Extra dimensions make new room to tackle old mysteries

Since Fermi's theory of the weak interactions, a great mystery in fundamental physics has been: why is even this most feeble subatomic force so much stronger than gravity? In the context of modern Grand Unified Theories, this disparity between forces is understood in terms of a giant Desert in energy scales stretching over seventeen orders of magnitude. The Desert extends from the electroweak scale, currently being probed by the highest energy accelerators, to the Planck scale, where gravity is expected to become as strong as the other interactions. Planckian energies probe miniscule distances of roughly 10^{-33} cm, where quantum gravitational effects are also supposed to come into play. Because these phenomena take place at such high energies, there is no hope for direct experimental tests of quantum gravity in the standard framework.

Leaving aside theoretical speculations about quantum gravity for a moment, what do we know about gravitational interactions experimentally? Due to its miniscule strength, we know surprisingly little: gravity has only been directly measured down to distances of about a millimeter! All of the above statements about the energy and distance scales where gravity becomes strong are based on a theoretical extrapolation of the inverse square law for gravity, over thirty orders of magnitude, from a millimeter where it is actually measured, down to the Planck length of 10^{-33} cm. Given the crucial way in which this extrapolation shapes our thinking about the relation of gravity to the other forces, it is important to scrutinize it.

In the last year, a new framework has been proposed for tackling the above questions, challenging the old assumption of a large energy Desert. Instead of altering the properties of particle physics at short distances, the properties of gravity are altered. This idea, proposed by Nima Arkani-Hamed (now at U.C. Berkeley), Savas Dimopoulos (Stanford) and Gia Dvali (NYU), postulates that gravity becomes strong at the electroweak scale, making quantum gravity accessible to the next generation of particle accelerators. The measured weakness of gravity at distances longer than a millimeter is due to the presence of new spatial dimensions in which gravitational force lines can spread out, diluting its strength. The idea that there may be new spatial dimensions in nature dates back to the 20's and is a central ingredient of modern string theories. However, these dimensions are normally thought to be rolled up into tiny circles about 10^{-33} cm big, making it impossible to detect them experimentally. The dimensions in this new proposal are enormous by comparison, perhaps as large as a millimeter. That we have not so far detected them is because only gravity can propagate in these extra dimensions. The particles and forces of which matter is composed are stuck to a three-dimensional ``wall" in the extra dimensions. Remarkably, this new picture is not excluded by any known experimental observation, surviving laboratory, astrophysical and cosmological constraints.

Many implications of this framework have been explored intensively in the past months. Some of the most interesting possibilities involve populating the extra dimensions with new particles and parallel ``walls" where other universes live. Interactions between the parallel universe and our own have been used to provide explanations for many of the outstanding mysteries in the Standard Model, providing possible answers to questions such as: Why do the neutrinos have such tiny masses? Why is the electron a million times lighter than the top quark? Why is the proton so long-lived? Why do the strong, electromagnetic and weak forces seem to unify at ultrahigh energies? Given the radical revision in the notion of what our space-time looks like, the picture of very early universe cosmology is also changed in interesting ways. Old ideas, such as the inflationary universe, can be realized in terms of the dynamics of the extra dimensions or the motion of parallel universes. Very interesting variations on these ideas have also been proposed. For instance, it may be that gravity itself can be trapped to a three-dimensional wall in four spatial dimensions. Among other things, this proposal, put forward recently by Lisa Randall (MIT) and Raman Sundrum (now at Stanford), allows for the possibility that the new dimension can be infinitely large in extent.

One of the most interesting aspects of the above picture is that it predicts remarkable new phenomena that will soon be tested experimentally. In this framework, the next generation of particle accelerators, such as the Large Hadron Collider (LHC) at CERN, should observe strong quantum gravitational effects; for instance, the high-energy particle beam at the LHC can cool by boiling off gravitons into the extra dimensions. More exotic gravitational objects, such as small black holes, can also be produced at LHC energies. If the true theory of quantum gravity at short distances is string theory, new particles corresponding to vibrations of the strings may be produced, as well as states where strings wrap around new dimensions.

Another exciting aspect of this proposal is that, in some cases, it predicts deviations from Newtonian gravity that may be observable in a new generation of table-top experiments measuring gravity at sub-millimeter distances. The possible signals include observation of a transition in gravitational force from the inverse square law to an inverse fourth-power law, and new attractive or repulsive forces anywhere between one and a million times stronger than gravity operative at sub-millimeter scales. The first results from these important experiments will become available in the next couple of years.

-Nima Arkani-Hamed