By Anna Vaughan, Australian National University
It has long been realised that mathematics provides a beautiful and powerful framework to describe the universe in which we live. From Newton’s development of classical mechanics up until the present day, mathematicians have been trying to find a mathematical theory which is able to describe everything in the universe, often known as a ‘theory of everything’. Such a theory must be able to describe the four fundamental types of forces in the universe – electromagnetism, the weak nuclear force, the strong nuclear force and gravity, as well as how every type of particle behaves when interacting through these forces. Given that mathematicians have been working on this problem for hundreds of years it is surprising to learn that despite numerous attempts a complete self consistent ‘theory of everything’ still hasn’t been developed. One of the key problems that any potential mathematical theory of the universe faces is that it must be able to work on both an extremely small scale and an extremely large scale. We already have a good theory of the very small, known as quantum mechanics, and also of the very large given by Einstein’s general relativity. Unfortunately however, these two theories seem in their current state to be incompatible.
This is where string theory comes in. All previous attempts at fixing this problem have had one thing in common – they are all particle theories. This means that the fundamental objects or ‘building blocks’ of the theory are various types of point like particles which can be combined to form more interesting objects. String theory has one major difference- instead of point like particles, the building blocks are extended one dimensional objects known as ‘strings’. These aren’t difficult to visualize – just imagine an ordinary length of string, but on a scale far far smaller than an atom. If you take an ordinary piece of string an shake one end it will oscillate up an down as waves travel along it. Going back to the strings in string theory, these also vibrate with various wave patterns, and it turns out that these different vibration patterns of the string correspond to different types of particles as predicted by experiments. Though it may seem like a trivial distinction that string theory is built up out of these extended ‘strings’ while a particle theory is built up out of points it turns out to have huge consequences in the mathematical description, and allows string theory to give a description of both general relativity and quantum mechanics.
There is still a lot of work to be done before string theory can be considered a true theory of the universe however – currently there are five separate self consistent string theories. If string theory is to be a ‘theory of everything’ it obviously needs to just be one theory giving one set of laws of physics, so it has been conjectured that these string theories are all special cases of some ultimate theory known as M-theory. One way of studying these five theories is to examine the relationships or dualities between them. In physics, a duality occurs when two mathematically distinct theories give the same physical laws. These five string theories turn out to have a number of dualities between them, allowing their relationships to be studied and giving us a hint as to what this ultimate M-theory may look like.
Anna Vaughan was one of the recipients of a 2015/16 AMSI Vacation Research Scholarship.