Imaging in the fourth dimension.

scientists find themselves in an odd, but perhaps not surprising, situation. As the number of studies increases, so does the number of conflicting results. On page 80 of this issue, Patel and Balaban provide an example of what has been missing in neuroimaging — a new approach that adds time as the fourth dimension. Usually, three-dimensional images of cerebral blood flow, metabolic changes or the activity of populations of neurons are corrections to Newton’s law to be consistent with experimental results. This remarkable insight has stimulated a flurry of subsequent papers developing the ideas and determining the implications for cosmology and particle physics. Directions being pursued include verifying in more detail how four-dimensional general relativity emerges on the three-brane, and studying ways in which the framework can be embedded in string theory. The implications for particle physics are particularly exciting because other closely related ideas published by Randall and Sundrum may provide a resolution to the ‘hierarchy problem’, one of the most important issues in going beyond the Standard Model of particle physics. The Standard Model is a fantastically successful theory of three of the forces of nature: electromagnetism, the weak nuclear force and the strong nuclear force. It unifies electromagnetism and the weak nuclear force into the electroweak force at characteristic length scales of around 10 cm (roughly the limit of the scales probed by current acceler-ators). There are strong arguments that unifying particle physics with the fourth known force, gravity, into a theory of quantum gravity (string theory, say) will have a characteristic length scale of around 10 cm. It is very difficult to account for such a vast gap between these two scales without fine tuning the theoretical parameters to an extraordinary extent. This is the hierarchy problem. The conventional approach for dealing with this problem is to invoke a new symmetry between matter and forces called supersymmetry, which could be detected by the next generation of particle accelerators. An alternative approach (which might also include supersymmetry) is to assume that our world is a three-brane. The first proposals along these lines considered a single three-brane embedded in a space–time with at least two extra dimensions that are compact and flat. These dimensions could be as large as 1 mm without violating known experiments. In a string theory setting it is possible that the string length scale could be just below that probed by current accelerators, rather than about 10 times smaller as previously supposed. These schemes are fascinating although they do introduce another hierarchy that needs explaining. By contrast, Randall and Sundrum suggest that a curved ambient space–time with one extra dimension might provide a better setting. They consider a slab of this space– time bounded at each end by a three-brane. (Slabs of space–time bounded by branes were first introduced in string theory in ref. 5.) One of these branes is our world and the other is a ‘hidden’ world. Particles on our three-brane interact with the extra dimension and the hidden world through gravitational interactions. By assuming that the distance between the branes is very small, Randall and Sundrum showed that these interactions are weak enough to be consistent with experiment. They also showed how the hierarchy of scales on our three-brane can be accounted for in a fascinating way by the curvature of space–time without introducing any extra hierarchy. The Randall–Sundrum papers do not provide a detailed model of particle physics beyond the Standard Model. Indeed there are considerable difficulties to be overcome to achieve this goal. But they have provided exciting alternatives to conventional ways in which people thought the unification of particle physics and gravity might occur. Particle physicists, string theorists and cosmologists are currently devoting much effort to developing ideas and deriving predictions that could be tested by the next generation of particle accelerators and gravity experiments. If Randall and Sundrum are on the right track, there could be exciting experimental evidence in the near future. ■ Jerome Gauntlett is in the Department of Physics, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK. e-mail: [email protected]