Warped Passages: Unravelling the Universe's Hidden Dimensions

  • Lisa Randall
Allen Lane: 2005. 512 pp. £25 To be published in the US in September by Ecco (HarperCollins) 0060531088 0713996994. | ISBN: 0-060-53108-8

In 1884 a curious little book appeared called Flatland. Written by Edwin Abbott, an English mathematician, it was destined to become a minor classic. It describes a world of two-dimensional beings — entities of various shapes for whom ‘up’ and ‘down’ have no meaning. The book describes their baffling experiences when presented with three-dimensional processes that penetrate their universe. Apart from its entertainment value, Flatland serves to educate the reader in the possibility that our three-dimensional world might in fact be merely a ‘slice’ or section in a higher-dimensional space to which access is restricted. That is, there might be a direction in space, which we can neither see nor move through, that points at right-angles to the familiar perpendicular directions (latitude, longitude and altitude). The basic message of Flatland is that just because we can't visualize higher dimensions, it doesn't mean they don't exist.

Mathematicians have long known that spaces of more than three dimensions make good logical and mathematical sense. Indeed, they are routinely used as a calculational device in science and engineering. In recent years, some theories of fundamental physics have postulated that additional dimensions of space really exist in the physical world. Warped Passages explains the rationale behind this seemingly extravagant claim.

Like Jackson Pollock paintings, specialized science books can provide a rewarding cultural experience. Credit: THE ART ARCHIVE/GALLERIA D'ARTE MODERNA MILAN/DAGLI ORTI

There are two distinct ways in which one or more dimensions might be concealed from our senses. They could be rolled up to a very small size, just as a garden hose, which looks like a wiggly line from afar, turns out on closer inspection to be a two-dimensional sheet rolled into a thin tube. The idea that what we perceive as a point in space is in reality a tiny circle around a fourth dimension dates back to attempts in the 1920s to provide a unified geometrical description of gravitation and electromagnetism based on Einstein's general theory of relativity. These days physicists are more ambitious and are trying to incorporate all the forces of nature, including the weak and strong nuclear forces, in a grand unified scheme. The most promising candidate, string theory, describes all matter as little loops of string that vibrate in ten-dimensional space-time, of which six dimensions are rolled up in a complicated shape.

The other way to achieve hidden extra dimensions of space is to suppose that some sort of physical force barrier confines all normal matter, together with the light by which we see the world, to a three-dimensional ‘membrane’ embedded in a four-dimensional ‘bulk’. The author of Warped Passages, Lisa Randall, is an expert in these ‘brane’ theories, which emerge naturally as by-products of string theory.

These outlandish ideas would be pointless speculation unless there was some way for the extra dimensions to manifest themselves. String theory predicts that at energies a billion billion times those attained by particle accelerators, observable things would happen to the strings in the rolled-up dimensions. Brane theory is less demanding; it has been conjectured that the Large Hadron Collider (LHC), currently being built at the CERN particle-physics laboratory near Geneva, might reveal traces of a fourth space dimension. This is because gravitation is not confined to branes but leaks out into the bulk. Some versions of the theory predict that, as a result, mini black holes and wormholes could conceivably be created from the high-speed collisions between the LHC's protons and antiprotons.

Randall has to confront an uncomfortable fact that faces most authors who tackle sweeping ideas of unification in fundamental physics. The book's peg — the possible existence of extra dimensions in space — is easy enough to explain. But motivating the conjecture requires a grand tour of some of the toughest and most abstract topics in science. To make her case for higher dimensions, Randall must first explain the general theory of relativity, with its notion of warped space-time. She then needs to set out the standard model of particle physics, with its confusing proliferation of subatomic objects — quarks, leptons, bosons of various sorts — and the details of the forces that act between them. Then she has to go into esoteric topics such as spontaneous symmetry breaking, Higgs potentials and supersymmetry. Because unification physics is formulated in terms of quantum mechanics —or rather, the quantum theory of fields, a much more demanding extension — that has to be covered too. Randall must do all this before she can properly describe string theory, and must then proceed to a more obscure generalization called M-theory. Furthermore, the exposition must be crafted without the explicit use of mathematics. Only then can Randall explain how branes emerge from a welter of concepts that are largely unfamiliar to the general reader. She achieves this tour de force by cutting quite a few corners, but even so, this is a long and dense read by any standards.

I suppose it is in the nature of unification that one can't leave anything out. After all, the thrust to create a final ‘theory of everything’ sprang from a desire to bring all physical theory into a common conceptual scheme. Randall makes a heroic attempt at completeness, but I wonder how many non-physicists will stay with the narrative to the bitter end.

A paradox of ‘popular’ science publishing is that even highly technical and specialized books still sell well, especially when there is a new author or a new twist to the subject that attracts headlines. I suspect that these books are rarely understood. Perhaps readers don't really intend to follow them studiously, but wade through the expositions as a cultural experience, rather like reflecting on a Jackson Pollock painting — you know it's very clever and you assume it means something profound to the creator, but it belongs to an alien world. Maybe readers of popular physics and cosmology books simply enjoy being perplexed, or are satisfied merely to glimpse, voyeuristically, the arcane world of the theoretical physicist without actually having the foggiest idea of what is going on. Whatever it is that attracts these readers, Warped Passages has plenty of intriguing material to keep them happy.