CERN’s new LHC collider, which is scheduled to begin operations in 2005, aims to find the long-awaited “Higgs particle”, which endows other particles with mass. In an entirely new energy range and with its special experimental conditions, the LHC could also discover other new physics effects.

Why is gravity so weak? The traditional answer is because the fundamental scale of the gravitational interaction (i.e. the energy at which gravitational effects become comparable to the other forces) is up at the Planck scale of around 10^{19} GeV – far higher than the other forces. However, that only raises another question: what is the origin of this huge disparity between the fundamental scale of gravity and the scale of the other interactions?

A possible explanation currently gaining ground in theoretical circles is that the fundamental scale of gravity is not really up at the Planck scale, it just seems that way. According to this school of thought, what is actually happening is that gravity, uniquely among the forces, acts in extra dimensions. This means that much of the gravitational flux is invisible to us locked into our three dimensions of space and one of time.

Consider, by analogy, what two-dimensional flatlanders would make of three-dimensional electromagnetism. To them, the flux lines of the force between two charges would appear to travel in their planar world, whereas in reality we know that most of the flux lines would spread out through a third dimension, thus weakening the force between the two charges.

Of course, if this third dimension were infinite in size, as it is in our world, then the flatlanders would see a 1/r^{2 }force law between the charges rather than the 1/r law that they would predict for electromagnetism confined to a plane. If, on the other hand, the extra third spatial dimension is of finite size, say a circle of radius R, then for distances greater than R the flux lines are unable to spread out any more in the third dimension and the force law tends asymptotically to what a flatlander physicist would expect: 1/r. However, the initial spreading of the flux lines into the third dimension does have a significant effect: the force appears weaker to a flatlander than is fundamentally the case, just as gravity appears weak to us.

Turning back to gravity, the extra-dimensions model stems from theoretical research into (mem)brane theories, the multidimensional successors to string theories (April 1999 p13). One remarkable property of these models is that they show that it is quite natural and consistent for electromagnetism, the weak force and the inter-quark force to be confined to a brane while gravity acts in a larger number of spatial dimensions.

The requirement of correctly reproducing Newton’s constant, G, at long distances leads to the size of the extra dimensions in which gravity is free to act being related to the number of extra dimensions.

If there is just one extra dimension, then the model says that it should be of the order 10^{13} m, in which case solar system dynamics would be radically different and we would be taught a Newton’s 1/r^{3} law in school rather than the 1/r^{2} law that we know and love.

So one extra dimension doesn’t work. With two extra dimensions, the scale drops to slightly less than 1 mm and, small though that is, it at first seems surprising that extra dimensions of that size have not already been seen. However, because the extra dimensions only affect gravity, the most direct constraints come from experiments to measure G at short distances, and delving into the historical literature on the subject reveals that no measurements of G at the submillimetre scale have ever been made.

A team led by Aharon Kapitulnik at Stanford is currently in the process of accurately measuring G at submillimetre scales for the first time using a tabletop experiment.

For more than two extra dimensions their size begins to get quite small: 1 fm, for example, for six extra dimensions, outside the range of even the improved submillimetre gravity experiments. Nevertheless, the model still makes a number of dramatic predictions. If gravity does have extra dimensions at its disposal, they should manifest themselves at CERN’s LHC proton collider, which is scheduled to come on line in 2005, no matter what the number of extra dimensions might be.

This is because the fundamental scale of the gravitational interaction should be around a few tera-electron volts, so, at TeV energies, gravitational effects will become comparable to electroweak effects. Consequently, gravitons will be produced as copiously as photons, with the difference that the photons will remain in our familiar dimensions while many of the gravitons will escape into extra dimensions, carrying energy with them.

More dramatically still, the LHC could produce fundamental string relations of our familiar particles, such as higher-spin relatives of electrons or photons. There is also a possibility that, owing to the now much stronger gravitational interactions, microscopically tiny black holes could be produced with striking signals.

Fortunately, such small black holes are not at all dangerous, being much more similar to exotic particles than large astrophysical black holes, and they decay quite quickly as a result of Hawking radiation. With the recent outburst of ideas in these directions, it is clear that extraordinary discoveries at the LHC may be just around the (extra-dimensional) corner.