*The Universe in a Nutshell*

Stephen Hawking

2001 Bantam Press 224pp £20.00/$35.00hb

It is said that one of the world's most eminent quantum-gravity theorists was once asked to explain in his institution's annual report what he did. He declined, claiming that his work was far too complicated for the general public to understand. All the more credit to Stephen Hawking for having seized the challenge.

Hawking's previous attempt at popularization - *A Brief History of Time* - succeeded in sales beyond his wildest dreams. However, I never managed to steer my way through the realm of imaginary time and neither, I would guess, did 99.9999% of the other 25 million or so readers. Indeed, one can be virtually certain that very few of them went beyond chapter 3.

In fact, Hawking has got the message. *The Universe in a Nutshell* is different. It is far more accessible, and it is full of Hawking's wry humour. One can select chapters to read without needing to have mastered earlier chapters. One can even cherry pick the juicy bits with little loss of content. And the highlights are well worth reading, in large part because of Hawking's caustic asides and his infallible optimism.

The ebb and flow of time is a recurring theme that appears and reappears in the book. I must confess that I have still not completely got to grips with imaginary time, but the nutshell metaphor conjures up a much warmer image. The nutshell represents a "hypersphere" in which the roles of space and time have become reversed. It provides a somewhat individualistic approach to quantum gravity, but one that is near to the forefront of current research. In a nutshell, this mixing up of space and time is what happens just inside a black hole as one approaches the black-hole horizon and crosses the point of no return. This is standard black-hole physics, as laid down by Einstein's theory of gravitation, the theory of general relativity.

The classical view of a black hole is marred by one ugly feature: at the core of the black hole lies a singularity. This is a forbidding concept, since literally all hell may break loose should one get too near to the singularity. Hawking is convinced that such a singularity is never accessible, or "naked": it is always shrouded by the black-hole horizon. In other words, we can live our lives without undue fear of the horrors of confronting a singularity, with the inevitable breakdown of the physical laws that govern our existence and even our sanity.

Were we to find a naked singularity, it would immediately allow us to extract unlimited resources from other universes. Miracles could be performed. Time travel would become feasible, since space and time reverse their roles. One could travel in time, either far into the future to escape any of the unfortunate calamities of our current era, or into the past, to pursue our dreams of long-lost Elysian fields.

It is this prospect that horrifies Hawking, for one could, if sufficiently perverse, go back in time, seek out one's grandfather in his infancy, and murder him in order to challenge future generations of physicists. For now our notions of causality would be overturned: the impossible is possible, and there is a fundamental contradiction in the laws of physics.

Kip Thorne proposed a solution to this paradox. Quantum gravity, he argued, tells us that such ventures are subject to the laws of uncertainty. The probability of actually finding a particular individual at a particular place and time would be vanishingly small. Time travel is a good exercise for the statistically inclined. Hawking's take on time travel is different: he argues that one could never succeed in constructing a workable time machine.

In one of the great *tours de force* of modern cosmology, Hawking - working with Roger Penrose - predicted that if the universe were causal, and time machines could never exist, then the universe must have begun from a physical singularity. This would be a catastrophe for cosmologists with fundamentalist inclinations.

As with religious movements, cosmologists who deal with the very early universe fall into two schools: the phenomenologists and the fundamentalists. The former deal with data, adopting empirical theory with its lack of rigour and all of its inevitable flaws to match. The latter start from pure mathematics, appeal to beauty and simplicity to guide the physics, and say to hell with any data that happen to clash with the theory. Not that there is usually much in the way of data, apart from rare exceptions.

Here is where the nutshell cosmology enters. The flaw in the deduction about the past singularity is that the theory of general relativity made no allowance for quantum gravity. According to Hawking, quantum gravity mathematically (thanks to imaginary time) provides a dual and singularity-free description of the universe, in which the roles of space and time are reversed. Time has no boundaries, nor does space.

Can we believe a word of this? The answer seems to be that as long as two alternative theories make identical predictions, it is meaningless to debate which one is true. This is positivist thinking. Theory never advances by proving anything is actually true, but rather by leading to predictions that conflict with observable data. All we can ever hope to do is to falsify a theory; then we move on to the next one.

The nutshell theory makes absolutely no predictions that are verifiable, at least not yet. But then neither does its immediate rival, superstring theory, now incorporated into the theory of M-branes, which consist of higher-dimensional space-time manifolds collectively called "p-branes", where *p* stands for any integer that represents the dimensionality of space. Physicists would very much like to be able to predict *p* from first principles.

We know that *p* cannot be 1 or 2, for we would be, respectively, sausage-like or pancake-like, with the accompanying adverse effects on our digestive systems, among other problems. Quantum gravity can be resolved, at least in principle, in spaces of higher dimensions. This has been one of the great messages from superstring theory. Troublesome infinities (and infinity really is troublesome to a physicist) can be removed if we settle for *p* in some higher-dimensional space. The preferred number is 10, although some hold out for 4. Certainly 3 is insufficient, for one needs the extra freedom of higher dimensionality.

However, there is a price to pay. The nutshell - and indeed any quantum-gravitational theory - gives rise to too many descriptions of our past. Most can have no bearing on reality. The universe would not resemble our observed universe. It might be immensely more chaotic or quiescent. Either would be a disaster for the predictive power of a fundamental theory. In the absence of any predictions, this line of reasoning about possible outcomes only takes us so far. Hawking, in good company, supplements it with the "anthropic principle".

Scientists, especially cosmologists, love principles. After all, the cosmological principle carried Einstein far, if at first in the wrong direction. The anthropic principle asserts that the universe is just so because we are here. If it were any different, there would be no cosmologists to observe it (see "Life, the cosmos and everything" *Physics World* October pp23-25).

One can now supplement the cosmic nutshell with this cosmic principle, and our very own big bang emerges. One can understand, so we are told, why the universe is so vast and relatively uniform, and why it is just beginning to undergo a phase of acceleration away from the big bang.

So we seem to be in good shape. Never mind that the most powerful minds in physics, so they tell us, have been working on superstring theory for two decades and have yet to show us a single unambiguous and experimentally verifiable prediction. Certainly, it is a phenomenally difficult theory. Is the anthropic principle part of the solution? I do not wish to overly dampen the party spirit, but I am underwhelmed by it.

The anthropic principle is one of the more remarkable swindles in physics. Indeed it is metaphysics, and that is the essence of the problem for most physicists in accepting it. The anthropic logic is either immensely subtle, by arguing that we, via our mere existence, control the cosmos, or unabashedly naive, by setting aside any physics explanations that any ultimate theory of physics might reasonably be expected to deliver. Metaphysics lacks predictive power, the very core of physics. The anthropic principle is an extreme expression of our ignorance.

It may well be that the ultimate theory of cosmology will have anthropic ramifications. We are some way yet from this promised land. In the meantime, Hawking's book is a delight to read. It discusses questions that are at the forefront of current thinking about quantum gravity, yet for the most part is highly readable. It conveys the author's sense of wonder and awe at the cosmos, and - like a child stepping into the darkness - illustrates his tentative gropings towards the ultimate theory of everything.