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The Universe in a Nutshell

By Avinash Patra, Sr. |  June, 12 2015

I believe 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.

A brief description of this title: 

The fact that his new offering fails to deliver on either count tells us something about publishing, something else about physics and, perhaps, something more about the limits of what theoretical physicists can convey to others about what they are thinking. It tells us rather less that is new about the universe. But that may be because the approaches now being taken to understanding the nature of things challenge the assumptions underpinning "popular science".

The unfinished business of Hawking's first book, and of many others since, was a way of uniting the two great theoretical edifices of 20th-century physics. If only some device could be found to link Einstein's framework for describing space, time and gravity with the picture of the other forces of physics painted by quantum mechanics, the way would be clear to a grand unified theory. This would explain all the features of the physical universe, from the Big Bang to as many billion years beyond our time as there turn out to be.

The Universe in a Nutshell is more episodic than A Brief History, but is mainly a commentary on the same ideas. The first problem with this is that not much has actually happened in physics since 1988. String theory - usually glossed as representing the fundamental physical entity as a minute vibrating loop of some ineffable stuff, with different modes of vibration manifesting as the particles and forces of more familiar physics - remains the best bet for the ultimate theory.

This means that your £20 buys you a lot of repetition of things you first read in A Brief History. If you had trouble understanding them then, you probably won't do any better this time around; many of the explanations are exactly the same. There are now a great many elaborate illustrations. If you are confident of shifting shedloads of books because Hawking's name is on the cover, then it is fair to spare no expense on the artwork. But look carefully, and most of the diagrams that actually explain something - the concept of particle spin, or the way light moves in the neighbourhood of a black hole - are the same as before, too. The images make this book a more handsome object, but also cloak the brevity of the text, a scant 100 pages of unadorned print. That means that quite a lot of things which should be explained are skimped. When he writes, for example, that "we have come to recognise that this standing still of real and imaginary time means that spacetime has a temperature", you expect an account of how "we" came to this realisation. But none appears.

There is a deeper problem, though. The developments in theory that have taken place since the earlier book have just made things less comprehensible - whether explained by Hawking or anyone else. Strings, for example, are no longer strings but a subset of a much larger range of "branes", which can extend in any number of dimensions - 10 or 11 are the hot bets. But when a caption alongside an abstract depiction of some wavy-looking, textured sheets in shades of brown simply says that "Black holes can be thought of as the intersections of p-branes in the extra dimensions of spacetime", neither words nor images yield any real purchase on the theory.

The fact is that p-branes make a lay reader feel like a pea-brain because they can only properly be thought of in mathematical terms. Words don't make it. These objects (if objects they are) have no correlates in our familiar world that we can sensibly say they are like, and diagrams tend to be bad at representing 10 dimensions.

Hawking offers a reason not to care. He is, he says several times, a positivist, so is concerned only with whether mathematical models with extra dimensions provide a good description of the universe, not with whether they have any real meaning. This is little comfort if the reader does not share this curiously old-fashioned philosophy of science. But even writers who have tried to convey the nature of these theories at much greater length have not been much help. The best of them, Brian Greene in The Elegant Universe, works very hard to describe the kinds of mathematics involved, but still leaves the outsider feeling that there is something very clever going on, but not really clear what it is.

The alternatives to string theory, which Hawking does not mention, are even further removed from recognisable concepts. Lee Smolin's recent Three Roads to Quantum Gravity calls for a synthesis of string theory with two other approaches that are even more baffling for the uninitiated.

There are other, less important reasons why there is little need for this book to appear apart from Bantam's urge to keep the franchise going. Aside from odd flashes of wit, the writing is pretty routine. The opening chapter on Einstein, for example, contains nothing that is not familiar from other popular accounts of relativity theory. An interlude on the future of life says little apart from the fact that it will probably depend on computers and genetic engineering, and the result will not look much like Star Trek. There is still poignancy in reading that "although we human beings are very limited physically, our minds are free to explore the whole universe" when you know the words were written by Hawking, but this is not enough to carry a whole book.

But perhaps as poignant is the persistence of the gap between the lay appetite for understanding the deepest theories about the universe and the attempts to feed it. Hawking helped usher in the current resurgence of popular-science writing. The millions who bought A Brief History showed how many really care what science can reveal, and we should all be grateful for the now-widespread assumption that anything can be made clear if the experts really try. For many sciences, the results are often remarkable; but the field that really helped popular science achieve lift-off remains elusive. If Hawking's books revolve around the question of whether cosmologists are about to unveil a theory of everything, they leave the reader with another, equally taxing question. If they did, how would we know?