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Welcome to the 11th Dimension

Dr Duncan L Copp

November 2003

String theory is a theory that attempts to answer everything – everything that we observe in the Universe, both on the large-scale and on the subatomic scale. In doing so, the theory must account for the unique behaviour of the fundamental particles and the four fundamental forces that have been measured; it must unify the theories of general relativity and quantum mechanics; and it must explain the birth of the Universe and all that we see within it. These issues are not new to scientists, but for the first time in a hundred years, physicists think they are on the scent of an answer – an answer that has the strangest of consequences.

Nobel Prize winner Steven Weinberg admires string theorists, but says he wouldn't touch it himself:

'They're trying to take the next big step by pure mathematical reasoning, and it's extraordinarily difficult. I hope they succeed. I think they're doing the right thing in pursuing this, because right now string theory offers the only hope of a really unified view of nature. They have to pursue it, but the progress is glacially slow. I'd rather study continental drift in real time than be a string theorist today. But I admire them for trying, because they are our best hope of making a great step toward the next big unified theory.'


Another dimension

At its simplest level, string theory states that the unique properties of fundamental particles are a direct consequence of the way strings vibrate. In turn, string vibration is defined by the space in which they are contained. But in order for string theory to work, to explain the existence of all known particles and forces [click on Elementary Particles], we must accept more than just the dimensions we know, because this framework is too restrictive. So just how many dimensions are required? Well, until recently, scientists thought ten dimensions were needed for strings to vibrate in such a way as to explain all the characteristics of the fundamental particles. Four dimensions are familiar to us, up-down, left-right, back-forth, and time, but there are six other dimensions which are so small that we can't possibly see them (known as Calabi-Yau manifold space).

But this created a problem. With ten dimensions, scientists could only explain string theory mathematically in five different ways; the theory of everything came in five different forms, or five different flavours, depending on how you did your sums, how you viewed the properties of your strings, and which fundamental particles you'd allow for in your mathematical treatment. Hardly a theory of everything then – more like a theoretical fix! That was until a brilliant scientist, Edward Witten, transformed string theory thinking, again.

M is for magic, matrix or mystery

The revolution came in 1995. The name – M theory. Witten succinctly transformed string theory into M theory by suggesting that the five different mathematical flavours were, in essence, simply different ways of looking at the same problem – the five different string theories can actually be connected to each other by mathematics and are different facets of one all-encompassing theory – M theory. It's a little like looking at your reflection in a lift that has five mirrors. You'd be right in saying each reflection is unique – but the image each mirror is reflecting is of the same object – it's you each time. What Witten concluded was that the five different versions of string theory were just five different ways of looking at the same thing.

But in order to assimilate the five different mathematical versions of string theory, Witten had to introduce an 11th dimension. This 'extra' dimension allows greater 'freedom' of movement for the physical behaviour of our minute strings of vibrating matter. The more degrees of freedom that strings have, the greater the ability of string theory to explain all the observed physical properties of the Universe. Put simply, more dimensions literally provides more space in which strings can vibrate, and the more powerful the theory. However, as string theorists soon found out, adding another dimension led to yet another startling implication – there may be more than one Universe!

Membranes and parallel Universes

Rather than being tiny and restrictive, the 11th dimension, which Edward Witten introduced, has a unique quality – it allows a string to be able to expand. An expanded string is known as a 'brane' (short for membrane). How do we visualise a brane? It turns out that this depends on how much energy the string has. Mathematics has shown that the more energy you give a string in the 11th dimension, the larger the brane can become – give it enough energy and it could be the size of the Universe. This begs the question that perhaps the Universe is a brane – are we all living on the skin of a brane?

Thinking about this, there is another logical question to ask – are there other branes? This is a startling prospect since another brane is in fact another Universe. Perhaps there is a brane right next to the one we call our Universe, another brane paralleling our brane – a parallel Universe! The laws of physics and the forces that act within any particular brane are considered to be a manifestation of the strings that are attached to that brane. And different branes may well have different strings and hence difference laws of physics.

If you are finding these concepts too weird and difficult, then bear in mind that the above is only a theory, based on mathematics – mathematics that is far from complete. Theoretically, all this is possible, even predicted, by the mathematics that's so far constructed. Nevertheless, such complex equations have set scientists thinking of ways to test the reality of their predictions. Below we'll explore two factors that suggest these weird concepts may be reality – gravity and the Big Bang.

Jim Gates, Professor of Physics at the University of Maryland, puts mathematics in perspective for us:

'It's not obvious from our everyday experience that mathematics has anything to do with nature. For me, this was astounding because mathematics is something we do in our heads. It's like a game of Dungeons and Dragons. It's a fantasy. But because mathematics must also adhere to logical precepts, it restricts our imagination. Why it is that mathematics is the only language that our species has found to describe nature is a mystery that will probably never be solved. But it is the way that we have found our deepest understanding of nature. For the theoretical physicist, mathematics is like an extra sensory perception organ that we use to see the Universe.'


Gravity and branes

Gravity is one of the four fundamental forces, instrumental in the workings of our Universe. However, it differs from the other three fundamental forces (being weak, strong and electromagnetic) in that it is much weaker. For example, gravity is a thousand billion, billion, billion, billion times weaker than the electromagnetic force responsible for holding atoms together. The weakness of gravity has perplexed scientists for decades. But the theory of strings may have an answer to this mystery. Again, it requires a new way of looking at an old problem.

Why should gravity be so weak in comparison to the other forces in our Universe? The clue comes in the words 'our Universe'. Returning to the idea that our Universe is in fact a brane, string theorists believe that each brane may have its own physical laws – if you could visit a parallel brane (a parallel Universe) the physical laws which govern the Universe you are visiting may be substantially different, just as different countries have different laws. The laws of any particular Universe are dictated by strings that are anchored to it.

But what if some strings were not anchored down to their Universe – what if some were free to move. This is the new thought behind gravity. The strings responsible for controlling the behaviour of the graviton (the messenger particle which 'transmits' gravity) is thought to be a closed loop which, because of its shape, is not tied down to any particular Universe. It is free to permeate through branes. Like sound waves, gravity can reverberate around branes, and also like sound waves, gravity gets weaker as it disperses. Gravity may well be as strong as the other fundamental forces, but owing to its ability to permeate through parallel Universes, it becomes diluted. If such a theory is correct, gravity may be the only way we could communicate with other parallel Universes, since it is the only force that is common to all Universes and dimensions.

Joe Lykken is a physicist at the Fermi National Accelerator Laboratory in the USA, he explains that it might be possible to find experimental evidence of extra dimensions:

'The key to testing extra dimensions in experiments has to do with gravity. The simplest way that you can see evidence for an extra dimension is to try to produce a high-energy graviton, the quantum of gravity, which could then move off into the extra dimensions. In a particle accelerator we try to collide very high-energy particles and hope occasionally to produce a high-energy graviton that moves off into extra dimensions and disappears.


This is something we don't see directly – we don't see the graviton that disappears – but we notice that energy and momentum were carried off by some invisible particle and from that we deduce that something strange happened. In this case a high-energy particle, a graviton, moved off into extra dimensions. So this is the simplest kind of experiment you can do, and if you can eliminate other kinds of possibilities for things that carry off energy invisibly, you would then be able to claim that you've seen evidence for extra dimensions of space.'

An ultimate answer to the theory of everything

String theory, which has now become M theory, is providing a revolution in the way we perceive the cosmos. Fundamental particles, gravity, quantum mechanics, dimensions, parallel Universes, the standard model, all have been constructed or revised based on the mathematics which describe the smallest building blocks of matter. But what about the ultimate question in the theory of everything – how did it all begin?

The idea of the Big Bang, the event that created everything in our Universe, is not new, but at the same time it is not watertight – it has considerable problems. The theory of the Big Bang states that everything we can observe was born from an infinitesimally small point which rapidly expanded out from a huge explosion of energy. What caused this Big Bang, and what preceded it has never been satisfactorily explained. A Big Bang occurring out of nothing is something most physicists can't stomach. But as you may have already guessed, string theory may be able to shed light on the mystery.

Today, some string theorists are toying with the idea that the Big Bang is the manifestation of the collision of branes – two or more parallel Universes colliding headlong, releasing a vast amount of energy and matter which eventually condensed to form the galaxies, stars, planets, you and I. In this way, the Big Bang is far from being unique. Big Bangs are just a by-product of the endless cycles within the cosmos. They happened before, and they will happen again. If correct, string theory answers how we got here – a truly powerful theory of everything indeed.

Amanda Peet, string theorist at the University of Toronto, explains how strings help understanding of the Big Bang:

'It's hard to say whether the colliding branes scenario will turn out to be the one that we'll all be using 40 years from now to explain the origin of the Universe to our students. It's fair to say that before the advent of branes, we were pretty unsure about whether we could make string theory match onto the dominant theory at that time of how the Universe began, which is called inflation. What inflation explains is how the Universe got to be so big and so flat and so forth. And once the notion of branes came along, that gave us more ingredients in our stringy tool box, and it provides us with potential new ideas about explaining the origin of the Universe.'


No wonder that in order for string theory to succeed both mathematically and experimentally, it requires a radical shift in the way we see the Universe – it has to unite so many different phenomena. But it's important to keep in mind that string theory with all its bizarre consequences, is based very much on thought rather than on experiment. In this sense, it's more like philosophy than physics and no one really knows if it's true or not. Having said that, it's no different to Einstein's revolutionary ideas almost 100 years ago, and his ideas were soon vindicated as scientific fact. Back then, special and general relativity were new and exciting scientific ways of thinking that pushed us into new worlds of understanding. String theory could well do the same, it certainly has some very clever and very ardent advocates.

Ed Witten, originator of M theory, is the theoretical physicist believed to be Einstein's true successor. He firmly believes that theory will eventually give way to fact:

'Just as the theory of neutron stars, black holes, gravity waves, and so many other things were tested because of things that nobody foresaw, there are just so many ways that nice surprises could happen that would lead to new advances in string theory. There are all kinds of possibilities, like literally seeing a string in a telescope if nature has chosen to be kind to us in that particular way. I think that nature will turn out to be kind to us and that there will be some nice surprises, as there have been so many times in the past in science. But if I could tell you what they were, they wouldn't be surprises.'


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