The Holographic Principle and M-theory

February 7, 2005

To them, I said, the truth would be literally nothing but the shadows of the images. -Plato, The Republic (Book VII)

Holography Through the Ages

Plato, the great Greek philosopher, wrote a series of `Dialogues' which summarized many of the things which he had learned from his teacher, who was the philosopher Socrates. One of the most famous of these Dialogues is the `Allegory of the Cave'. In this allegory, people are chained in a cave so that they can only see the shadows which are cast on the walls of the cave by a fire. To these people, the shadows represent the totality of their existence - it is impossible for them to imagine a reality which consists of anything other than the fuzzy shadows on the wall. However, some prisoners may escape from the cave; they may go out into the light of the sun and behold true reality. When they try to go back into the cave and tell the other captives the truth, they are mocked as madmen. Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are all initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality. What is equally interesting is the literal interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls.

The Holographic Principle and Modern Physics

In 1993 the famous Dutch theoretical physicist G. 't Hooft put forward a bold proposal which is reminiscent of Plato's Allegory of the Cave. This proposal, which is known as the Holographic Principle, consists of two basic assertions:

Assertion 1 The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory which `lives' on the boundary of that region. For example, if the region of space in question is the DAMTP Tearoom, then the holographic principle asserts that all of the physics which takes place in the DAMTP Tearoom can be represented by a theory which is defined on the walls of the Tearoom.

Assertion 2 The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area. A Planck area is the area enclosed by a little square which has side length equal to the Planck length, a basic unit of length which is usually denoted Lp. The Planck length is a fundamental unit of length, because it is the parameter with the dimensions of length which can be constructed out of the basic constants G (Newton's constant for the strength of gravitational interactions), (Planck's constant from quantum mechanics), and c (the speed of light). A quick calculation reveals that Lp is very small indeed:

To many people, the Holographic Principle seems strange and counterintuitive: How could all of the physics which takes place in a given room be equivalent to some physics defined on the walls of the room? Could all of the information contained in your body actually be represented by your `shadow'?

Man ponders shadow, or shadow ponders itself?

In fact, the way in which the Holographic Principle appears in M-theory is much more subtle. In M-theory we are the shadows on the wall. The `room' is some larger, five-dimensional spacetime and our four-dimensional world is just the boundary of this larger space. If we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. In fact, people have recently been trying to think of ways in which we might actually experimentally `probe' this fifth dimension. At the heart of many of these exciting ideas is a version of the Holographic Principle known as the adS/CFT correspondence.

Are YOU a Hologram? M-theory and the adS/CFT correspondence

More- http://www.damtp.cam.ac.uk/user/gr/public/holo/