Juan Maldacena,
Institute for Advanced Study,
School of Natural Sciences Princeton,
New Jersey 08540, USA
Скачать видеозапись (avi): Часть 1 (160 Мб), Часть 2 (170 Мб), Часть 3 (195 Мб)
- 1. Black Holes
- 2. Black Holes and Quantum Mechanics
- 3. Solving These Puzzles
- 4. The Structure of Space-Time
- 5. Bibliography
3. Solving These Puzzles
3.1. String Theory
Quantum mechanics and gravity are two theories that do not get along very well. Physicists have been trying to put them together in a consistent theory. For practical purposes in our everyday life it is not very important to develop a theory of quantum gravity because most physical phenomena that we encounter are such that we can neglect the effects of gravity or we can neglect the effects of quantum mechanics. On the other hand, if we want to understand the origin of the universe at the initial moments of the big bang, then we need a consistent theory. In the beginning both quantum mechanics and gravity are important. This is one of the main motivations for finding a theory of quantum gravity.
String theory is a theory of quantum gravity. It manages to put together quantum mechanics and gravity. We do not know whether it is the right theory, but it is the best candidate that we have. It is called "string" theory for reasons that are not important for our discussion here. The important thing is that it is a theory of quantum gravity.
3.2. Black Holes in String Theory
In string theory it is possible to consider black holes. In some special circumstances, it is possible to find a microscopic description for these black holes. For technical reasons it is easier to understand black holes that live in a space-time with constant negative curvature. These space-times are the simplest generalization of flat space. Flat space has zero curvature. An example of a space with positive curvature is the surface of a sphere. In figure 1 you can see a "map" of a two dimensional space with constant negative curvature. We can also consider space-times with zero, positive or negative curvature. Space-times with negative curvature effectively have a boundary at infinity. A particle can go to infinity and back in finite time, this is possible only because time flows differently at different positions, as we go far away time flows faster.
In 1997 I conjectured that the whole gravitational physics in this space can be described by a theory of ordinary particles on the boundary. This was further developed by S. Gubser, I. Klebanov, A. Polyakov, E. Witten, and many other people. The details of this are somewhat involved, but the crucial point is the following: the gravity theory, whose underlying dynamics we did not quite understand, becomes equivalent to an ordinary particle theory which we understand. More importantly, this boundary theory obeys the principles of quantum mechanics.
A black hole in the interior becomes a thermal state in terms of the particles at the boundary. The entropy of the black hole is just the entropy of these particles. The "elementary quanta" of spacetime geometry are the particles living at the boundary.
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Fig. 1: This drawing by Escher tries to capture the geometry of hyperbolic space. It is a projection of hyperbolic space onto a disk. Each figure has the same proper size, that is to say in the original hyperbolic space they all look the same size, but due to the distorting effects of the projection, they get smaller as we go to the boundary of the disk. In fact the boundary of the disk is an infinite distance away from any point in the interior. A similar distortion is present when we represent a world map on a plane. With the standard projection the region near the poles look disproportionately big on the map. In this projection of hyperbolic space, we have the opposite effect. Hyperbolic space is infinite in size, but it looks finite in the drawing because the region near the boundary has been re-scaled by a very large factor.
