The Universe Within (13 page)

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.
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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.”
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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
=
mc
2
.

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.