The Universe Within

by Neil Turok

  in the midst of an illimitable ocean of inexplicability. Our business in

  every generation is to reclaim a little more land.”

  — T. H. Huxley, 188752

  “Behind it all is surely an idea so simple, so beautiful,

  that when we grasp it — in a decade, a century, or a millennium — we will all

  say to each other, how could it have been otherwise?”

  — John Archibald Wheeler, 198653

  SOMETIMES I THINK I’M the luckiest person alive. Because I get to spend my time wondering about the universe. Where did it come from? Where is it going? How does it really work?

  In 1996, I took up the Chair of Mathematical Physics at the University of Cambridge. It was an opportunity for me to meet and to work with Stephen Hawking, holder of the Lucasian Chair — the chair Isaac Newton held. It was Hawking who, three decades earlier, had proved that Einstein’s equations implied a singularity at the big bang — meaning that all the laws of physics fail irretrievably at the beginning of the universe. In the eighties, along with U.S. physicist James Hartle, Hawking had also proposed a way to avoid the singularity so that the laws of physics could describe how the universe began.

  During the time Stephen and I were working together, he invited me to be interviewed on TV as part of a series about the cosmos he was helping to produce. Soon after the program was aired, a letter appeared in my mailbox. It was from Miss Margaret Carnie, my grade school teacher in Tanzania. I jumped up and down with joy. Margaret had always held a special place in my heart, but we had lost touch when I was ten years old and my family moved to England. Margaret was now back in Scotland and had spotted my name on TV. She wrote: “Are you the same Neil Turok who I taught as a little boy at Bunge Primary School in Dar es Salaam?”

  Margaret had devoted her life to teaching. She was a part of a long tradition of maths and science teaching dating back to the Scottish Enlightenment. She and her identical twin sister, Ann, had both taught in the little government school in Dar es Salaam and lived with their mother, also a teacher, in the flat above. The secret of Margaret’s approach was not to instruct her students but to gently point them in interesting directions. She gave me lots of freedom, and lots of materials. I made plans and maps of the school, drew living creatures and plants, experimented with Archimedes’ principle, played with trigonometry, and explored mathematical formulae. At home, I made electric motors and dynamos from old car parts, collected beetles, watched ant lions for hours, caused explosions, and made huts out of palm fronds — though you had to watch out for the snakes moving in! It was a wonderful childhood.

  Just before Margaret had written to me, I’d been told about one of Cambridge’s oldest traditions, that newly appointed professors were invited to give an inaugural public lecture. I’d also learned that very few bothered anymore. Having heard from Margaret, I simply had to give mine in her honour. So I called her up and invited her and her sister, and after that we kept in touch regularly. A few years later, I visited them in Edinburgh. They were in their late seventies but still very active — volunteering for the museum, organizing and attending public lectures, and generally being the life and soul of their community.

  As we sat in their little apartment drinking tea, Margaret asked me what I was working on. When I answered “Cosmology” and started to explain, she waved all the details away. She said in her strong Scottish accent, “There’s only one really important question. Every time I go to a public lecture on astronomy, I ask the lecturer: ‘What banged?’ But I never get a sensible reply.”

  “Margaret, that’s exactly what I’m working on!” I said. “I always knew you were a clever boy,” she replied. And she pulled out an old photo of me grinning at her while wielding a hoe in the schoolyard farm. I did look pretty enthusiastic.

  I tried to explain to Margaret the latest model I’d been working on, where the big bang is a collision between two three-dimensional worlds. But her eyes glazed over and I could tell that she thought it was all too complicated and technical. She was a down-to-earth, pragmatic person. She wanted a simple, straightforward, and believable answer. Sadly, she and her sister passed away a few years ago. I’m still looking for an answer that would satisfy them.

  IN THIS MODERN AGE, where our lives are so focused on human concerns, cosmology may seem like a strange thing to be thinking about. Einstein to some extent was expressing this when he said, “The most incomprehensible thing about the world is that it is comprehensible.” 54 Even he thought it a surprise that we — people — can look out at it — the universe — and understand how it works.

  In ancient Greece, they saw things quite differently. The early Greek philosophers viewed themselves as a part of the natural world, and for them understanding it was basic to all other endeavours. They thought of the universe as a divine, living being whose innermost essence was harmony. They called it kosmos, and believed it to represent the ultimate truth, wisdom, and beauty. The word “theory,” or theoria, which the ancient Greeks also invented, means “I see (orao) the divine (theion).”55 They believed nature’s deep principles should guide our notions of justice and of how to best organize society. The universe is far greater than any of us, and through its contemplation we may gain a proper perspective of ourselves and how we should live. According to the ancient Greeks, understanding the universe is not a surprise: it is the key to who we are and should be. They believed the universe to be comprehensible, and history has certainly proven them right. We should draw encouragement from their example and gain optimism and belief in ourselves.

  In the Middle Ages, cosmology also played a major role in society. There was a great debate pitting Renaissance thinkers against the Catholic Church over its insistence that the Earth was the centre of the universe. In overturning this view, Copernicus and Galileo revived many of the ideals of ancient Greece, including the power of rational argument over dogma. In showing that Earth is just a planet moving around the sun, they liberated us from the centre of the cosmos: we are space travellers, with a whole universe to explore. Galileo’s proposal, inspired by the ancient Greeks, of universal, mathematical laws was a profoundly democratic idea. The world could be understood by anyone, and the only tools one needed were reason, observation, and mathematics, none of which depended on your position or authority.

  Built upon Galileo’s intuition, Isaac Newton’s unification of the laws of motion and gravity, along with his invention of calculus, laid the foundations for all of engineering and the industrial age. But remember that Newton’s key discoveries were learned from the solar system, though all of their applications for the next few centuries were terrestrial. The universe has been very good at teaching us things.

  Two hundred years later, Michael Faraday learned more secrets from nature. His experiments and his intuition guided Maxwell, just as Galileo’s had guided Newton. Maxwell unified electricity, magnetism, and light, and laid the ground for quantum theory and relativity. Einstein was so impressed with Maxwell’s theory that, in his 1905 paper on the quantization of light, he wrote, “The wave theory of light . . . has proven to be an excellent model of purely optical phenomena and presumably will never be replaced by another theory.” 56 And later, in an essay on Maxwell in 1931, Einstein wrote, “Before Maxwell, physical reality was thought of as consisting of material particles . . . Since Maxwell’s time, physical reality has been thought of as represented by continuous fields . . . This change in the conception of reality is the most profound and most fruitful that physics has experienced since the time of Newton.”57

  Maxwell’s theory inspired Einstein’s theory of space, time, and gravity, which would eventually describe the whole cosmos. Its quantum version would lead to the development of subatomic physics and the description of the hot big bang. And late in the twentieth century, the quantum theory of fields would produce theories explaining the density variations that gave rise to galaxies. Physics has come full circle: what Newt
on gleaned from the heavens inspired the development of mathematical and physical theories on Earth. Now these in turn have extended our understanding of the cosmos. Think of how delighted the ancient Greek thinkers would have been with this progress. The virtuous cycle of learning from the universe and extending the reach of our knowledge continues, and we need to take heart from it.

  When I was a very young child, as I have already mentioned, I thought the sky above was a vaulted ceiling with painted-on stars. But when I stand and look out at the universe now, I appreciate the extent to which we have been able to comprehend it through the work of Maxwell, Einstein, and all the others who followed. To me, this understanding is an incredible privilege, and a glimpse of what we are and should be. When we look up at the sky, we’re actually seeing inside ourselves. It is an act of wonder to stand there and realize how the world really works. And even more so to peer over the edge of our understanding, and anticipate the answers to even bigger questions. The mathematics that gets us there is a means to an end. For me, the real world is the awesome thing, and what I’m most interested in is what it all means.

  · · ·

  IMAGINE A PERFECT BALL of light, just a millimetre across. It is the brightest, most intense light you can possibly conceive of. If you can think of compressing the sun down to the size of an atomic nucleus, that will give you some sense of the searing brilliance inside the ball. At these extreme temperatures, it is far too hot for any atoms or even atomic nuclei to survive. Everything is broken down into a plasma of elementary particles and photons, the energy packets of light.

  Now imagine the ball of light expanding, faster than anything you have ever seen or can imagine. Within one second, it is a thousand light years across. It didn’t get there by the light and particles travelling outwards in an explosion — nothing can travel that fast. Instead, the space inside the ball expanded. As it grew, the wavelength of the photons was stretched out. They became far less energetic, and the plasma temperature fell. One second after the expansion began, the temperature is ten billion degrees. The photons are still energetic enough to tear atomic nuclei apart.

  As the space within the ball expands and the plasma cools further, the matter particles are able to clump into atomic nuclei. Ten minutes after the expansion began, the atomic nuclei of the lightest chemical elements — hydrogen, helium, lithium — are formed. The nuclei of the heavier chemical elements, such as carbon, nitrogen, and oxygen, will form later in stars and supernovae.

  The ball of light continues to expand, at an ever decreasing rate. After four hundred thousand years, it is ten million light years across. The conditions are cool enough now for the atomic nuclei to gather electrons around them and form the first atoms. The conditions are similar to those at the surface of the sun, with the temperature measured in thousands of degrees. Space is still expanding, though at a far slower rate, and it is still filled with an almost perfectly uniform plasma consisting of matter and radiation. However, as we look across space, we see small variations in the density and temperature from place to place, at a level of just one part in a hundred thousand. These mild ripples in the density occur on all scales, small and large, like a pattern of waves on the ocean.

  As the universe expands, gravity causes the ripples to grow in strength, like waves approaching the shore. The slightly denser regions become much more dense and collapse like giant breakers to form galaxies, stars, and planets. The slightly less dense regions expand out into the empty voids between the galaxies. Today, 13.7 billion years after the expansion began, the millimetre-sized brilliant ball of light has grown to a vast region encompassing hundreds of billions of galaxies, each containing hundreds of billions of stars.

  Although the events I have just described were in our past, we can check that they happened just by looking out into space. Since light travels at a fixed speed, the farther out we look, the younger the objects we witness. The moon, for example, is a light second away, meaning that we see it as it was a second ago. Likewise we see the sun as it was eight minutes ago, and Jupiter as it was forty minutes ago. The nearest stars are ten light years beyond the solar system, and we see them as they were a decade ago. The Andromeda Galaxy, one of our nearest galaxy neighbours, is two million light years away, so we are seeing it as it was before our species appeared on Earth.

  As we look farther out, we see farther back in time. Around us is the middle-aged universe: quieter and more predictable, slowly spreading. By detecting chemical elements within stars, we can measure their abundances throughout the universe and check that they agree with predictions. Reaching out to around twelve billion light years, we see the universe’s tumultuous adolescence with the collapsing clouds of matter creating quasars — powerful sources of radiation formed around massive black holes, as well as newly formed spiral and elliptical galaxies. Beyond those, we see baby galaxies, some just nascent wisps of gas starting to pull themselves together. Looking out farther, we can see all the way back to a time just four hundred thousand years after the big bang, when space was filled with a hot plasma at a temperature roughly that of the surface of the sun.

  We can see no farther, because at earlier times the atoms were broken up into charged particles, which scatter light and obscure our view of the earlier universe. The radiation that emanates from this hot plasma rind all around us has been stretched out by the expansion of the universe to microwave wavelengths. As we look back to this epoch, it appears from our perspective as if we are in the centre of a giant, hot, spherical microwave oven.

  We have just described the hot big bang theory, a spectacularly successful description of the evolution of the universe. “But what banged?” I hear you ask. There is no bang in the picture, just the expansion of space from a very dense assumed starting point. Space expanded in the same way and at once, everywhere. There was no centre of the expansion: the conditions in the universe were the same across all of space. Our millimetre-sized ball is just the portion of the primeval universe that expanded into everything we can now see today (click to see photo).

  IN 1982, I WAS a graduate student at Imperial College, London, and just beginning to get interested in cosmology. I heard about a workshop taking place at Cambridge called “The Very Early Universe,” and I went there for a day to listen to the talks. All the most famous theorists were there: Alan Guth, Stephen Hawking, Paul Steinhardt, Andrei Linde, Michael Turner, Frank Wilczek, and many others. And they were all very excited about the theory of inflation.

  The goal of inflation was to explain the initial ball of light. The ball had many puzzling features. In addition to being extremely dense, it must have been extremely smooth throughout its interior. The space within it was not curved, as Einstein’s theory of gravity allowed, but almost perfectly flat. How could it be that such an object emerged at the beginning of the universe? And how could it have produced the tiny density variations needed to seed the formation of galaxies?

  The theory of inflation was invented by MIT physicist Alan Guth as a possible explanation. Guth’s idea was that even if the very early universe was random and chaotic, there might be a mechanism for smoothing it out and filling it with a vast amount of radiation. He thought he had found such a mechanism in grand unified theories, which attempted to connect our description of all the particles in nature and all the forces except gravity. In these theories, there are certain kinds of fields, called “scalar fields,” which take a value at each point in space. They are similar to electric and magnetic fields, but even simpler in that they have only a value, not a direction, at each point. In grand unified theories, sets of these scalar fields, called “Higgs fields,” were introduced in order to distinguish between the different kinds of particles and forces. They were generalizations of the electroweak Higgs field, which we shall discuss in Chapter Four, recently reported to have been discovered at the Large Hadron Collider.

  These theories postulated a form of energy called “scalar potential energy,” w
hich unlike ordinary matter was gravitationally repulsive. Guth imagined a tiny patch of the universe starting out full of nothing but this energy. Like our ball of light, it would be extremely dense. Its repulsive gravity would accelerate the expansion of space even faster than the interior of our ball of light, causing space to grow exponentially in its first phase. Guth called this scenario “cosmic inflation.”

  In Guth’s picture the universe might have started from a region far smaller than a millimetre, far smaller even than an atomic nucleus, and containing far less energy. In fact, you could contemplate the universe starting out with a patch of space not much larger than the Planck length, a scale believed to be an ultimate limit imposed by quantum theory. And it need contain only as much energy as the chemical energy stored in an automobile’s gas tank.58 The inflationary expansion of space, filled with scalar potential energy at a fixed density, would create all the energy in the universe from a tiny seed. Guth called this effect the “ultimate free lunch.” The notion is beguiling but, as I shall discuss later, potentially misleading because energy is not constant when space expands. The idea that you might get “something for nothing” nevertheless underlies much of inflationary thinking. Upon more careful examination, as we shall see, there is always a price to pay.

  If a tiny patch of the universe started out in this state, the scalar potential energy would blow it up exponentially, almost instantly making it very large, very uniform, and very flat. When it reached a millimetre in size, you could imagine the scalar potential energy decaying into radiation and particles, producing a region like the ball of light at the start of the big bang. In Guth’s picture, the scalar potential energy was a sort of self-replicating dynamite. Just a tiny piece of it would be enough to create the initial conditions for the hot big bang.

  Inflation brought an unexpected bonus: a quantum mechanism for producing the small density variations — the cosmic ripples — that later seeded the formation of galaxies. The mechanism is based on quantum mechanics: the scalar potential energy develops random variations as a consequence of Heisenberg’s uncertainty principle, causing it to vary from place to place, on microscopic scales. The exponential expansion of the universe blows up these tiny ripples into very large-scale waves in the density of the universe. These density waves are produced on all scales, and it was a triumph for inflation that the density waves were predicted to have roughly the same strength on every scale. The level of the density variation in these waves can be adjusted by a careful tuning of the inflationary model to one part in a hundred thousand, the level of density variations required to explain the origin of galaxies.