2009kr} that gravity is one kind of entropic force. In this letter, we try to discuss its applications to the modified gravities by using three different corrections to the area law of entropy which are derived from the quantum effects and extra dimensions. According to the assumption of holographic principle, the number of bits $N$ which is related to the equipartition law of energy is modified. Then, the modified law of Newton's gravity and the modified Friedmann equations are obtained by using the new notion. By choosing …
The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing cosmological constant.
We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious …
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