THREE
WHAT BANGED?
“The known is finite, the unknown infinite; intellectually we stand on an islet
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 Newton 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.
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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,” which 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.
As a young scientist, I was amazed to see the confidence that these theorists placed in their little equations when describing a realm so entirely remote from human experience. There was no direct evidence for anything they were discussing: the exponential blow-up of the universe during inflation, the scalar fields and their potential energy which they hoped would drive it, and — what they were most excited about at the meeting — the vacuum quantum fluctuations that they hoped inflation would stretch and amplify into the seeds of galaxies. Of course, they drew their confidence from physics’ many previous successes in explaining how the universe worked with mathematical ideas and reasoning.
But there seemed to me a big difference. Maxwell and Einstein and their successors had been guided by a profound belief that nature works in simple and elegant ways. Their theories had been extremely conservative, in the sense of introducing little or no arbitrariness in their new physical laws. Getting inflation to work was far more problematic. The connection to grand unified theory sounded promising, but the Higgs fields, which were introduced in order to separate the different particles and forces, would typically not support the kind of inflation needed: they would either hold the universe stuck in an exponential blow-up forever or they would end the inflation too fast, leaving the universe curved and lumpy. Working models of inflation required a fine tuning of their parameters and strong assumptions about the initial conditions. Inflationary models looked to me more like contrivances than fundamental explanations of nature.
At the same time, the attention theorists were now giving to cosmology was enormously energizing to the field. Although the inflationary models were artificial, their predictions gave observers a definite target to aim at. Over the next three decades, the inflationary proposal, along with other ideas linking fundamental physics to cosmology, helped drive a vast expansion of observational efforts directed at the biggest and most basic questions about the universe.
THE STORY OF MODERN cosmology begins with Einstein’s unification of space, time, energy, and gravity, which closely echoed Maxwell’s unification of electricity, magnetism, and light. When Einstein visited London, a journalist asked him if he had stood on the shoulders of Newton. Einstein replied, “That statement is not quite right; I stood on Maxwell’s shoulders.” 59 Just as happened with Maxwell’s theory, many spectacular predictions would follow from Einstein’s. Maxwell’s equations had anticipated radio waves, microwaves, X-rays, gamma rays — the full spectrum of electromagnetic radiation. Einstein’s equations were even richer, describing not only the fine details of the solar system but everything from black holes and gravitational waves to the expansion and evolution of the cosmos. His discoveries brought in their wake an entirely new conception of the universe as a dynamic arena. Einstein’s theory was more complicated than Maxwell’s, and it would take time to see all of its implications.
The most spectacular outcome of Maxwell’s unified theory of electricity and magnetism had been its prediction of the speed of light. This prediction raised a paradox so deep and far-reaching in its implications that it took physicists decades to resolve. The paradox may be summarized in the simplest of questions: the speed of light relative to what? According to Newton, and to everyday intuition, if you see something moving away and chase after it, it will recede more slowly. If you move fast enough, you can catch up with it or overtake it. An absolute speed is meaningless.
In every argument, there are hidden assumptions. The more deeply they are buried, the longer it takes to reveal them. Newton had assumed that time is absolute: all observers could synchronize their clocks and, no matter how they moved around, their clocks would always agree. Newton had also assumed an absolute notion of space. Different observers might occupy different positions and move at different velocities, but again they would always agree on the relative positions of objects and the distances between them.
It took Einstein to realize that these two seemingly reasonable assumptions — of absolute time and space — were incompatible with Maxwell’s theory of light. The only way to ensure that everyone would agree on the speed of light was to have them each experience different versions of space and time. This does not mean that the measurements of space and time are arbitrary. On the contrary, there are definite relations between the measurements made by different observers.
The relations between the measurements of space and time made by different observers are known as “Lorentz transformations,” after the Dutch physicist Hendrik Lorentz, who inferred them from Maxwell’s theory. In creating his theory of relativity, Einstein translated Lorentz’s discovery into physical terms, showing that Lorentz’s transformations take you from the positions and times measured by one observer to those measured by another. For example, the time between the ticks of a clock or the distance between the ends of a ruler depends on who makes the observation. For an observer moving past them, a clock goes more slowly and a ruler aligned with the observer’s motion appears shorter than for someone who sees them at rest. These phenomena are known as “time dilation” and “Lorentz contraction,” and they become extremely important when observers move relative to one another at speeds close to the speed of light.
The Lorentz transformations mix up the space and time coordinates. Such a mixing is impossible in Newton’s theory, because space and time are entirely different quantities. One is measured in metres, the other in seconds. But once you have a fundamental speed, the speed of light, you can measure both times and distances in the same units: seconds and light seconds, for example. This makes it possible for space and time to mix under transformations. And because of this mixing, they can be viewed as describing a single fundamental entity, called “spacetime.”
The unification of space and time in Einstein’s theory, which he called “special relativity,” allowed him to infer relationships between quantities which, according to Newton, were not related. One of these relations became the most famous equation in physics.
IN 1905, THE SAME year that he introduced his theory of special relativity, Einstein wrote an astonishing little three-page paper that had no references and a modest-sounding title: “Does the Inertia of a Body Depend Upon Its Energy-Content?” This paper announced Einstein’s iconic formula, E = mc2.
Einstein’s formula related three things: energy, mass, and the speed of light. Until Einstein, these quantities were believed to be utterly distinct.
Energy, at the time, was the most abstract of them: you cannot point at something and say, “That is energy,” because energy does not exist as a physical object. All you can say is that an object possesses energy. Nevertheless, energy is a very powerful idea, because under normal circumstances (not involving the expansion of space), while it can be converted from one form into another, it is never created or destroyed. In technical parlance, we say energy is conserved.
The concept of mass first arose in Newton’s theory of forces and motion, as a measure of an object’s inertia: how much push is required to accelerate the object. Newton’s second law of motion tells you the force you need to exert to create a certain acceleration: force equals mass times acceleration.
So how does energy equal the mass of an object times the speed of light squared? Einstein’s argument was simple. Light carries energy. And objects like atoms or molecules can absorb and emit light. So Einstein just looked at the process of light emission from an atom, from the points of view of two different observers.
The first observer sees the atom at rest emit a burst of electromagnetic waves. From energy conservation, it follows that the atom must have had more energy before it emitted the light than it had afterward. Now let’s look at the same situation from the point of view of a second observer, moving relative to the first. The second observer sees the atom moving, both before and after the emission. According to the second observer, the atom has some energy of motion, or kinetic energy. The second observer also sees a slightly more energetic burst of radiation compared to the first, just because she is in motion. This extra energy can be calculated from Maxwell’s theory, using a Lorentz transformation.
Now Einstein just wrote down the equations for energy conservation. The total energy before the emission must equal the energy after it, according to both observers. From these two equations it follows that the atom’s kinetic energy after the emission, as seen by the second observer, must equal the atom’s kinetic energy before the emission plus the extra energy in the burst of radiation. This equation relates the energy in the burst of radiation to the mass of the atom before and after the emission. And the equation implies that the atom’s mass changes by the energy it emits divided by the square of the speed of light. If the atom loses all of its mass in this process, and just decays completely into the burst of radiation, the same relation applies. The amount of radiation energy released must be equal to the original mass times the speed of light squared, or E = mc2.
Einstein put it this way: “Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substances and the two conservation laws. The answer is: No. According to the theory of relativity, there is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy.”60 E = mc2 is a unification. It tells us that mass and energy are two facets of the same thing.
What Einstein’s magical little formula tells us is that we are surrounded by vast stores of energy. For example, that sachet of sugar you are about to stir into your coffee has a mass energy equivalent to a hundred kilotons of TNT — enough to level New York. And of course, his discovery prefigured the development of nuclear physics, which eventually led to nuclear energy and the nuclear bomb.
In Newton’s theory, there was no limit to the speed of an object. But in Einstein’s theory, nothing travels faster than light. The reason is fundamental: if something did travel faster than light, then according to Lorentz’s transformations, some observers would see it going backward in time. And that would create all sorts of causality paradoxes.
IN DEVELOPING THE THEORY of relativity, the next question facing Einstein, which echoed concerns raised by Michael Faraday more than half a century earlier, was whether the force of gravity could really travel faster than light. According to Newton, the gravitational force of attraction exerted by one mass on any other mass acts instantaneously — that is, it is felt immediately, right across the universe. As a concrete example, the tides in Earth’s oceans are caused by the gravitational attraction of the moon. As the moon orbits Earth, the masses of water in the oceans follow. According to Newton, the moon’s gravity is felt instantly. But moonlight takes just over a second to travel from the moon to Earth. Faraday and Einstein both felt it unlikely that the influence of gravity travelled any faster.
In constructing a theory of gravity consistent with relativity, one of the key clues guiding Einstein was something that Galileo had noticed: all objects fall in the same way under gravity, whatever their mass. An object in free fall behaves as if there is no gravity, as we know from the weightlessness that astronauts experience in space: an astronaut and her space capsule fall together. This behaviour suggested to Einstein that gravity was not the property of an object, but was instead a property of spacetime.
What then is gravity? Gravity is replaced, in Einstein’s theory, by the bending of space and time caused by matter. Earth, for example, distorts the spacetime around it, like a bowling ball sitting in the centre of a trampoline. If you roll marbles inwards, the curved surface of the trampoline will cause them to orbit the bowling ball, just as the moon orbits Earth. As the physicist John Wheeler would later put it, “Matter tells spacetime how to curve, and spacetime tells matter how to move.”61
After ten years of trying, in 1916 Einstein finally discovered his famous equation — now called Einstein’s equation — according to which the curvature of spacetime is determined by the matter contained within it. He used the mathematical description of curved space invented by the German mathematician Bernhard Riemann in the 1850s. Before Riemann, a curved surface, such as a sphere, had always been thought of as embedded within higher dimensions. But Riemann showed how to define the key concepts in geometry, like straight lines and angles, intrinsically within the curved surface, without referring to anything outside it. This discovery was very important, because it allowed one to imagine that the universe was curved, without it having to be embedded inside anything else.
Einstein’s new theory, which he called “general relativity,” brought our view of the universe much closer to that of the ancient Greeks: the universe as a vital, dynamic entity with a delicate balance between its elements — space, time, and matter. Einstein altered our view of the cosmos, from the inert stage I had envisaged as a child to a changeable arena that could curve or expand.
In welcoming Einstein to London, the celebrated playwright George Bernard Shaw told a jokey story about how a young professor — Albert Einstein — had demolished the Newtonian picture of the world. Upon learning that Newton’s gravity was no more, people asked him: “But what about the straight line? If there is no gravitation, why do not the heavenly bodies travel in a straight line right out of the universe?” And, Shaw continues, “The professor said, ‘Why should they? That is not the way the world is made. The world is not a British rectilinear world. It is a curvilinear world, and the heavenly bodies go in curves because that is the natural way for them to go.’ And at last the whole Newtonian universe crumbled up and vanished, and it was succeeded by the Einsteinian universe.”62
In the early days Max Born described Einstein’s theory of general relativity thus: “The theory appeared to me then, and it still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art to be admired from a distance.”63 Today, Born’s statement is no longer true. Einstein’s younger successors applied his theory to the cosmos and found it to work like a charm. Today, general relativity is cosmology’s workhorse, and almost every observation we make of the universe — whether from the Hubble Telescope or giant radio arrays or X-ray or microwave satellites — relies on Einstein’s theory for its interpretation.
General relativity is not an easy subject. As an undergraduate, I trudged my way through a famously massive textbook on the subject called Gravitation, which weighs 2.5 kilograms. It was a quixotic attempt — while the subject is conceptually simple, its equations are notoriously difficult. After six months of trying, I decided instead to take a course. That made it all so much easier. Physics, like many other things, is best learned in person. Seeing someone else do it makes you feel you can do it too.
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THE DISCOVERY OF GENERAL relativity, and its implication that spacetime was not rigid, raised a question: what is the universe doing on the very largest scales, and how is it affected by all the matter and energy within it? Like everyone else at the time, when Einstein started to think about cosmology, he assumed the universe was static and eternal. But immediately a paradox arose. Ordinary matter attracts other ordinary matter under gravity, and a static universe would just collapse under its own weight. So Einstein came up with a fix. He introduced another, simpler form of energy that he called the “cosmological term.” Its main properties are that it is absolutely uniform in spacetime, and it looks exactly the same to any observer. The best way to visualize the cosmological term is as a kind of perfectly elastic, stretchy substance, like a giant sponge filling space. It has a “tension,” or negative pressure, meaning that as you stretch it out it stores up energy just like an elastic band. But no matter how much you stretch it, its properties do not change — you just get more of it.
At first, a negative pressure sounds like exactly what you don’t want holding up the universe. It would suck things inward and cause a collapse. However, as we described earlier, the expansion of the universe is not like ordinary physics. It is not an explosion: it is the expansion of space. And it turns out that the effect of a negative pressure, in the Einstein equations, is exactly the opposite of what you might expect. Its gravity is repulsive and causes the size of the universe to blow up. (This effect of repulsive gravity is the same one that Guth used in his theory of inflation.)
So Einstein made his mathematical model of the universe stand still by balancing the attractive gravity of the ordinary matter against the repulsive gravity of his cosmological term. The model was a failure. As noticed by the English astrophysicist Arthur Eddington, the arrangement is unstable. If the universe decreased a little in size, the density of the ordinary matter would rise and its attraction would grow, causing the universe to collapse. Likewise, if the universe grew a little in size, the matter would be diluted and the cosmological term’s repulsion would win, blowing the universe up.
It would fall to two very unusual people to see what Einstein could not: that his theory describes an expanding universe.
THE FIRST WAS ALEXANDER Friedmann, a gifted young Russian mathematical physicist who had been decorated as a pilot in the First World War. Due to the war and the Russian Revolution that followed it, news of Einstein’s theory of general relativity did not reach St. Petersburg, where Friedmann worked, until around 1920. Nevertheless, within two years, Friedmann was able to publish a remarkable paper that went well beyond Einstein. Like Einstein, Friedmann assumed the universe, including ordinary matter and the cosmological term, to be uniform across space and in all directions. However, unlike Einstein, he did not assume that the universe was static. He allowed it to change in size, in accordance with Einstein’s equation.
What he discovered was that Einstein’s static universe was completely untypical. Most mathematical solutions to Einstein’s equations described a universe which was expanding or collapsing. Einstein reacted quickly, claiming Friedmann had made mathematical errors. However, within a few months, he acknowledged that Friedmann’s results were correct. But he continued to believe they were of exclusively mathematical interest, and would not match the real universe. Remember, at the time of these discussions, very little was known from observations. Astronomers were still debating whether our own Milky Way was the only galaxy in the universe, or whether the patchy clouds called “nebulae,” seen outside its plane, were distant galaxies.
Einstein’s reason for disliking Friedmann’s evolving universe solutions was that they all had singularities. Tracing an expanding universe backward in time, or a collapsing universe forward in time, you would typically find that at some moment all of space would shrink to a point and its matter density would become infinite. All the laws of physics would fail at such an event, which we call a “cosmic singularity.”
Friedmann nevertheless wondered what would happen if you followed the universe through a singularity and out the other side. For example, in some models he studied, the universe underwent cycles of expansion followed by collapse. Mathematically, Friedmann found he could continue the evolution through the singularity and out into another cycle of expansion and collapse. This idea was again prescient, as we will discuss later.
Today, Friedmann’s mathematical description of the expansion of the universe provides the cornerstone of all of modern cosmology. Observations have confirmed its predictions in great detail. But Friedmann never saw his work vindicated. In the summer of 1925, he made a record-breaking ascent in a balloon, riding to 7,400 metres, higher than the highest mountain in all Russia. Not long afterwards, he became ill with typhoid and died in hospital.
TWO YEARS LATER, UNAWARE of Friedmann’s work, a Belgian Jesuit, Abbé Georges Lemaître, was also considering an evolving universe. Lemaître added a new component: radiation. He noticed that the radiation would slow the expansion of the universe. He also realized that the expansion would stretch out the wavelength of electromagnetic waves travelling through space, causing the light emitted from distant stars and galaxies to redden as it travelled towards us. The U.S. astronomer Edwin Hubble had already published data showing a reddening of the starlight from distant galaxies. Lemaître interpreted Hubble’s data to imply that the universe must be expanding. And if he traced the expansion back in time, billions of years into our past, he found the size of the universe reached zero: it must have started at a singularity.
Once more, Einstein resisted this conclusion. When he met Lemaître in Brussels later that year, he said, “Your calculations are correct, but your grasp of physics is abominable.”64 However, he was once more forced to retract. In 1929, Hubble’s observations confirmed the reddening effect in detail and were quickly recognized as confirming Lemaître’s predictions. Still, many physicists resisted. As Eddington would say, the notion of a beginning of the world was “repugnant.”65
Lemaître continued to pursue his ideas, trying to replace the singular “beginning” of spacetime with a quantum phase. What he had in mind was to use quantum theory to prevent a singularity at the beginning of the universe, just as Bohr had quantized the orbits of electrons in atoms to prevent them from falling into the nucleus. In a 1931 article in Nature, Lemaître stated: “If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning: they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.” 66 Lemaître called his hypothesis “the Primeval Atom,” and as we’ll see, it prefigured the ideas of the 1980s.
In January 1933, there was a charming encounter between Einstein and Lemaître in California, where they had both travelled for a seminar series. According to an article in the New York Times,67 at the end of Lemaître’s talk, Einstein stood and applauded, saying, “This is the most beautiful and satisfactory explanation of creation to which I have ever listened.” And they posed together for a photo, which appeared with the caption: “Einstein and Lemaître — They have a profound admiration and respect for each other.”
If ever one needed confirmation of the idea that diversity feeds great science, it is provided by these strange encounters between Einstein, and, first, a Russian aviator, and then a Belgian priest. The meetings must have been intense: our whole understanding of the cosmos rested in the balance.
SHORTLY AFTER THE SECOND World War, George Gamow, a former student of Friedmann’s at St. Petersburg, made the next big step forward by bringing nuclear physics into cosmology. “Geo,” as he was known to his friends, was a Dionysian personality — fond of jokes and pranks, a heavy drinker, larger than life. His great strength as a scientist was his audacious insight: he wasn’t one to bother with details, but enjoyed the big picture. He did much to encourage others to work on interesting problems, especially applications of nuclear physics. For example, in 1938, he and Edward Teller, best known as “the father of the hydrogen bomb,” organized a conference called “Problems of Stellar Energy Sources,” bringing physicists and astronomers together to work out the nuclear processes that power the sun and other stars. This historic meeting launched the modern description of stars in the universe, one of the most successful areas of modern science.
After the Russian Revolution, Gamow had been the first student to leave on an international exchange, spending time in Copenhagen with Bohr and then in Cambridge with Rutherford. Eventually, and with many regrets, he defected to the West and became a professor at George Washington University in Washington, D.C. No doubt due to his Russian connections, Gamow was not cleared to work on the atomic bomb, but he did consult for the U.S. Navy’s Bureau of Ordnance. In this capacity he played the role of go-between, carrying documents up to Princeton for Einstein to examine at his home there. Apparently, they would work on these documents in the mornings and discuss cosmology in the afternoons.68
Gamow was an expert in nuclear physics. In 1928, he had explained the radioactive decay of heavy atomic nuclei, discovered by Curie, as being due to the quantum tunnelling of subatomic particles out of the nuclei’s interiors. When Gamow started thinking about cosmology, his goal was typically ambitious: to explain the abundances of every chemical element in nature, from hydrogen through the whole periodic table.
His idea was simplicity itself: if the early universe was hot, it would behave like a giant pressure cooker. At very high temperatures, space would be filled with a plasma of the most basic particles — like electrons, protons, and neutrons. At those temperatures, they would be flying around so fast that none of them could stick together. As the universe expanded, it would cool, and the neutrons and protons would stick together to form atomic nuclei.
His student Ralph Alpher, and another young collaborator, Robert Herman, worked out the details, combining Friedmann and Lemaître’s equations with the laws of nuclear physics to figure out the abundances of the chemical elements in the universe today. The approach worked well for the lightest elements — hydrogen and its heavier isotopes, and helium and lithium — and is now the accepted explanation for their relative abundances. But it failed to explain the formation of heavier elements, like carbon, nitrogen, and oxygen, later understood to have formed in stars and supernovae, and for this reason did not attract the interest it deserved.
Lying buried in Alpher, Gamow, and Herman’s papers was a most wonderful prediction: the hot radiation that filled space in the early universe would never entirely disappear. One second after the singularity, when the first atomic nuclei started to form, the radiation’s temperature would have been billions of degrees. As the universe expanded, the temperature of the radiation would fall, and today it would be just a few degrees above absolute zero.
Alpher, Gamow, and Herman realized that today’s universe should be awash with this relic radiation — the cosmic microwave background radiation. In terms of its total energy density, it would greatly exceed all of the energy ever radiated by every star formed in the universe. And its spectrum — how much energy there is in the radiation at each wavelength — would be the same as that of a hot object, the very same spectrum described by Max Planck in 1900 when he proposed the quantization of light.
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UP TO THIS POINT, discussions of the hot big bang theory were almost entirely theoretical. That situation was about to change dramatically. In 1964, working in Holmdel, New Jersey, Arno Penzias and Robert Wilson unintentionally detected the cosmic microwave background radiation. Their instrument was a giant, ultrasensitive radio antenna that had been built at Bell Labs, AT&T’s research laboratory in New Jersey, for bouncing radio signals off a large metallic balloon in space, called Echo 1. The experiments with Echo 1 were part of the effort to develop global communications technologies following the wartime development of radar.
The trials with Echo 1 were followed by the deployment of the first global communications satellite, Telstar. Launched in 1962 and looking a bit like R2-D2, the 170-pound satellite was blasted into space on the back of a modified missile. Telstar relayed the first transcontinental live TV show, watched by millions. It inspired a hit song, titled “Telstar,” by a British band called the Tornados. The song opens with sounds of radio hiss, crackle, and electronic blips that give way to a synthesizer tune with an optimistic melody line. Even now it sounds futuristic. The song was an instant hit — the first British record to reach number one in the U.S., it ultimately sold five million copies worldwide. Ironically, Telstar was felled by atmospheric nuclear tests — the increases in radiation in the upper atmosphere overwhelmed its fragile transistors. According to the U.S. Space Objects Registry, its corpse is still in orbit.69
Telstar transformed TV’s grasp of the world. In parallel with NASA’s plans for the first lunar landing in 1969, a global network of communications satellites was placed into geosynchronous orbit. The network was ready just in time for the world to watch on TV as the Apollo 11 astronauts stepped onto the moon.70
With Telstar’s deployment, the giant radio antenna for receiving signals from Echo 1 was no longer required. Penzias and Wilson, who both earned Ph.D.s in astronomy before joining Bell Labs, were allowed to use the antenna as a radio telescope, and they jumped at the chance. But as they collected their first data, they discovered a persistent hiss from the antenna, at microwave wavelengths, no matter which direction it faced on the sky. Try as they might, they could not get rid of the noise. Famously, they even tried scrubbing pigeon guano off the antenna, but the noise still came through.
Eventually, Penzias and Wilson’s attention was drawn to a lecture that had just been given by James Peebles, a young theorist working with Robert Dicke nearby at Princeton, predicting radiation from the cosmos at just the wavelengths that would account for the hiss in their antenna. Unaware of Alpher, Gamow, and Herman’s earlier calculations, Dicke and Peebles had reproduced their prediction of cosmic background radiation at a temperature of a few degrees Kelvin, corresponding to millimetre wavelengths — microwaves. So Penzias and Wilson phoned Dicke, then planning an experiment to search for the background radiation. As soon as Dicke put the phone down, he told his younger colleagues, “We’ve been scooped.” Penzias and Wilson’s discovery was the “shot heard around the world,” immediately convincing almost all physicists that the universe had started with a hot big bang.
IN 1989, A DEDICATED NASA satellite called the Cosmic Background Explorer (COBE) took these background radiation measurements to a whole new level of precision. At the time, I was a professor at Princeton and had been working for a decade on how to test unified theories through cosmological observations. It was an exciting field, using the universe itself as the ultimate laboratory to test ideas about physics at extremely high energies, well beyond the reach of any conceivable experiment. However, I was worried about two things: first, that many of the theories we were discussing were too contrived; and second, that the data was too limited to tell which theory was right.
Then I went to the most dramatic seminar I have ever attended. Held in the basement of the physics department in Princeton, it was the first unveiling of data from the COBE satellite. The speaker was my colleague in the department, David Wilkinson. Dave had been part of Bob Dicke’s original team that had been narrowly scooped by Penzias and Wilson. By now he had become one of the pioneers of experimental cosmology, having made increasingly refined measurements of the background radiation, culminating in his involvement with COBE. COBE marked a transition in the subject: before it, almost nothing in cosmology was known to a better accuracy than a factor of two. But after COBE, one precision measurement followed another. Theories are now routinely proved wrong on the basis of discrepancies with the data of only a few percent.
One of COBE’s main experiments was the Far Infrared Absolute Spectrophotometer (FIRAS), designed to measure the spectrum of the background radiation. The hot big bang theory predicted that this spectrum should be the Planck spectrum predicted by Max Planck when he first proposed the quantization of light to describe radiation from a hot body. The background radiation was emitted from the hot plasma of the early universe four hundred thousand years after the expansion began, when the temperature had fallen to a few thousand degrees. At that time, the radiation took the form of red light. Once released, the radiation was stretched out a thousand-fold as it travelled across space, so that today most of the energy is carried in wavelengths of a few millimetres. Today, its spectrum is that of a hot body at just a few degrees Kelvin. In fact, to calibrate its measurements, FIRAS compared the sky with a perfectly black internal cavity whose temperature was dialled up and down to match that of the sky.
As Wilkinson put up a slide showing the measured spectrum, he said: “Here’s a plot to bring tears to your eyes.” There was an audible gasp from the audience. The data looked too good to be true. After just ten minutes of data, the measurements from the sky fit the Planck spectrum perfectly. By the time FIRAS completed its work, at every single frequency of radiation measured, the intensity matched the Planck spectrum to better than one part in a hundred thousand, and the temperature of the sky was measured at 2.725 degrees Kelvin. The measurements showed, in the most convincing way possible, that we live in a universe full of radiation left over from a hot big bang.
All I could think was, “Wow. The whole universe is shining down on us, saying, ‘Quantum mechanics, quantum mechanics, quantum mechanics.’”
COBE HAD MORE IN store. Its measurements would indicate that quantum mechanics not only governed the cosmic radiation, it controlled the structure of the universe.
Following Penzias and Wilson’s discovery, astrophysicists such as Peebles had been trying to work out how galaxies and other structures could have been formed from small density variations present in the very early universe. Einstein’s equations predict how such variations grow with time. Places where there is greater density expand more slowly, and their gravity pulls more mass towards them. And places where there is less density expand more rapidly and empty out. In this way, gravity is the great sculptor of the universe, shaping planets, stars, galaxies, galaxy clusters, and all the other structures within the cosmos. Using Einstein’s equations, we can trace this shaping process in reverse to figure out how the universe looked at earlier times. In other words, we can use the equations to retrace cosmic evolution. And then we can work out how the density variations should appear in the background radiation’s temperature as it is mapped across the sky.
The COBE satellite carried another experiment called the Differential Microwave Radiometer (DMR). It was designed to scan for tiny differences in the temperature of the background radiation across the sky. The principal investigator of that experiment was George Smoot of the University of California, Berkeley. Smoot, like Wilkinson, had pioneered measurements of the cosmic background radiation throughout his career.
I first met Smoot in 1991 at a summer school in Italy. Everyone wanted to know whether COBE’s DMR experiment had detected any variations in the temperature across the sky (click to see photo). In Smoot’s lectures, he showed a perfectly uniform map of the temperature. In private, he showed me slides of the actual measurements, which showed faint milky patches. Smoot was at that time still skeptical about whether the patches were real, and thought they might be an artefact of the experiment. And he had little confidence in theory: ever since the 1960s, theorists had been steadily lowering their predictions for the level of the expected temperature variations — from one part in a thousand, to a part in ten thousand, to one part in a hundred thousand, making them harder and harder for experimentalists like Smoot to detect.
The theorists had a reason to lower their predictions: they did so because of the growing evidence for dark matter (click to see photo). Dark matter’s existence was first inferred in the 1930s by Swiss astronomer Fritz Zwicky, from observations of galaxies orbiting other galaxies in clusters. Their high velocities implied that more mass was present than could be accounted for by the visible stars. In the 1970s, U.S. astronomer Vera Rubin observed a similar effect in the outskirts of galaxies, where stars are seen to orbit so fast that if it were not for some extra gravity holding them in, they would escape from the galaxies.
Dark matter may consist of an unknown type of particle that does not interact with light or with ordinary matter. The only way to see these particles would be through their gravity. In the 1980s, astronomers found more evidence for dark matter by observing the bending of light by gravitational fields. This effect is called “gravitational lensing” and is similar to the effect water has on light passing through it. Although water is perfectly transparent, you can tell that it is there because it bends the light and distorts the image of whatever is behind it. If you’re in the bathtub and hold your hand up and look at the water droplets on the ends of your fingers, you’ll see a distorted image of the room behind every drop. Astronomers have found similarly distorted images of distant galaxies behind galaxy clusters. And by figuring out how the light was bent, they can reconstruct the distribution of the dark matter within the clusters.
In the evolution of the universe, dark matter would have played a very important role, assisting the formation of galaxies by providing an extra gravitational pull. In many ways, dark matter forms a kind of cosmic backbone, holding the other matter together in the universe. Dark matter’s gravitational pull lowered the minimal level of density variations required in the early plasma to form galaxies by today, bringing it down to one part in a hundred thousand. It was very hard to see how galaxies could have formed from density variations any smaller than that. So as COBE reached this crucial sensitivity level, it was also reaching the smallest level of variations that could possibly have formed our current universe’s structure.
Fortunately, the milky patches Smoot showed me turned out to be real. The temperature across the sky really does vary by a part in a hundred thousand, and in an incredibly simple way. The observations matched precisely expectations from inflationary theories like those discussed in the workshop I’d attended in Cambridge in 1982. When DMR’s result was announced a decade later, Stephen Hawking was quoted as saying the finding was the greatest discovery of the twentieth century, and perhaps of all time. Although his comment was hyperbolic, there was good reason to be excited.
AS MEASUREMENTS OF THE universe became far more accurate and extended to a greater and greater volume, it became possible to envisage using the entire visible universe as a giant laboratory. The big bang is the ultimate high-energy experiment. We and everything around us are its consequence. So understanding the very early universe allows us to probe physics at the shortest distances and the very highest energies. Equally, looking at today’s universe allows us to probe the largest distances and the very lowest energies. And in this probing, cosmology made another of the greatest discoveries of twentieth-century physics, the full implications of which we are still struggling to understand.
I have already mentioned Einstein’s earliest cosmological model and how it included the cosmological term. The model was a failure, but the idea of the cosmological term was a good one. In fact, it was Lemaître who persisted with it, arguing that it was a plausible addition to Einstein’s theory and should be thought of as a special, simple kind of matter that could be expected to be present in the universe. Later on, it was realized that the cosmological term represents the energy per unit volume of empty space, what we now call the “vacuum energy.” It is the very simplest form of energy, being completely uniform across space and appearing exactly the same to any observer.71
For any physical process that does not involve gravity, the vacuum energy makes no difference. It is just there all the time as an unchanging backdrop. The only way to detect it is through its gravity, and the best way to do that is to look at as big a chunk of it as possible. Of course, the biggest piece of space we have is the entire visible universe. By watching the expansion history of this whole region, you can directly measure the vacuum energy’s gravity.
In 1998, the High-Z Supernova Search Team and the Supernova Cosmology Project — two international ventures led by Australian National University’s Brian Schmidt, Johns Hopkins’s Adam Reiss, and Saul Perlmutter at the University of California, Berkeley — measured the brightness and recession speeds of exploding stars called “supernovae,” which are so bright that they are visible even in very distant galaxies. Their measurements showed conclusively that the expansion of the universe has begun to speed up, pointing to a positive vacuum energy. Perlmutter, Reiss, and Schmidt shared the 2011 Nobel Prize for this discovery. An article on the Nobel Prize website describes the vacuum energy’s repulsive effect: “It was as if you threw a ball in the air and it kept speeding away until it was out of sight.”
The discovery of a positive vacuum energy was a key step towards settling the makeup of the universe. In today’s universe, the vacuum energy accounts for 73 percent of the total energy. Dark matter accounts for 22 percent, ordinary matter like atoms and molecules 5 percent, and radiation a tiny fraction of a percent. Dark matter, ordinary matter, and radiation emerged from the early universe with gentle ripples, at a level of one part in a hundred thousand on all scales, which seeded the creation of galaxies. This “concordance model” of the universe has, over the past decade, enjoyed one success after another as all kinds of observations fell in line with it. So far, there are no clouds on its horizon.
So far, we have no idea how to use dark matter or vacuum energy, but it is tempting to speculate that, some day, they might provide a ready source of fuel that we could use to travel across space. In fact, special relativity makes the universe far easier to explore than you might think at first sight. Lorentz contraction means that, for space travellers, the universe can be crossed in a relatively short period of time.
Think about a spaceship that escapes from Earth’s gravity and continues thereafter at one g — that is, with the same acceleration that a falling object has on Earth. This would be quite comfortable for the space travellers, since they would feel an artificial gravity of just the same strength as gravity on Earth. After a year or so, the spaceship would approach the speed of light, and it would get closer and closer to light speed as time went on. As the universe flashed by, Lorentz contraction would make it appear more and more compressed in the direction of travel. After just twenty-three years of the space travellers’ time, they would have crossed the whole region of space we can currently see. Of course, it would take another twenty-three years to slow down the ship so they could get off and explore. And due to time dilation, billions of years would have elapsed back on Earth.
For now, these prospects seem very distant. But if history is anything to go on, they may be nearer than we think.
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THE PICTURE OF COSMOLOGY I have described has been remarkably successful. It has accommodated every new observation, and it now forms the foundation for more detailed studies of the formation of galaxies, stars, and planets in the universe. We have built the science of the universe. Why, then, aren’t we theorists satisfied?
The problem, as I mentioned earlier, is that working models of inflation are no more beautiful today than they were in 1982. Inflationary models do not explain what happened just before inflation, or how the universe emerged from a cosmic singularity. It is simply imagined that the universe somehow sprang into being filled with inflationary energy.
And the more we have learned about unification, the more contrived inflationary models appear. In addition to assuming the universe started out inflating, the models’ parameters have to be adjusted to extremely small values in order to fit the data. There is no shortage of inflationary models: there are thousands of them. The problem is that they are all ad hoc, and it would be impossible to distinguish many of them from each other through observations.
The small patch of space that started out inflating was assumed to be filled with inflationary energy at extremely high density. The inflationary energy will ultimately decay, at the end of inflation, into matter and radiation. However, in any realistic model there must also, at the end, be a tiny residue of vacuum energy to explain what we see today. In any inflationary model, one can ask: what is the ratio of the assumed inflationary energy density at the beginning of inflation to the vacuum energy density we now measure in the universe? That ratio must appear in the description of the model: it is a vast number, typically a googol (a one with a hundred zeros after it) or so. In every known model so far, this number is just assumed, or picked from a vastly greater number of models according to a principle we do not yet understand.
Every inflationary model suffers from this fine-tuning difficulty in addition to all of the other problems. Remember, inflationary theory was invented in order to explain the peculiar fine-tuned, smooth, and flat initial conditions required in the ball of light at the start of the hot big bang. But now we find that inflation is itself based on a strange and artificial initial condition in which the inflationary energy takes a vast value for no apparent reason.
You can think of inflationary energy as a highly compressed spring, like the one you compress when you start a game of pinball. To get the ball going as quickly as possible, you must condense the spring as much as you can. This is similar to what you need for inflation: you need an enormous density of inflationary energy, compressed into a tiny region of space. But how likely would it be for you to come across a pinball machine that spontaneously shot the ball up into the machine? It is possible that the random vibrations of the spring and the collisions of all the surrounding air molecules conspire to kick the ball up, but it is extremely unlikely. The conditions required to initiate inflation are, it turns out, vastly more improbable.
It is true that the total amount of energy required to get inflation going isn’t so great, and Guth relies on this in his “free lunch” argument. But energy is not a good measure of how extreme such an inflating region is, because energy is not conserved when space is expanding, and certainly not during inflation. There is a known measure of the rarity of inflationary initial conditions, known as the “gravitational entropy.” Roughly speaking, it allows you to ask how unusual it would be to find a patch of the universe with inflating initial conditions. The answer is that inflating initial conditions would be expected around one time in 10 raised to the power of 10 raised to the power of 120. That is an extremely small probability, and points to a serious problem with the inflationary hypothesis.
The most serious attempt so far to describe the initial conditions required for inflation was made by James Hartle and Stephen Hawking, building on earlier ideas of the Russian cosmologist Alexander Vilenkin. They noticed that because inflationary energy is repulsive, it is possible for universes to avoid a singularity. They considered a curved universe where space takes the form of a small three-dimensional sphere, and showed that such a universe, if you filled it with inflationary energy, could be started out set at some time in a static condition. If you followed time forward, the universe would grow exponentially in size. Likewise, if you followed time backward it would also grow exponentially. So if you followed time forward from some point long before the universe was static, you would see the universe first shrink and then “bounce” from contraction to expansion.
The effect is like a bouncing ball. Imagine someone shows you a time-lapse movie whose first frame shows the ball at the moment of the bounce, squished up against the floor. As time proceeds, the ball pushes itself off from the floor and becomes spherical again. Now they play the movie again, but this time running backward in time from the moment of the bounce. There is no difference! The laws of physics are unchanged if time is reversed: going backward in time, the ball will do just as it did going forward. Of course, if they show the whole movie, starting at some time well before the bounce, you will see the ball start out spherical as it hits the floor, squish up against the ground, and then unsquish itself as it bounces off.
Hartle and Hawking, following Vilenkin, employ the powerful mathematical trick of imaginary time, which I explained at the end of the previous chapter. Hawking had applied this trick successfully to black holes, showing that they possess a tiny temperature and emit radiation called “Hawking radiation.” Now he and Hartle tried to apply it to the beginning of the universe. If you follow time back to the bounce, you can use the imaginary number i to change time into another direction of space. And now, it turns out, with four space dimensions the geometry of the universe can be “rounded off” smoothly, with no singularity. Hartle and Hawking called this idea the “no boundary” proposal because in their picture, the universe near its beginning would be a four-dimensional closed surface, like the surface of a sphere, with no boundary. In spirit, their idea is highly reminiscent of Lemaître’s “Primeval Atom” proposal.
When I moved to Cambridge, in 1996, I worked with Hawking and a number of our Ph.D. students to develop the predictions of the Hartle–Hawking proposal for general theories of inflation. We showed that in such theories, the universe in the imaginary time region could generally be described as a deformed four-dimensional sphere, a configuration that became known as the “Hawking–Turok instanton.” It turns out you can work out all the observational quantities within this region, and then follow them forward to the moment of the “bounce” and then into the normal, expanding region of spacetime, where they determine what observers would actually see.
A beautiful feature of the Hartle–Hawking proposal is that it does not impose an arbitrary initial condition on the laws of physics. Instead, the laws themselves define their own quantum starting point. According to the Hartle–Hawking proposal, the universe can start out with any value for the inflationary energy. Their proposal predicts the probability for each one of these possible starting values. It turns out that this calculation agrees with the estimate of gravitational entropy I mentioned earlier: the probability of getting realistic inflationary initial conditions is around one in 10 to the power of 10 to the power of 120. The most probable starting point, by far, is the one with the smallest possible value of the inflationary energy, that is, today’s vacuum energy. There would be no period of inflation, no matter or radiation. Hartle and Hawking’s proposal is a wonderful theory, but at least in the most straightforward interpretation, it predicts an empty universe.
Hartle and Hawking and their collaborator Thomas Hertog, of the University of Leuven, propose to avoid this prediction by invoking the “anthropic principle” — the idea that one should select universes according to their ability to form galaxies and life.
It is not a new notion that the properties of the universe around us were somehow “selected” by the fact that we are here. The idea has grown increasingly popular as theory has found it more and more difficult to explain the specific observed properties of the universe. The problem is that the anthropic arguments are vague: in order to make them meaningful, one needs a theory of the set of possible universes and also the precise condition for us to be located in one of them. Neither of these requirements are yet close to being met. Nevertheless, Hartle, Hawking, and Hertog argue that even if a priori an empty universe is the most likely, the predictions of the Hartle–Hawking proposal, supplemented by anthropic selection, are consistent with what we observe. In principle, I have no objection to this kind of argument, as long as it can really be carried through.
However, a realistic universe like ours has a minuscule a priori probability in this setup, of one in 10 raised to the power of 10 raised to the power of 120 (the same tiny number mentioned earlier). Anthropic selection has to eliminate all of the other possible universes, and this seems an extremely tall order. A universe in which ours was the only galaxy, surrounded by empty space, would seem to be quite capable of supporting us. And, according to the Hartle–Hawking proposal, it would be vastly more likely than the universe we observe, which is teeming with galaxies (Hartle, Hawking, and Hertog exclude such a universe by fiat in their discussion). When the a priori probabilities are so heavily stacked against a universe like ours, as they are with the Hartle–Hawking proposal, it seems to me very unlikely that anthropic arguments will save the day.
A THEORY THAT PREDICTS a universe like ours a priori, without any need for anthropic selection, would seem vastly preferred. Even if anthropic selection could rescue Hartle and Hawking’s theory (which seems to me unlikely), the non-anthropic theory would be statistically favoured over the anthropic one by a huge factor, of 10 raised to the power of 10 raised to the power of 120.
For the past decade, with Paul Steinhardt of Princeton University and other collaborators, I have been trying to develop such theories as an alternative to inflation. Our starting point is to tackle the big bang singularity. What if it was not the beginning of time, but instead was a gateway to a pre–big bang universe? If there was a universe like ours before the singularity, could it have directly produced the initial ball of light, and if it did, would there be any need for a period of inflation?
Most of the universe today is very smooth and uniform on scales of a millimetre, and we have no problem understanding why. Matter and radiation tend to spread themselves out through space, and the vacuum energy is completely uniform anyway. Let us imagine following our universe forward into the future. The galaxies and all the radiation will be diluted away by the expansion: the universe will become a cold, empty place, dominated by the vacuum energy. Now imagine that for some reason the vacuum energy is not absolutely stable. It could start to slowly decay, tens of billions of years into our future. We can easily build mathematical models where it declines in this way, becoming smaller and smaller and then going negative. Its repulsive gravity would become attractive, and the universe would start to collapse.
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).
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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.