The Universe Within

by Neil Turok

  When we studied this idea, we discovered that the pressure of the unstable energy would become large and positive, and it would quickly dominate everything else. As the universe collapsed, this large positive pressure would quickly make the universe very smooth and flat.When the universe shrunk down to zero size, it would hit a singularity. Then, plausibly, the universe would rebound, fill with radiation, and start expanding again. In fact, immediately after the bounce we would have conditions just like those in our millimetre-sized ball of light: the very initial conditions that were needed to explain the hot big bang.

  Much to our surprise, we found that during the collapse initiated by the unstable vacuum energy, our high-pressure matter develops quantum variations of exactly the form required to fit observations. So in this picture, we can reproduce inflationary theory’s successes, but with no need for initial inflationary conditions.

  Our scenario is far more ambitious than inflation in attempting to incorporate and explain the big bang singularity. We have based our attempts on M-theory, a promising but still developing framework for unifying all the laws of physics. M-theory is the most mathematical theory in all of physics, and I won’t even try to describe it here.

  Einstein used the mathematics of curved space to describe the universe. M-theory uses the same mathematics to describe everything within the universe as well. For example, string theory, which is a part of M-theory, describes a set of one-dimensional universes — pieces of string — moving within higher-­dimensional space. Some strings describe force-carrier particles like photons, gluons, or gravitons, while others describe matter particles like electrons, quarks, or neutrinos. As well as strings, M-theory includes two-dimensional universes, called “membranes,” and three-dimensional universes, called “3-branes,” and so on. According to M-theory, all of these smaller universes are embedded within a universe with ten space dimensions and one time dimension, which seems more than rich enough to contain everything we see.

  In the best current versions of M-theory, three of the ten space dimensions — the familiar dimensions of space — are very large, while the remaining seven are very small. Six of them are curled up in a tiny little ball whose size and shape determine the pattern of particles and forces we see at low energies. And the seventh, most mysterious dimension, known as the “M-theory dimension,” is just a tiny gap between two three-dimensional parallel worlds.

  Until our work, most M-theorists interested in explaining the laws of particle physics today had assumed that all the extra, hidden dimensions of space were static. Our new insight was to realize that the extra dimensions could change near the big bang, and that the higher-dimensional setting would cast the big bang singularity in a new light.

  What we found was that, according to M-theory, the big bang was just a collision between the two three-dimensional worlds living at the end of the M-theory dimension. And when these worlds collide, they do not shrink to a point — from the point of view of M-theory, the three-dimensional worlds are like two giant parallel plates running into each other. What our work showed was that, within M-theory, the big bang singularity was, after all, not as singular as it might first appear, and most physical quantities, like the density of matter and radiation, remain completely finite.

  Recently, we have discovered another, very powerful way to describe how the universe passes through the singularity, which turns out not to rely on all the details of M-theory. The trick uses the same idea of imaginary time which Hartle and Hawking used to describe the beginning of spacetime. But now we use imaginary time to circumvent the singularity, passing from a pre-bang collapsing universe to a post-bang expanding universe like the one we see today. We are close to finding a consistent and unique description of this process and to opening a new window on the pre-bang world.

  If the universe can pass through a singularity once, then it can do so again and again. We have developed the picture into a cyclic universe scenario, consisting of an infinite sequence of big bangs, each followed by expansion and then collapse, with the universe growing in size and producing more and more matter and radiation in every cycle. In this picture of the universe, space is infinite and so too is time: there is no beginning and there is no end. We called this an “endless universe.”72 A cyclical universe model may, in its evolution, settle down to a state in which it repeats the same evolution, in its broad properties, over and over again. In this way, the vast majority of space would possess the physical properties of the universe we see. There would be no need for anthropic arguments, and the theoretical predictions would be clearer.

  IF THERE IS ONE rule in basic physics, I would say it is “in the long run, crime does not pay.” Cosmology in the twentieth century was, by and large, based on ignoring the big bang singularity. Yet the singularity represents a serious flaw in the theory, one which it is possible to ignore only by making arbitrary assumptions, which, in the end, may have little foundation. By continuing to ignore the singularity, we are in danger of building castles of sand. The singularity may just be our greatest clue as to where the universe really came from. Our work on the cyclic universe model has shown that all of the successes of the inflationary model can be reproduced in a universe that passes through the singularity without undergoing any inflation at all.

  The competition between the cyclic and inflationary universe models highlights one of the most basic questions in cosmology: did the universe begin? There are only two possible answers: yes or no. The inflationary and cyclic scenarios provide examples of each possibility. The two theories could not be more different: inflation assumes a huge burst of exponential expansion, whereas the cyclic model assumes a long period of slow collapse. Both models have their weak points, mathematically, and time will tell whether these are resolved or prove fatal. Most exciting, the models make different observational predictions which can be tested in the not-too-distant future.

  At the time of writing, the European Space Agency’s Planck satellite is deep in space, mapping the cosmic background radiation with unprecedented precision. I have already discussed how inflation can create density variations in the universe. The same mechanism — the burst of inflationary expansion — amplifies tiny quantum gravitational waves into giant, long-wavelength ripples in spacetime, which could be detectable today. One of the Planck satellite’s main goals is to detect these very long wavelength gravitational waves though their effects on the temperature and polarization of the cosmic background radiation across the sky. In many inflationary models, including the simplest ones, the effect is large enough to be observed.

  Throughout his career, Stephen Hawking has enjoyed making bets. It’s a great way of focusing attention on a problem and encouraging people to think about it. When I gave my first talk on the cyclic model in Cambridge, I emphasized that it could be observationally distinguished from inflation because, unlike inflation, it did not produce long wavelength gravitational waves. Stephen immediately bet me that the Planck satellite would see the signal of inflationary gravitational waves. I accepted at once, and offered to make the bet at even odds for any sum he would care to name. So far we haven’t agreed on the terms, but we will do so before Planck announces its result, which may be as soon as 2013. Another leading inflationary theorist, Eva Silverstein of Stanford University, has agreed to a similar, though more cautious bet: the winner will get either a pair of ice skates (from me, in Canada) or a pair of rollerblades (she being from California).

  · · ·

  LOOKING BACK OVER PAST millennia, we have to feel privileged to be alive at a time when such profound questions about the universe are being tackled, and when the answers seem finally within reach. In ancient Greece, there was a debate that in many ways prefigured the current inflationary/cyclic competition. Parmenides of Elea held the view — later echoed by Plato — that ideas are real and sensations are illusory, precisely the opposite of the views later espoused by David Hume. If thought is reality, then anything one can
conceive of must exist. Parmenides reasoned that since you cannot think of something not existing without first thinking of the thing itself, then it is logically impossible for anything to come into existence. Hence he believed all change must be an illusion: everything that happens must already be implicit in the world. This is a fairly accurate description of Hartle and Hawking’s “no boundary” proposal. To work out the predictions of their proposal, one works in “imaginary time” — in the primordial, quantum region of spacetime where everything that happens subsequently in the universe is implicit, and one continues the predictions into real time to see what they mean for today’s observations.

  On the other hand, Heraclitus of Ephesus, like Anaximander before him, held the opposite point of view. “All is flux” was his dictum: the world is in constant tension between its opposing tendencies. Everything changes and nothing endures. The goal of philosophy, he argued, is to understand how things change, both in society and in the universe. Starting with Zeno, the Stoic philosophers introduced the concept of ekpyrosis, meaning “out of fire,” to describe how the universe begins and ends in a giant conflagration, with a period of normal evolution in between. In his treatise On the Nature of the Gods, Cicero explains, “There will ultimately occur a conflagration of the whole world . . . nothing will remain but fire, by which, as a living being and a god, once again a new world may be created and the ordered universe restored as before.” 73 There were similar ideas in ancient Hindu cosmology, which presented a detailed cyclic history of the universe.

  In the Middle Ages, the idea of a cyclic universe became less popular as Christianity took hold and the biblical explanation of a “beginning” became the norm. Nevertheless, cyclic ideas regularly appeared — Edgar Allan Poe wrote an essay titled “Eureka” that proposed a universe resembling the ancient ekpyrotic picture. And the German philosopher Friedrich Nietzsche also advocated a repeating universe. He argued that since there can be no end to time and there are only a finite number of events that can occur, then everything now existing must recur, again and again for eternity. Nietzsche’s model of “eternal recurrence” was popular in the late nineteenth century.

  In fact, Georges Lemaître, even as he worked on the idea of a “quantum beginning,” commented favourably on Friedmann’s oscillating cosmological solutions. In 1933, he wrote that these cyclic models possessed “an indisputable poetic charm and make one think of the phoenix of the legend.”74

  For now, we stand on the verge of major progress in cosmology. Both theory and observation are tackling the big bang in our past, and they will determine whether it was really the beginning of everything or merely the latest in a series of bangs, each one of which produced a universe like ours. They are also tackling the deep puzzle of the vacuum energy that now dominates the universe, and which will be overwhelmingly dominant in the future. What is it composed of, and can we access it? Will it last forever? Will the exponential expansion it drives dilute away all of the stars and galaxies that surround us and lead to a vacuous, cold eternity? Or will the vacuum energy itself seed the next bang? These questions have entered the realm of science and of scientific observation. I, for one, cannot wait for the answers.

  FOUR

  THE WORLD IN AN EQUATION

  “If you are receptive and humble, mathematics will lead you by the hand.

  Again and again, when I have been at a loss how to proceed, I have just had

  to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path,

  a path where new vistas open up, a path leading to new territory, where one ca

  set up a base of operations, from which one can survey the surroundings and plan future progress.”

  — Paul Dirac, 197575

  USING THE MOST POWERFUL radio telescope on earth, astronomers have just detected an encrypted signal emanating from Vega, one of the brightest stars in the sky and about twenty-five light years away. The message contains instructions for building a machine to teleport five human beings across space to meet with the extraterrestrials. After an intense international search, world leaders select the five delegates. Among them is the brilliant young Nigerian physicist Dr. Abonnema Eda, who has just won the Nobel Prize for discovering the theory of superunification, combining all known physics into a single, unified picture.

  The storyline comes from Carl Sagan’s 1985 novel Contact, later made into a movie starring Jodie Foster. Sagan was a renowned U.S. astronomer and, with his TV series Cosmos, one of science’s greatest popularizers. In casting Eda as a hero in his novel, Sagan was making two points: first, that discovering the basic laws of the universe is a global, cross-cultural field of research. People from every country are fascinated by the same questions about how the world works. Second, genius knows no national boundaries. Although Africa has so far been woefully under-represented in the history of physics, like other disadvantaged regions, in the future it may be a source of incredible talent. Science benefits greatly from a diversity of cultures, each bringing a new stimulus of energy and ideas.

  OVER THE PAST DECADE I have led a dual existence. On the one hand, I have been trying to understand how to describe the beginning and the far future of the universe. On the other, I have been fascinated by the problem of how to enable young people to enter science, especially in the developing world.

  My interest is rooted in my African origins. As I described earlier, I was born in South Africa, where my parents were imprisoned for resisting the apartheid regime. Upon their release, we left as refugees, first to East Africa and then the U.K. When I was seventeen, I returned to Africa to teach for a year in a village mission school in Lesotho, a tiny, landlocked country surrounded by South Africa. Lesotho is one of the poorest nations on Earth: 80 percent of the jobs available are migrant labour, mostly in the mines over the border. In the village of Makhakhe, where I worked, I met many wonderful people and great kids with loads of potential but zero opportunity. No matter how bright or talented they were, they would never have the chances I’d had. A clerical position in the mines was the height of their aspiration.

  The kids in the mission school were eager, responsive, and bright. But by and large, the education they’d received consisted of rote learning: memorizing times tables, copying notes from the blackboard and reproducing them in exams. They had no real experience of figuring things out or learning to think for themselves. School was a dry exercise you had to submit to: its sole purpose was to get a certificate. The teachers had been taught that way themselves, and they perpetuated a cycle of harsh discipline and low expectations.

  I tried to take the kids outside as often as possible, to try to connect what we did in class with the real world. One day I asked them to estimate the height of the school building. I expected them to put a ruler next to the wall, stand back and size it up with finger and thumb, and make an estimate of the wall’s height. But there was one boy, very small for his age and the son of one of the poorest families in the village, who was scribbling with chalk on the pavement. A bit annoyed, I said, “What are you doing? I want you to estimate the height of the building.” He said, “I measured the height of a brick. Then I counted the number of bricks and now I’m multiplying.” Well, needless to say, I hadn’t thought of that!

  People often surprised me with their enthusiasms and interests. Watching a soccer match at the school one day, I sat next to a miner, at home on his annual leave. He told me, “There’s only one thing that I really loved at school: Shakespeare.” And he recited some lines to me. Many similar experiences convinced me of the vast potential for intellectual development which is sorely needed for the continent’s progress.

  Evolution was not on the school curriculum, because the church objected, but we nevertheless had excellent classroom discussions about it. Most African children are unaware of modern scientific discoveries showing how Homo sapiens originated in Africa around two hundred thousand years ago and began to migra
te out of Africa between seventy thousand and fifty thousand years ago. I believe they could draw motivation from learning how humankind, and mathematics, and music and art, arose in Africa. Instead, young Africans are all too often made to feel like helpless bystanders, with every advance happening elsewhere in the world.

  With the end of apartheid in 1994, my parents were allowed to return to South Africa. Both won election as members of the new parliament for the African National Congress, alongside Nelson and Winnie Mandela. They kept saying to me, “Can’t you come back and help in some way?” At the time, I was too busy with my own scientific career. Eventually, in 2001, I took a leave from my position at Cambridge to visit the University of Cape Town, near where my parents lived. Most of the time, I was pursuing new cosmological theories, like the cyclic universe scenario. But I took time out from my research to meet with colleagues and discuss what we might do to help speed Africa’s scientific development.

  In these conversations, it quickly emerged that Africa’s deficiency in maths is a serious problem. There is an acute scarcity of engineers, computer scientists, and statisticians, making it impossible for industry to innovate or, more generally, for governments to make well-informed decisions regarding health, education, industry, transport, or natural resources. African countries are highly dependent on the outside world; they export raw and unprocessed commodities, and import manufactured goods and packaged food. Cellphones have transformed the lives of many Africans, but none are yet made in Africa. If Africa is to become self-­sufficient, it urgently needs to develop its own community of skilled people and scientists to adapt and invent the technologies that will allow it to catch up to the rest of the world.