Prof. Lisa Randall's new book, Warped Passages, is a grand tour of some of the most important recent developments in high-energy physics.

The book is intended for a popular audience, but is also a very interesting read for anybody with a background in theoretical physics (like myself). The first part contains an overview of modern physics - Einstein's theories of relativity, quantum mechanics and the Standard Model of particle physics. The last part concentrates on the idea of extra dimensions beyond the standard four we know about, which can be motivated by string theory and its discovery of the so-called D-branes. Specifically, she explains the work, pioneered by herself, Raman Sundrum and others, on the so-called "braneworld scenarios". Basically, this is the idea that our four dimensional space-time is embedded in some higher dimensional space, usually called the "bulk".

You might think, that extra dimensions are just part of a set of crazy ideas? On the contrary. You should know, that the idea of extra dimensions is actually not at all new. Already in 1884, the original book, "Flatland: A Romance of Many Dimensions" (written by the English mathematician Edwin Abbott) described a world of two-dimensional beings, who only have indirect knowledge of the extra third space-dimension. But, from a mathematical point of view, one can imagine as many dimensions as one wants to. In physics, the story is somewhat different.

In physics, there are basically two distinct ways in which one can add extra dimensions to our four-dimensional universe. Already in the 1920's, Klein suggested that our universe is five-dimensional, where the extra dimension is rolled up in a circle, which is so tiny, that the universe looks four-dimensional at long enough distance-scales. The motivation was to give a unified geometrical description of electromagnetism and gravitation using Einstein's general theory of relativity. However appealing, this theory was destined to fail. Today we know, that there are other forces which should be included in a unified theory: namely the weak and strong nuclear forces. Presently there is only one theory which can possibly do the work, and this is string theory. Perturbative string theory tells us, that our space-time is ten-dimensional, and that the extra six dimensions should be rolled up in a small but complicated shape (which is determined by some mathematical restrictions).

Another way to achieve hidden extra dimensions of space is to suppose, that all normal matter, as well as the light by which we see the world, is confined to a four-dimensional "brane" embedded in a five-dimensional "bulk" - or larger universe. These so-called braneworld theories are the ones of Lisa Randall, Raman Sundrum and others. Warped Passages explains - in excellent style - the logic behind these seemingly fancy ideas.

What I particularly liked about the first part of this book is how Prof. Randall makes people envision extra dimensions. As Randall writes, "we are not physiologically equipped to envision more than three dimensions of space", so it might be difficult for the general reader to comprehend this idea. But, as Prof. Randall also explains, readers need not imagine a dimension only in spatial terms. Here is an example from the book: If you are buying a house, the factors you might consider include its location (specified by three numbers), price (one number), size (one number), and possibly many other things. So, the number of dimensions in your house search simply equals "the number of quantities you find worth investigating".

What Prof. Randall describes in the last part is - in more technical terms - her work with Raman Sundrum on solving the flavor-changing problem, the gaugino mass problem (and other things) that occur in supersymmetric models with the supersymmetry breaking sector on another brane, separated from ours, or in the bulk; the Randall-Sundrum warped geometry with two branes (a so-called "weak-brane", where we are supposed to live, and a "gravity-brane") and the Randall-Sundrum warped geometry with an infinite extra dimension, using so-called AdS geometry.

The main point guiding Randall's research - described in the last part of the book - is the fact that gravity is such a profoundly weak force. Indeed, gravity is the puniest of the fundamental forces governing the matter in the universe, by a huge margin (typically a 10^36 times weaker than the electromagnetic force between two charged particles). Why is this so?

Why this is so, Prof. Randall suggests, is because we live in a universe containing at least one extra dimension beyond those we can perceive. And gravity is weak because it has been "diluted" into this extra space. This is indeed a very simple and persuasive idea. (And also from the point of view of string theory a very compelling idea, with a simple explanation, related to objects in string theory called D-branes - like an infinite string (a 1-brane), a membrane (a 2-brane) etc). But note that Prof. Randall's original models are not inherently string-theoretical; it is just that her models have an elegant and simple interpretation in string theory. So you don't need to know *anything* about string theory to understand this book).

The breakthrough research by Randall and Sundrum proposed that gravity's dilution can be explained in terms of a cosmic configuration featuring two branes - or two infinite planes, separated by a higher dimensional bulk space. Roughly speaking, the "center of gravity" is on the "gravity-brane" - and some gravity leaks out of this brane, through the bulk, and onto the other brane, usually called the "weak-brane", which is where we live, and which contain the Standard Model fields. Later on, Randall and Sundrum found, that their concept is also theoretically consistent with a configuration which includes only one brane. Usually, one would think that Newton's 1/r^2 law of gravitation implies that there are four and only four non-compact dimensions of infinite extend. Randall and Sundrum showed that this is not correct.

The fact that branes are an important part of modern string theory meant that string theorists took an early interest in the Randall-Sundrum models. Furthermore, since Prof. Randall's research did not directly challenge string theory models, the string theory community actually accepted and recognized the profound significance of her work very early on.

One of the long outstanding problems of the Standard Model of particle physics, that braneworlds do provide an interesting answer for, is the "hierarchy problem", or why the weak and Planck scales are so disparate (10^2 GeV compared with 10^19 GeV). In these scenarios, the fundamental gravitational scale is not the Planck scale, but something closer to the weak scale. The conjecture is that gravity is not weak because the Planck scale is so large, but because braneworlds provide various geometrical mechanisms for making the gravitational force much weaker than the others.

All this would of course be pointless speculation unless there was some way for the extra dimensions to manifest themselves. So, can these ideas be experimentally tested? As Prof. Randall explains in detail, the answer is: yes indeed! It is possible that evidence supporting the braneworld models could appear within a decade or so, after the Large Hadron Collider (LHC), currently being built at the particle-physics laboratory CERN, starts operating in 2007. Here the traces of extra dimensions could come from "gravitons" (the fundamental constituents of gravity) moving into the extra dimension(s).

Some versions of the theory even predict that, as a result, small black holes could conceivably be created from the high-speed collisions at the LHC! (but don't worry, the black holes will only exist for about 10^{-26} sec and the Earth will not disáppear into a black hole). If the LHC sees the kinds of effects predicted by these models, be sure that there will be some well-earned Nobel prizes for the people involved in this story.

Let me say a few words about the style of the book. The book's central point - the possible existence of extra dimensions in space - is easy enough to explain; at least if the reader can comprehend the idea, that our universe has more than four space-time dimensions, which might not be easy. However, to motivate the conjecture of higher dimensions, Prof. Randall must first explain the General Theory of Relativity, quantum mechanics and the Standard Model of particle physics, with its zoo of subatomic objects - quarks, leptons, bosons of various sorts - and the details of the forces that act between them. To ensure the convergence of her ideas in the readers mind, she then has to go into more advanced topics such as "quantum field theory", "spontaneous symmetry breaking", the "Higgs potentials" and "supersymmetry". (But all these concepts are explained in much detail).

All this is a prerequisite for being able to properly describe string theory, and Prof. Randall must then proceed to the less understood generalization called 'M-theory' (which is an eleven-dimensional theory containing two-branes and five-branes). Only then can Prof. Randall explain how branes emerge from a jumble of concepts and ideas, that most likely might be unfamiliar to the general reader. But as far as I can judge, she accomplish this tour de force with *much* success. The immanent "problem" with such theories of unification is that one cannot leave anything out and therefore - to be explained and understood - they require background knowledge in virtually all of physics. But I think that Prof. Randall has done a very good job in explaining all the required physics in terms of analogies, simple illustrations and so on.

Finally I would like to stress that this book is *very* different from many of the random popular books about physics because Lisa Randall actually knows what she is talking about And you should know, that Prof. Randall is not by any standards a random person: she has become the most cited high-energy physicist since 1999.

In conclusion, I'll give Warped Passages some more than well-deserved 5 stars.