Black hole entropy: inside or out?

A trialogue. Ted, Don, and Carlo consider the nature of black hole entropy. Ted and Carlo support the idea that this entropy measures in some sense ``the number of black hole microstates that can communicate with the outside world.'' Don is critical of this approach, and discussion ensues, focusing on the question of whether the first law of black hole thermodynamics can be understood from a statistical mechanics point of view.Comment: 42 pages, contribution to proceedings of Peyresq

Exotic plasma as classical Hall Liquid

A non-relativistic plasma model endowed with an ``exotic'' structure associated with the two-parameter central extension of the planar Galilei group is constructed. Introducing a Chern-Simons statistical gauge field provides us with a self-consistent system; when the magnetic field takes a critical value determined by the extension parameters, the fluid becomes incompressible and moves collectively, according to the Hall law.Comment: 11 pages, LaTex, no figures. Revised version: Some details better explained. To appear in Int. Journ. Mod. Phys.

On a Matrix Model of Level Structure

We generalize the dimensionally reduced Yang-Mills matrix model by adding d=1 Chern-Simons term and terms for a bosonic vector. The coefficient, \kappa of the Chern-Simons term must be integer, and hence the level structure. We show at the bottom of the Yang-Mills potential, the low energy limit, only the linear motion is allowed for D0 particles. Namely all the particles align themselves on a single straight line subject to \kappa^2/r^2 repulsive potential from each other. We argue the relevant brane configuration to be D0-branes in a D4 after \kappa of D8's pass the system.Comment: 1+6 pages, No figure, LaTeX; Minor changes; To appear in Class. Quant. Gra

Optimal phase measurements with pure Gaussian states

We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive local measurement schemes that attain the Heisenberg limit asymptotically. One of them is described by a positive operator-valued measure and its efficiency is exhaustively explored. We also study Gaussian measurement schemes based on phase quadrature measurements. We show that homodyne tomography of the appropriate quadrature attains the Heisenberg limit for large samples. This proves that this limit can be attained with local projective Von Neuman measurements.Comment: 9 pages. Revised version: two new sections added, revised conclusions. Corrected prose. Corrected reference

Black Hole Horizons and Complementarity

We investigate the effect of gravitational back-reaction on the black hole evaporation process. The standard derivation of Hawking radiation is re-examined and extended by including gravitational interactions between the infalling matter and the outgoing radiation. We find that these interactions lead to substantial effects. In particular, as seen by an outside observer, they lead to a fast growing uncertainty in the position of the infalling matter as it approaches the horizon. We argue that this result supports the idea of black hole complementarity, which states that, in the description of the black hole system appropriate to outside observers, the region behind the horizon does not establish itself as a classical region of space-time. We also give a new formulation of this complementarity principle, which does not make any specific reference to the location of the black hole horizon.Comment: Some minor modifications in text and the title chang

Quantum Information and Entropy

Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.Comment: 21 pages, 3 figure

The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.Comment: LaTeX2e. 12 pages, 3 Postscript figures; Added references, some comment

Black Hole Complementarity vs. Locality

The evaporation of a large mass black hole can be described throughout most of its lifetime by a low-energy effective theory defined on a suitably chosen set of smooth spacelike hypersurfaces. The conventional argument for information loss rests on the assumption that the effective theory is a local quantum field theory. We present evidence that this assumption fails in the context of string theory. The commutator of operators in light-front string theory, corresponding to certain low-energy observers on opposite sides of the event horizon, remains large even when these observers are spacelike separated by a macroscopic distance. This suggests that degrees of freedom inside a black hole should not be viewed as independent from those outside the event horizon. These nonlocal effects are only significant under extreme kinematic circumstances, such as in the high-redshift geometry of a black hole. Commutators of space-like separated operators corresponding to ordinary low-energy observers in Minkowski space are strongly suppressed in string theory.Comment: 32 pages, harvmac, 3 figure

Wilson Loops as Precursors

There is substantial evidence that string theory on AdS_5 x S_5 is a holographic theory in which the number of degrees of freedom scales as the area of the boundary in Planck units. Precisely how the theory can describe bulk physics using only surface degrees of freedom is not well understood. A particularly paradoxical situation involves an event deep in the interior of the bulk space. The event must be recorded in the (Schroedinger Picture) state vector of the boundary theory long before a signal, such as a gravitational wave, can propagate from the event to the boundary. In a previous paper with Polchinski, we argued that the "precursor" operators which carry information stored in the wave during the time when it vanishes in a neighborhood of the boundary are necessarily non-local. In this paper we argue that the precursors cannot be products of local gauge invariant operators such as the energy momentum tensor. In fact gauge theories have a class of intrinsically non-local operators which cannot be built from local gauge invariant objects. These are the Wilson loops. We show that the precursors can be identified with Wilson loops whose spatial size is dictated by the UV-IR connection.Comment: 23 pages, no figure

The Landau problem and noncommutative quantum mechanics

The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= \Omega \aleph$ with $\aleph$ defined in the text, then for the value ${\tilde \theta} = 0.22 \times 10^{-11} cm^2$ (that measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find differents values for ${\tilde \theta}$ and, therefore, the possible bounds for ${\tilde \theta}$ should be searched in a physical independent scenario. This last fact could explain the differents bounds for $\tilde \theta$ found in the literature.Comment: This a rewritten and corrected version of our previous preprint hep-th/010517