• 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 as L_p. 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), ħ (Planck’s constant from quantum mechanics), and c (the speed of light, i.e. 299.792 kilometres per second). A quick calculation reveals that L_p is very small indeed: L_p = 1.6 x 10^-33 centimetres.

According to quantum mechanics when distances are shorter than Planck’s distance (i.e. 10^-33 centimetre – 0,000 … 0001, that is 32 zeroes after the decimal point!), we enter a new and strange world. The causal relationship between events breaks down; movements become jerky (‘digital [?]’) rather than smooth (‘analogue [?]’). Time and space may become ‘grainy’ or ‘chunky’ – i.e. digital.

Now, the way in which the Holographic Principle appears in M-theory (sometimes also called U-theory) is much more subtle. In M-theory, we are the shadows on the wall. The ‘room’ is some larger, five-dimensional space-time 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, physicists have recently been trying to think of ways in which we might actually, experimentally ‘probe’ this fifth dimension.

To many people the Holographic Principle and M-theory 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’?

M-theory is a cutting-edge theory of physics that deals with the extension of superstring theory. It is somewhat contentious in the physics community, as it lacks empirical evidence. If ever experimentally verified, M-theory and string theory would represent remarkable advances in science.

To understand M-theory it is necessary first to get some understanding of string theory. For hundreds of years physics has operated on the paradigm that the fundamental particles, like the familiar electron, are point-like or (in mathematical jargon) zero-dimensional. This is known as the standard model of particle physics.

In the standard model of particle physics, particles are considered points moving through space, tracing out a line called the World Line. To take into account the different interactions observed in nature one has to provide particles with more degrees of freedom than only their position and velocity, such as mass, electric charge, colour (which is the ‘charge’ associated with the strong interaction), or spin.

The standard model was designed within a framework known as quantum field theory (QFT), which gives physicists the tools to build theories consistent with both quantum mechanics and the special theory of relativity.

If string theory were to be summed up in a single idea, it is that this assumption is incorrect. Instead, string theory posits that the universe is fundamentally composed of 1-dimensional objects – things that are similar to a string.

These strings would be so small that on even the tiny scale of particles they would seem like points. In string theory, each fundamental particle is created in some sense by different patterns of vibration of the strings. One might ask why physicists have constrained themselves to 0-dimensional points for all this time; the answer is that 1-dimensional objects are much harder to work with and often cause technical problems with causality and violations of special relativity’s mandate that nothing can travel faster than the speed of light.

In 1995, mathematical physicist Edward Witten (1951- ) initiated what has been called the Second Superstring Revolution by introducing M-theory to the world. This theory combines the five different string theories (along with a previously abandoned attempt to unify general relativity and quantum mechanics called ‘eleven-dimensional super-gravity’) into one theory. This is accomplished by knitting together a web of relationships between each of the theories called dualities (specifically, S-duality, T-duality, and U-duality). Each of these dualities provides a way of converting one of the string theories into another.

In the early 1990s, it was shown that the various superstring theories were related by dualities, which allow physicists to relate the description of an object in one string theory to the description of a different object in another theory. These relationships imply that each of the string theories is a different aspect of a single underlying theory (proposed by Witten) and named ‘M-theory’.

M-theory is not yet complete; however, it can be applied in many situations (usually by exploiting string theoretic dualities). The theory of electromagnetism was also in such a state in the mid-19^th century; there were separate theories for electricity and magnetism and, although they were known to be related, the exact relationship was not clear until Scottish physicist James Clerk Maxwell (1831-1879) published his equations, in his 1864 paper, A Dynamical Theory of the Electromagnetic Field.

Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language. However, some scientists have questioned the tangible successes of M-theory given its current incompleteness, and limited predictive power, even after so many years of intense research.