Relatively, how long is a piece of superstring?

Why is our universe the way it is, given the bewildering array of possibilities? Joseph Silk isn't the only one with a theory or two up his sleeve...

Everything not forbidden is compulsory, somewhere, some time; this is a slogan adapted from the epic novel The Once and Future King by T. H. White and beloved by physicists. It provides scope for such bizarre concepts as black holes, now detected in great numbers, and worm holes, which are potential time machines and portals to other universes. Of course, we are far from detecting worm holes, but their potential existence has inspired countless science-fiction sagas about time travel. It is a shame that their application to time travel appears to defy the laws of quantum mechanics.

Perhaps the most far-reaching idea in this genre has come about with the notion of alternative universes. As we are well on the way to making a mess of our own, these provide an intriguing escape route. The theme of parallel universes has inspired the successful popular trilogy His Dark Materials by Philip Pullman and popularisations of science such as Michio Kaku's latest book, about quantum gravity and parallel universes.

We are at an interesting moment in physics. The year 2005 is the centenary of Einstein's explosive arrival in physics. Indeed, in 1905 he virtually defined modern physics with three major discoveries in one year. Curiously, none of these discoveries involved gravitation. It was the confirmation, in 1919, of his predicted light-bending of distant star images by the gravity field of the sun - twice the value expected in Newton's theory - that made him world-famous overnight.

His new theory was heralded by his contemporaries as one of the greatest achievements of human thought. But Einstein was not satisfied with mastering gravity. The quantum theory, pioneered by Niels Bohr, made provocative claims that Einstein refused to accept. How could the deterministic macroscopic world be one of probability that seemingly could not achieve reality until it was observed? Schrodinger's famous thought experiment about the quantum world involved a cat in a closed cage subject to lethal poisoning by the probabilistic decays of a radioactive isotope.

After triggering the isotope, one cannot immediately predict, when the cage is opened, whether the cat is alive, dead or merely very sick. The cat does not achieve a "real" state until it is observed. But, as Eugene Wigner asked, how do we know the observer is real? We must specify who observes the observer. And so on, to an infinity of observers.

One solution is that quantum uncertainty becomes irrelevant on macroscopic scales - quantum effects are relevant for atoms but not for cats. This solution evades the real issue. At some level, a choice has to be made. Is the cat, or its microscopic equivalent, alive or dead? To avoid this dilemma, the Copenhagen view of quantum theory, developed by Bohr, postulates that there are two distinct realities, one in which the cat is dead and another in which the cat is alive. These are parallel universes whose existence becomes relevant once the cat's cage is viewed. Of course, the cat is a trivial example. Consider any quantum event. There are always alternative outcomes. There is an infinity of parallel universes, all equally real.

The resolution of Einstein's dilemma requires a theory that unites gravity and quantum mechanics. Our best candidate for such a unified theory is superstring theory. Superstrings may provide the elusive infrastructure that allows a unified theory of particle physics and gravity. Progressive refinements in superstring theory over the past two decades, by some of the best mathematical physicists in the world, have constructed a beautiful mathematical edifice, yet the ultimate dream of a parameter-free theory of everything remains as remote as ever.

To some theorists, the superstring characterises a theory that has no predictive power, and is more philosophy than physics. It is a theory valid at the smallest scale feasible in the theory of quantum gravity, the Planck scale, which is where the size of a black hole confronts the uncertainty principle. There are, as yet, no hard connections to the low-energy universe. Superstring theory exists in 11 dimensions. We do not live in an 11-dimensional universe, and physicists meekly conclude that seven space dimensions have curled up to be comparable to the Planck-length scale - the only natural scale of the theory - to leave behind our three dimensions of space and one of time.

Despite the vast energy gap with superstrings, optimists live in hope that some discordancies in the observable universe may reveal the need for new physics that is a possible signature of superstring theory. Suppose that the Newton-Einstein law of gravity were found to break down, either at very small or very large scales where it has not yet been adequately tested. On very small scales, for example below 1mm, one might hope to see a deviation that could hint at the presence of curled-up extra dimensions. On very large scales, at the horizon and beyond, an anomaly in the law of gravitation might hint at the influence of a higher dimensional space - in essence, another universe that only connects to our own via gravity. And at the Large Hadron Collider, the world's most powerful particle accelerator now under construction on the Franco-Swiss border, the hidden dimensions might manifest themselves by revealing unexpected structure in particles such as the electron.

The theory of superstrings is our best candidate for the ultimate theory of quantum gravity. However, we may have too much of a good thing. As Kaku elegantly describes, at the last count there were some 10100 candidates for the superstring theory. There are far more if we accept the Copenhagen view of quantum mechanics. There is no reason to doubt their reality. But this brings up the following question: why is our universe the way it is, given the bewildering array of alternative possibilities?

Could our place in the multiverse arise from self-selection? The so-called anthropic principle, in its weakest form, argues that all of the other universes are inimical to life. This cannot be the whole story, of course, if only because a vast range of possibilities survives. There must be an element of randomness to explain. For example, the Earth must be within a certain range of distance from the Sun for life to develop. But to account for its precise location within the habitable zone around the Sun requires more than the anthropic principle. Presumably, the Earth is at a random location within the habitable zone. What is more disconcerting is the apparent tuning of fundamental physical forces and masses. If the ratio of the proton to electron mass were larger by 1 per cent, atoms would not be stable. If the weak nuclear force were weaker by 4 per cent, carbon would not have formed. Yet life is only part of this story, for these masses and force strengths are measured to much higher precision in the laboratory.

The anthropic principle is, by its nature, imprecise. One has to combine it with a throwing of the dice. So, if the element of randomness plays such a crucial role, why not dispense entirely with the anthropic principle? The only response appeals to the enormous degree of fine-tuning needed to select a universe that allows the potentiality of life. This is so unlikely that randomness cannot provide a viable explanation.

But one has to be very careful when the probability of life is discussed.

We know that on the biological level, the origin of life is not a random process. Likewise, there is no reason to believe that selection of universes is necessarily a random process. Quantum gravity theory is incomplete in this regard. Recourse must be had to data. Indeed, there are indications that our observed universe may have formed from non-random initial conditions. As yet, these are but hints. However, cosmologists have been greatly exercised in the past year by the unexpected smoothness of the universe on the largest scales, as viewed in the cosmic microwave background. Moreover, the infinitesimal temperature fluctuations seen on the largest angular scales are unusually aligned. Does our visible universe have a preferred direction? This would provide a global element of cosmology that could not possibly have an anthropic explanation.

Once one opens the Pandora's Box of non-random conditions, we can no longer apply probability arguments with any confidence to the initial creation of the universe. The ultimate theory of quantum gravity will surely play a role in understanding the initial conditions of the universe. There is no compelling need to appeal to anthropic arguments, or their shallowly disguised counterpart - the presence of a Grand Designer - to explain the universe we inhabit. If we cannot compute the statistical probability of our universe arising from an array of some 10100 vacuum states, or the even larger multiplicity of universes present in a multiverse, discussion of fine-tuning is meaningless. Perhaps the universe we inhabit arose out of non-randomness that some future "theory of everything" will have to address.

Parallel Worlds takes us on a breathless tour of what is and is not feasible, in which more or less anything goes. There are uncountable numbers of parallel universes to be discovered, Kaku argues, almost all of which are far beyond anything we can imagine. The book is, for the most part, very readable. When the topics are too stringy (superstrings are Kaku's speciality), the going gets tough. In fact, quantum gravity is a field where only the tough, mathematically speaking, go. It is not easy to find an accessible explanation for a general readership of the concepts that bind the quantum theory and gravity. This book almost succeeds. There are excellent descriptions of how strings have come to dominate the theory of quantum gravity, and of the motivation for postulating that parallel universes exist. Such ideas are central to the future of physics.

Joseph Silk is professor of astronomy, Oxford University.