# Mathematical Physicists Aim to String Together a Theory of Everything

## Can string theory unify physics?

When we think about symmetry, most of us picture an object that looks the same when reflected about itself. The human face is a good example; draw a line down the middle of the nose and the left half is essentially a mirror image of the right. But this is just symmetry in three dimensions. The symmetries that excite physicists and mathematicians probing fundamental questions about the structure of the universe are far more complex. They often involve multiple dimensions, or are conceptual symmetries in which members of a system of elementary particles each has an equivalent partner particle.

In what is known as the standard model of particle physics, particles such as electrons are described by an infinitely small point in space. This point can then move through 3 dimensional space, or even an extended multi dimensional universe, and as it does so creates what physicists call a 'world line'. For example, the world line of a cannon ball is a parabola extending from the muzzle of the cannon to the point of impact. In a similar but much more complex way, all the bosons and fermions that make up the universe can be described in terms of infinitely small points on world lines.

So where does symmetry come in? Some physicists believe that the universe is organised along super-symmetrical principles, each particle has a symmetrical twin of identical mass and charge - creating so called super-symmetry. Adding supersymmetry to the standard model, makes the mathematics far more elegant. Infinities that arise from fermions tend to be cancelled by those arising from their supersymmetric partner bosons and visa versa.

However, with or without supersymmetry, the standard model has a problem. It doesn’t describe quantum gravity and including it in a naive way gives rise to inconsistencies. This rules out the standard model’s contention as a unified theory of everything. This is where many scientists believe that the relatively new field of string theory may lead to a breakthrough. Rather than describing the universe as points, particles are described as vibrational modes of one dimensional strings in much the same way as the strings of musical instruments generate different tones. In a closed string theory the string forms a loop. If you imagine something like a rubber band in which the rubber gets progressively thinner and thinner whilst the loop remains the same size, you approach a string. Unlike the particle (or a cannon ball) the string traces out tubes in four dimensional space creating a world volume.

Real particles often collide or fragment into sub particles and the standard model describes the resulting world line using 29 additional parameters (if we include neutrino mass). Professor Peter Bouwknegt, of the ANU Mathematical Science Institute, explains that, “In the ten dimensional spacetime of string theory, only a single parameter is required to describe the world volume making the mathematics a lot more elegant. Although additional parameters do have to be introduced when condensing the system down to our familiar four dimensions.”

The mathematical elegance of string theory raises the hopes of many scientists of finding the elusive Theory of Everything. But why do physicists think that a theory of everything should exist in the first place?

The four fundamental forces that describe the universe; gravity, the electromagnetic force, the strong nuclear force and the weak nuclear force may all be manifestations of a single entity. This idea arises because the coupling constants between the four forces vary with energy. If you increase the energy enough, the electromagnetic force and weak nuclear force coalesce into a single entity. Increase the energy further and the strong nuclear force also coalesces. At present, scientists don’t have powerful enough colliders to reach energies at which gravity also unifies with the other forces but extrapolation of the data they have, suggests that this might ultimately happen.

If this turns out to be the case, and it happens in a way the extrapolated data suggests, it would imply that the universe exhibits supersymmetry. This is not so important for the standard model, but a supersymmetrical universe is critical to string theory. The existence of supersymmetry would not of course prove current string theory models to be correct, but it would raise that intriguing possibility.

Given this, physicists are intensely interested to find out if supersymmetry does exist. Further evidence should emerge when the massive LHC collider being built at CERN reaches completion, enabling physicists to get closer to the energies at which the gravitational force coalesces with the other three.

Meantime, theorists are grappling with the immensely complex mathematical problems underlying string theory. At ANU, scientists in the Department for Theoretical Physics and at the Mathematical Science Institute are collaborating in understanding the mathematics behind string theory. This involves applying fairly recent mathematical disciplines, such as noncommutative geometry, to string theory, but also involves developing and studying new mathematics suggested by, and needed for, a further development of string theory. A recent example of this is the discovery of a generalization of geometry, a joint effort between String Theorists and Mathematicians.

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