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Leonard Susskind

Publications and source records attributed to Leonard Susskind.

At least 91 records · Page 5Linked to original sources
arXiv2012

Eternal Symmetree

In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously analyze its properties. Although simple and easy to solve, it has a rich mathematical structure underlying it. Despite the discreteness of the space-time the theory exhibits an unexpected non-perturbative analog of conformal symmetry that acts on the boundary of the geometry. The symmetry is rooted in the mathematical properties of trees, p-adic numbers, and ultrametric spaces; and in the physical property of detailed balance. We provide self-contained elementary explanations of the unfamiliar mathematical concepts, which have have also appeared in the study of the p-adic string. The symmetry acts on a huge collection of very low dimensional "multiverse fields" that are not associated with the usual perturbative degrees of freedom. They are connected with the late-time statistical distribution of bubble-universes in the multiverse. The conformal symmetry which acts on the multiverse fields is broken by the existence of terminal decays - to hats or crunches - but in a particularly simple way. We interpret this symmetry breaking as giving rise to an arrow of time. The model is used to calculate statistical correlations at late time and to discuss the measure problem. We show that the natural cutoff in the model is the analog of the so-called light-cone-time cutoff. Applying the model to the problem of the cosmological constant, we find agreement with earlier work.

hep-th↗
arXiv2011

The Multiverse Interpretation of Quantum Mechanics

We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

hep-th↗
arXiv2011

Addendum to Fast Scramblers

This paper is an addendum to [arXiv:0808.2096] in which I point out that both de Sitter space and Rindler space are fast scramblers. This fact naturally suggests that the holographic description of a causal patch of de Sitter space may be a matrix quantum mechanics at finite temperature. The same can be said of Rindler space. Some qualitative features of these spaces can be understood from the matrix description.

hep-th↗
arXiv2010

Crunches, Hats, and a Conjecture

Our purpose in this paper is to discuss criteria for the existence of a precise dual description of a cosmology. A number of exact descriptions exist for flat and anti de Sitter backgrounds and possibly for open FRW universes that nucleate in an eternally inflating background. In addition duals have been proposed for de Sitter space, and for crunching FRW bubbles with negative cosmological constant. In the latter cases there is reason to think the dualities are at best approximate. One of our primary purposes is to analyze the quality of these descriptions, i.e., how exact they can be made. Maldacena's recent discussion of dualities involving crunching FRW cosmologies provides an opportunity for exploring some of these question.

hep-th↗
arXiv2010

On the Topological Phases of Eternal Inflation

Eternal inflation is a term that describes a number of different phenomena which have been classified by Winitzki. According to Winitzki's classification these phases can be characterized by the topology of the percolating structures in the inflating, "white," region. In this paper we discuss these phases, the transitions between them, and the way they are seen by a "Census Taker"; a hypothetical observer inside the non-inflating, "black," region. We discuss three phases that we call, "black island," "tubular," and "white island." The black island phase is familiar, comprised of rare Coleman De Luccia bubble nucleation events. The Census Taker sees an essentially spherical boundary, described by the conformal field theory of the FRW/CFT correspondence. In the tubular phase the Census Taker sees a complicated infinite genus structure composed of arbitrarily long tubes. The white island phase is even more mysterious from the black side. Surprisingly, when viewed from the non-inflating region this phase resembles a closed, positively curved universe which eventually collapses to a singularity. Nevertheless, pockets of eternal inflation continue forever. In addition there is an "aborted" phase in which no eternal inflation takes place. Rigorous results of Chayes, Chayes, Grannan and Swindle establish the existence of all of these phases, separated by first order transitions, in Mandelbrot percolation, a simple model of eternal inflation.

hep-th↗
arXiv2010

Census Taking in the Hat: FRW/CFT Duality

In this paper a holographic description of eternal inflation is developed. We focus on the description of an open FRW universe that results from a tunneling event in which a false vacuum with positive vacuum energy decays to a supersymmetric vacuum with vanishing cosmological constant. The observations of a "Census Taker" in the final vacuum can be organized into a holographic dual conformal field theory that lives on the asymptotic boundary of space. We refer to this bulk-boundary correspondence as FRW/CFT duality. The dual CFT is a Euclidean two-dimensional theory that includes a Liouville 2-D gravity sector describing geometric fluctuations of the boundary. The RG flow of the theory is richer than in the ADS/CFT correspondence, and generates two space-time dimensions--one space-like and one time-like. We discuss a number of phenomena such as bubble collisions, and the Garriga, Guth, Vilenkin "persistence of memory," from the dual viewpoint.

hep-th↗
arXiv2008

Fast Scramblers

We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom; pairwise interactions would be an example. Based on previous work, we conjecture: 1) The most rapid scramblers take a time logarithmic in the number of degrees of freedom. 2) Matrix quantum mechanics (systems whose degrees of freedom are n by n matrices) saturate the bound. 3) Black holes are the fastest scramblers in nature. The conjectures are based on two sources, one from quantum information theory, and the other from the study of black holes in String Theory.

hep-th↗
arXiv2008

Future Foam

We study pocket universes which have zero cosmological constant and non-trivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.

hep-th↗
arXiv2007

The Census Taker's Hat

If the observable universe really is a hologram, then of what sort? Is it rich enough to keep track of an eternally inflating multiverse? What physical and mathematical principles underlie it? Is the hologram a lower dimensional quantum field theory, and if so, how many dimensions are explicit, and how many "emerge?" Does the Holographic description provide clues for defining a probability measure on the Landscape? The purpose of this lecture is first, to briefly review a proposal for a holographic cosmology by Freivogel, Sekino, Susskind, and Yeh (FSSY), and then to develop a physical interpretation in terms of a "Cosmic Census Taker:" an idea introduced in reference [1]. The mathematical structure--a hybrid of the Wheeler DeWitt formalism and holography--is a boundary "Liouville" field theory, whose UV/IR duality is closely related to the time evolution of the Census Taker's observations. That time evolution is represented by the renormalization-group flow of the Liouville theory. Although quite general, the Census Taker idea was originally introduced in \cite{shenker}, for the purpose of counting bubbles that collide with the Census Taker's bubble. The "Persistence of Memory" phenomenon discovered by Garriga, Guth, and Vilenkin, has a natural RG interpretation, as does slow roll inflation. The RG flow and the related C-theorem are closely connected with generalized entropy bounds.

hep-th↗
arXiv2006

Holographic Views of the World

This note has been written on the occasion of Gerard 't Hooft's 60th birthday celebration. It is not a technical paper but just a collection of discussions that the three authors had with Gerard, mostly in relation with the idea of holography and aspects of quantum black hole physics.

physics.hist-ph↗
arXiv2006

A Holographic Framework for Eternal Inflation

In this paper we provide some circumstantial evidence for a holographic duality between bubble nucleation in an eternally inflating universe and a Euclidean conformal field theory. The holographic correspondence (which is different than Strominger's dS/CFT duality) relates the decay of (3+1)-dimensional de Sitter space to a two-dimensional CFT. It is not associated with pure de Sitter space, but rather with Coleman-De Luccia bubble nucleation. Alternatively, it can be thought of as a holographic description of the open, infinite, FRW cosmology that results from such a bubble. The conjectured holographic representation is of a new type that combines holography with the Wheeler-DeWitt formalism to produce a Wheeler-DeWitt theory that lives on the spatial boundary of a k=-1 FRW cosmology. We also argue for a more ambitious interpretation of the Wheeler-DeWitt CFT as a holographic dual of the entire Landscape.

hep-th↗
arXiv2005

Observational Consequences of a Landscape

In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the "overshoot" problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.

hep-th↗
arXiv2005

Wormholes and Time Travel? Not Likely

Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental principles physics, namely local energy conservation and the energy-time uncertainty principle.

gr-qc↗
arXiv2005

Rebuttal to a Paper on Wormholes

In a recent paper on wormholes (gr-qc/0503097), the author of that paper demonstrated that he didn't know what he was talking about. In this paper I correct the author's naive erroneous misconceptions.

gr-qc↗
arXiv2004

A Framework for the Landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background and contains metastable de Sitter space as an intermediate state.

hep-th↗
arXiv2004

Supersymmetry Breaking in the Anthropic Landscape

In this paper I attempt to address a serious criticism of the ``Anthropic Landscape" and "Discretuum" approach to cosmology, leveled by Banks, Dine and Gorbatov. I argue that in this new and unfamiliar setting, the gauge Hierarchy may not favor low energy supersymmetry. In a added note some considerations of Douglas which substantially strengthen the argument are explained.

hep-th↗