Another key insight into string theory comes from the holographic principle, which relates a theory in space to a theory defined only on the boundary of that space. The holographic principle isn’t strictly an aspect of string theory (or M-theory), but applies more generally to theories about gravity in any sort of space. Because string theory is such a theory, some physicists believe the holographic principle will lie at the heart of it.
Capturing multidimensional information on a flat surface
It turns out, as shown by Gerard ‘t Hooft in 1993 (and developed with much help from Leonard Susskind), the amount of “information” a space contains may be related to the area of a region’s boundary, not its volume. (In quantum field theory, everything can be viewed as information.) In short, the holographic principle amounts to the following two postulates:
A gravitational theory describing a region of space is equivalent to a theory defined only on the surface area that encloses the region.
The boundary of a region of space contains at most one piece of information per square Planck length.
In other words, the holographic principle says that everything that happens in a space can be explained in terms of information that’s somehow stored on the surface of that space. For example, picture a 3-dimensional space that resides inside the 2-dimensional curled surface of a cylinder, as in Figure 11-2. You reside inside this space, but perhaps some sort of shadow or reflection resides on the surface.
Figure 11-2:
The holographic principle says information about a space is contained on the surface.
Now, here’s a key aspect of this situation that’s missing from our example: A shadow contains only your outline, but in ‘t Hooft’s holographic principle, all of the information is retained. (See the nearby sidebar, “Inside a hologram.”)
Another example, and one that is perhaps clearer, is to picture yourself inside a large cube. Each wall of the cube is a giant television screen, which contains images of the objects inside the cube. You could use the information contained on the 2-dimensional surface of the space to reconstruct the objects within the space.
Again, though, this example falls short because not all of the information is encoded. If I were to have objects blocking me in all six directions, my image wouldn’t be on any of the screens. But in the holographic principle view of the universe, the information on the surface contains all the information that exists within the space.
Connecting the holographic principle to our reality
The holographic principle is totally unexpected. You’d think that the information needed to describe a space would be proportional to the volume of that space. (Note that in the case of more than three space dimensions, “volume” isn’t a precise term. A 4-dimensional “hypervolume” would be length times width times height times some other space direction. For now, you can ignore the time dimension.)
Inside a hologram
A hologram is a 2-dimensional image that contains all the 3-dimensional information of an object. When viewing a hologram, you can tilt the image and see the orientation of the shape move. It’s as if you see the object in the picture from a different angle. The process of making a hologram is called holography.
This is achieved through the interference patterns in light waves. The process involves using a laser — so all of the light has exactly the same wavelength — and reflecting it off of the object onto a film. (When I performed this experiment in my college Optics class, I used a small plastic horse.)
As the light strikes the film, it records interference patterns that, when properly developed, allow the film to encode the information about the 3-dimensional shape that was holographed. The encoded information then has to be decoded, which means the laser light again has to be shown through the film in order to see the image.
“White light” holograms exist, which don’t need laser light to view them. These are the holograms that you’re most familiar with, which manifest their image in ordinary light.
You can consider this principle in two ways:
Our universe is a 4-dimensional space that is equivalent to some 3-dimensional boundary.
Our universe is a 4-dimensional boundary of a 5-dimensional space, which contains the same information.
In scenario 1, we live in the space inside the boundary, and in scenario 2, we are on the boundary, reflecting a higher order of reality that we don’t perceive directly. Both theories have profound implications about the nature of the universe we live in.
Considering AdS/CFT correspondence
Though presented in 1993, even Leonard Susskind says he thought it would be decades before there would be any way to confirm the holographic principle. Then, in 1997, Argentinean physicist Juan Maldacena published a paper, inspired by the holographic principle, that proposed something called the anti-de Sitter/conformal field theory correspondence, or AdS/CFT correspondence, which brought the holographic principle to center stage in string theory.
In Maldacena’s AdS/CFT correspondence, he proposed a new duality between a gauge theory defined on a 4-dimensional boundary (three space dimensions and one time dimension) and a 5-dimensional region (four space dimensions and one time dimension). In essence, he showed that there are circumstances in which the holographic principle scenario 2 is possible (see the preceding section).
As usual in string theory, one of those conditions is unbroken supersymmetry. In fact, the theoretical world he studied had the most amount of supersymmetry possible — it was maximally supersymmetrical.
Another condition was that the 5-dimensional region was something called an anti-de Sitter space, which means it had negative curvature. Our universe (at least at present) is more similar to a de Sitter space, as mentioned in topic 9. As such, it hasn’t yet been proved that the AdS/CFT correspondence (or something similar) specifically applies to our own universe (though thousands of papers have been written on the subject).
Even if the duality turns out not to be completely true, a growing body of theoretical work supports the idea that there is some sort of correspondence between string theory and gauge theory, even if only at some low levels of approximation. Calculations that are hard in one version of the theory may actually be easy in the other one, meaning that it may be crucial in figuring out how to complete the theory. This has helped support the idea that the holographic principle may ultimately prove to be one of the fundamental principles of M-theory.
The holographic principle, and specifically the AdS/CFT correspondence, may also help scientists further understand the nature of black holes. The entropy (or disorder) of a black hole is proportional to the surface area of the black hole, not its volume. This is one of the arguments in support of the holographic principle, because it’s believed that it would offer further physical explanation of black holes.
