Black Holes and the Structure of Space-Time

Juan Maldacena,
Institute for Advanced Study,
School of Natural Sciences Princeton,
New Jersey 08540, USA

Русский перевод

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• 1. Black Holes
• 2. Black Holes and Quantum Mechanics
• 3. Solving These Puzzles
• 4. The Structure of Space-Time
• 5. Bibliography

4. The Structure of Space-Time

These ideas have a very profound implications for the structure of space-time. Notice that we start with a particle theory on the boundary, which has 2+1 space+time dimensions and we end up with a gravitational theory in 3+1 dimensions. One of the dimensions of space-time has appeared out of nowhere! This dimension appears from the interactions of the particles in 2+1 dimensions.

This is saying that space-time is not a fundamental entity. It is a derived concept, valid at long distances. Let me give an analogy. Suppose that we are looking at a lake. We can see water waves, we can see small insects walking on the surface, etc. The surface of the lake looks like a very sharp and well defined concept. In fact we can write equations governing the propagation of the waves and so on. Suppose that now we would like to understand the structure of the surface at very short distances. At microscopic distances this surface is not very sharp. Once we look at the water with atomic resolution, we see that there are water molecules coming and leaving the water constantly and that it is hard to define exactly where the boundary is located. At short distances the surface of the lake is simply not a well defined concept, we need to talk about the individual molecules and describe what they are doing. Similarly, space-time ceases to be a well defined concept at short distances. The well defined concept are the particles living on the boundary and space-time only emerges as a collective property.

If we lived in a negatively curved space, all we would need to do to understand our universe would be to understand the theory that lives on the boundary.

Interestingly, we do not live in a negatively curved space-time, actually on large scales our universe looks more like a positively curved space-time. As of now, we do not know whether a similar description exists for positively curved space-times. Such a description, if it existed, would solve the problem of the big bang singularity.

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