Read more: “Instant Expert: Theory of everything“
Our leading candidate for a theory of everything is known as M-theory. It grew from a merger of the two seemingly different approaches: 11-dimensional supergravity and 10-dimensional superstring theory. Could this be the final theory of everything?
Advertisement
Brane power
Superstring theory had some serious shortcomings. One problem is that there is not one, but five, mathematically consistent superstring theories, each competing for the title of the theory of everything. We faced an embarrassment of riches.
A second puzzle soon became apparent, too. Supersymmetry says that the universe has a maximum of 11 dimensions, yet the mathematics of superstring theory states there should be 10. What gives? And there was a related question: why stop at one-dimensional strings? Why not two-dimensional membranes which might take the form of a sheet or the surface of bubble?
It turns out that supersymmetry and membranes do go together. Just as superstrings live in 10 dimensions, it was calculated in 1987 that “supermembranes” can live in an 11-dimensional space-time dictated by supergravity.
Moreover, if the 11th dimension is curled up, as Kaluza and Klein’s early work suggested it could be, then it is possible to wrap the membrane around it. If curled up tightly enough, this wrapped membrane would look like a string in 10 dimensions (see diagram).
Despite these attempts to revive 11 dimensions with the new ingredient of membranes, most string theorists remained sceptical. For many years there were two camps: string theorists with their 10-dimensional theory, and the membrane theorists working in 11 dimensions. It wasn’t clear whether they were on the same page or not.
The M-theory revolution
All the work on strings, membranes and 11 dimensions was brought together in 1995 by Edward Witten, the string-theory guru at the Institute for Advance Study in Princeton, under one umbrella called M-theory. M, he says, stands for magic, mystery or membrane according to taste.
Witten showed that the five different string theories and 11-D supergravity were not rival theories at all. They were merely different facets of M-theory. Having one unique theory was a huge step forward. It also turned out that M-theory and its membranes were able to do things strings alone could not.
Take black holes, for example, which are excellent laboratories for testing our theories. In 1974, Stephen Hawking showed that black holes are not entirely black – instead they can radiate energy due to quantum effects. This means that black holes have temperature and another thermodynamic property called entropy, which is a measure of how disorganised a system is.
Hawking showed that a black hole’s entropy depends on its area. Yet it should also be possible to work out its entropy by accounting for all the quantum states of the particles making up a black hole. However, all attempts to describe a black hole in this way had failed – until M-theory came along. Amazingly, M-theory exactly reproduces Hawking’s entropy formula. This success gave us confidence that we were on the right track.
In 1998, Juan Maldacena, also of the Institute for Advanced Study, used membranes to explore what would happen inside a hypothetical universe with many dimensions of space and gravity. He showed that everything happening on the boundary of such a universe is equivalent to everything happening inside it: ordinary particles interacting on the boundary’s surface correspond precisely to how membranes interact on the interior. When two mathematical approaches describe the same physics in this way, we call it a duality.
This duality is remarkable because the world on the surface of the universe looks so different to the world inside. If Maldacena’s idea is applied to our universe, it could mean that we are just shadows on the boundary of a higher-dimensional universe.
Maldacena’s paper has been cited over 7000 times. This is partly because his idea has found applications in unexpected areas of physics, including superconductivity and fluid mechanics, regardless of whether M-theory is the theory of everything or not.
More recently, my colleagues and I have found yet another area of physics to which M-theory can be applied: the black-hole/qubit correspondence. A classical bit is the basic unit of computer information and takes the value 0 or 1. A quantum bit, or qubit, can be both 0 and 1 at the same time. Only when we measure it do we fix which one it is, and the outcome cannot be predicted with certainty. This gives rise to the phenomenon of entanglement between two or more qubits, where measuring one qubit affects the other no matter how far apart they are. Einstein called this effect “spooky action at a distance”.
For reasons we do not fully understand, the mathematics that describes qubit entanglement is exactly the same as that which governs certain black holes in M-theory. It turns out that these black holes fall into 31 classes, depending on their mass, charge and entropy. We recently used this to predict that four qubits can be entangled in 31 different ways. This can, in principle, be tested in the lab and we are urging experimentalists to find ways of doing just that.
A landscape of universes
The geometrical and topological properties of the curled-up extra dimensions dictate the appearance of our four-dimensional world, including how many generations of quarks and leptons there are, which forces exist, and the masses of the elementary particles. A puzzling feature of M-theory is that there are many (possibly infinitely many) ways of curling up these dimensions, leading to a “multiverse” – a number of different universes. Some may look like ours, with three generations of quarks and leptons and four forces; many will not. But from a theoretical point of view they all seem plausible.
The traditional view is that there is one universe and a unique set of fundamental laws. The alternative view, which is gaining credibility, says that there are multiple universes out there with different laws of physics, and one of these universes just happens to be the one we are living in. Each of these universes must be taken seriously.
So is M-theory the final theory of everything? In common with rival attempts, falsifiable predictions are hard to come by. Some generic features such as supersymmetry or extra dimensions might show up at collider experiments or in astrophysical observations, but the variety of possibilities offered by the multiverse makes precise predictions difficult.
Are all the laws of nature we observe derivable from fundamental theory? Or are some mere accidents? The jury is still out.
In my opinion, many of the key issues will remain unresolved for quite some time. Finding a theory of everything is perhaps the most ambitious scientific undertaking in history. No one said it would be easy.
Read previous article: “Theory of everything: The road to unification“
Read next article: “Theory of everything: Answering the critics“
