Introduction

The concept of extra dimensions originated in the 1920s as a serious approach to unifying electromagnetism and gravity by Theodor Kaluza and Oscar Klein. Just as Einstein introduced the extra dimension of time to create the idea of space-time, the four dimensional fabric of our universe, so Kaluza and Klein proposed that there might in fact be five dimensions. The reason for extension to higher dimensions was geometrical. The mathematics of Kaluza-Klein theory matches reality more closely if an extra dimension is included in the calculations. However, in subsequent years, it was found that the theory suffered from extreme faults, thus the idea of a higher number of dimensions was abandoned until the rise of superstring theory in the 1980s. 

Superstring theory is a combination of string theory and supersymmetry, and so far is the only viable way of combining general relativity and quantum mechanics, the cornerstones of modern physics. Therefore, it will be necessary to give a general overview of these theories to show their conflicting points and to show how superstring theory resolves some problems.

It emerged that superstring theory requires one dimension of time and nine of space for the mathematics involved to be functional. Therefore, to correborate string theory, the physics community must endeavour to detect these possible higher dimensions. The difficulty of this task and the accuracy of the required experiments will be discussed. 

Unfortunately, the adaptation to ten dimensions allowed five different string theories to be mathematically possible, none of which was a perfect approximation for the universe we observe. This cast doubt on the validity of string theory until the advent of a new eleven-dimensional theory, M-theory, which emcompassed all five possible string theories. 

M-theory is as yet incomplete, but its implications are astounding. It may help to explain many of the problems facing cosmologists and particle physicists in the future, such as dark matter, the cosmological constant and the search for a plausible Grand Unification Theory (GUT). Therefore, this report aims not only to explain the basic concept but also to assess what level of experimentation is needed to obtain evidence for any higher dimension designated by M-theory. 


The possibility of extra dimensions

Intuition tells us that there are three dimensions of space and one of time, making it difficult to conceptualise how six extra dimensions could manifest themselves in reality. If these dimensions do exist, why do we not experience them? Brian Greene gives an answer to these salient points in "The Elegant Universe" (ref. 1) by drawing an analogy to the surface of a garden hose.

Imagine viewing an unfurled taut garden hose from a great distance. When considering an ant on the hose, only one coordinate (along the length of the hose) is needed to specify the ant's position. This is because the width of the hose looks negligible from the viewing point, so that effectively the hose has become a line. Nevertheless, the ant, restricted to the surface of the hose, knows that there is another dimension it can move in: the curvature of the hose. To the human observer, it is as though the extra dimension is curled up within every point on the line.

An extension of this analogy must be made for three-dimensional space in order to imagine how higher dimensions could exist. For every point in our three-dimensional universe,there must be curled-up dimensions which must be very small in relation to human scale to have avoided perception. 

In fact, since at least six extra dimensions are necessary, current opinion is that for every point in space-time there is attached a Calabi-Yau shape: a curled-up six-dimensional structure on the scale of the Planck length. This is about (ten to the ****whatever) and is the scale below which constant fluctuations in the fabric of time become significant, causing many conflicting theoretical problems. These inconsistencies are due to the contradictory natures of general relativity and quantum mechanics, which were combined to form string theory.  


Superstring Theory

Superstring theory is string theory that incorporates the principle of supersymmetry. String theory arose from the need to unify gravity with the weak, strong and electromagnetic forces as the incompatibility of quantum theory and general relativity became apparent. 

Quantum theory versus general relativity

          
Quantum mechanics has been used to unify the weak, strong and electromagnetic forces successfully. Nevertheless, until superstring theory, a quantum theory of gravity remains elusive. This is because quantum theory is non-deterministic and probability-based, whereas general relativity, the theory we use to understand gravitational forces, is decidedly based in classical (Newtonian) physics. 

The basic principle of quantum theory is that all particles obey a wave function. The probability of a particle existing at any point is given by the square of the value of its wave function at that point. Thus all particles display wave-like properties. Consequently, the outcome of an event can never be absolutely deteremined, only a measure of probability of possible outcomes can be calculated. 

Quantum mechanics is only important on a microscopic scale since the microscopic world contains a huge number of particles    so that their overall behaviour follows classical mechanics. General relativity is used on a cosmological scale, since gravity is negligible in comparison to the other fundamental forces at short ranges. Therefore it is a classical theory. Also, gravity poses a problem when attempting to achieve a theory that unifies the forces as it is so mysteriously weak. 

General relativity was born when Einstein introduced the idea that what we concieve of as space is actually four-dimensional space-time. Matter distorts the fabric of space-time so that gravitational forces are nearly due to the curvature of the surroundings. Somehow, this model has to be made compatible with the interpretation of the fundamental forces as a result of the exchange of their respective force particles, widely accepted by quantum theory and supersymmetry. Previous quantum gravity theories have proved to be inadequate since the calculations kept stumbling upon inponderable infinities, making the equations unworkable or resulting in outcomes with probabilities of less than 0 or greater than 1, a sure sign that the theories were unfeasible at scales less than the Planck length.