From Eternity to Here (9 page)

There is no real contradiction, nor is there a nefarious conspiracy on the part of textbook writers to keep the central role of cosmology hidden from students of statistical mechanics. For the most part, people interested in statistical mechanics care about experimental situations in laboratories or kitchens here on Earth. In an experiment, we can control the conditions before us; in particular, we can arrange systems so that the entropy is much lower than it could be, and watch what happens. You don’t need to know anything about cosmology and the wider universe to understand how that works.

But our aims are more grandiose. The arrow of time is much more than a feature of some particular laboratory experiments; it’s a feature of the entire world around us. Conventional statistical mechanics can account for why it’s easy to turn an egg into an omelet but hard to turn an omelet into an egg. What it can’t account for is why, when we open our refrigerator, we are able to find an egg in the first place. Why are we surrounded by exquisitely ordered objects such as eggs and pianos and science books, rather than by featureless chaos?

Part of the answer is straightforward: The objects that populate our everyday experience are not closed systems. Of course an egg is not a randomly chosen configuration of atoms; it’s a carefully constructed system, the assembly of which required a certain set of resources and available energy, not to mention a chicken. But we could ask the same question about the Solar System, or about the Milky Way galaxy. In each case, we have systems that are for all practical purposes isolated, but nevertheless have a much lower entropy than they could.

The answer, as we know, is that the Solar System hasn’t always been a closed system; it evolved out of a protostellar cloud that had an even lower entropy. And that cloud came from the earlier galaxy, which had an even lower entropy. And the galaxy was formed out of the primordial plasma, which had an even lower entropy. And that plasma originated in the very early universe, which had an even lower entropy still.

And the early universe came out of the Big Bang. The truth is, we don’t know much about why the early universe was in the configuration it was; that’s one of the questions motivating us in this book. The ultimate explanation for the arrow of time as it manifests itself in our kitchens and laboratories and memories relies crucially on the very low entropy of the early universe.

You won’t usually find any discussion of this story in conventional textbooks on statistical mechanics. They assume that we are interested in systems that start with relatively low entropy, and take it from there. But we want more—why did our universe have such a small entropy at one end of time, thereby setting the stage for the subsequent arrow of time? It makes sense to start by considering what we do know about how the universe has evolved from its beginning up to today.

THE VISIBLE UNIVERSE

Our universe is expanding, filled with galaxies gradually moving apart from one another. We experience only a small part of the universe directly, and in trying to comprehend the bigger picture it’s tempting to reach for analogies. The universe, we are told, is like the surface of a balloon, on which small dots have been drawn to represent individual galaxies. Or the universe is like a loaf of raisin bread rising in the oven, with each galaxy represented by one of the raisins.

These analogies are terrible. And not only because it seems demeaning to have something as majestic as a galaxy be represented by a tiny, wrinkled raisin. The real problem is that any such analogy brings along with it associations that do not apply to the actual universe. A balloon, for example, has an inside and an outside, as well as a larger space into which it is expanding; the universe has none of those things. Raisin bread has an edge, and is situated inside an oven, and smells yummy; there are no corresponding concepts in the case of the universe.

So let’s take another tack. To understand the universe around us, let’s consider the real thing. Imagine standing outside on a clear, cloudless night, far away from the lights of the city. What do we see when we look into the sky? For the purposes of this thought experiment, we can grant ourselves perfect vision, infinitely sensitive to all the different forms of electromagnetic radiation.

We see stars, of course. To the unaided eye they appear as points of light, but we have long since figured out that each star is a massive ball of plasma, glowing through the energy of internal nuclear reactions, and that our Sun is a star in its own right. One problem is that we don’t have a sense of depth—it’s hard to tell how far away any of those stars are. But astronomers have invented clever ways to determine the distances to nearby stars, and the answers are impressively large. The closest star, Proxima Centauri, is about 40 trillion kilometers away; traveling at the speed of light, it would take about four years to get there.

Stars are not distributed uniformly in every direction. On our hypothetical clear night, we could not help but notice the Milky Way—a fuzzy band of white stretching across the sky, from one horizon to the other. What we’re seeing is actually a collection of many closely packed stars; the ancient Greeks suspected as much, and Galileo verified that idea when he turned his telescope on the heavens. In fact, the Milky Way is a giant spiral galaxy—a collection of hundreds of billions of stars, arranged in the shape of a disk with a bulge in the center, with our Solar System located as one of the distant suburbs on one edge of the disk.

For a long time, astronomers thought that “the galaxy” and “the universe” were the same thing. One could easily imagine that the Milky Way constituted an isolated collection of stars in an otherwise empty void. But it was well known that, in addition to pointlike stars, the night sky featured fuzzy blobs known as “nebulae,” which some argued were giant collections of stars in their own right. After fierce debates between astronomers in the early years of the twentieth century,
³⁴
Edwin Hubble was eventually able to measure the distance to the nebula M33 (the thirty-third object in Charles Messier’s catalog of fuzzy celestial objects not to be confused by when one was searching for comets), and found that it is much farther away than any star. M33, the Triangulum Galaxy, is in fact a collection of stars comparable in size to the Milky Way.

Upon further inspection, the universe turns out to be teeming with galaxies. Just as there are hundreds of billions of stars in the Milky Way, there are hundreds of billions of galaxies in the observable universe. Some galaxies (including ours) are members of groups or clusters, which in turn describe sheets and filaments of large-scale structure. On average, however, galaxies are uniformly distributed through space. In every direction we look, and at every different distance from us, the number of galaxies is roughly equal. The observable universe looks pretty much the same everywhere.

BIG AND GETTING BIGGER

Hubble was undoubtedly one of the greatest astronomers of history, but he was also in the right place at the right time. He bounced around a bit after graduating from college, spending time variously as a Rhodes scholar, high school teacher, lawyer, soldier in World War I, and for a while as a basketball coach. But ultimately he earned a Ph.D. in astronomy from the University of Chicago in 1917 and moved to California to take up a position at the Mount Wilson Observatory outside Los Angeles. He arrived to find the brand-new Hooker telescope, featuring a mirror 100 inches across, at the time the world’s largest. It was at the 100-inch that Hubble made the observations of variable stars in other galaxies, establishing for the first time their great distance from the Milky Way.

Meanwhile other astronomers, led by Vesto Slipher, had been measuring the velocity of spiral nebulae using the Doppler effect.
³⁵
If an object is moving with respect to you, any wave it emits (such as light or sound) will get compressed if it’s moving toward you, and stretched if it’s moving away. In the case of sound, we experience the Doppler effect as a raising of the pitch of objects that are coming toward us, and a lowering of the pitch as they move away. Similarly, we see the light from objects moving toward us shifted toward the blue (shorter wavelengths) than we would expect, and light from objects moving away is shifted toward the red (longer wavelengths). So an approaching object is blueshifted, while a receding object is redshifted.

Figure 7:
Edwin Hubble, surveyor of the universe, smoking a pipe.

What Slipher found was that the vast majority of nebulae were redshifted. If these objects were moving randomly through the universe, we would expect about as many blueshifts as redshifts, so this pattern came as a surprise. If the nebulae were small clouds of gas and dust, we might have concluded that they had been forcibly ejected from our galaxy by some unknown mechanism. But Hubble’s result, announced in 1925, scotched that possibility—what we were seeing was a collection of galaxies the size of our own, all running away from us as if they were afraid or something.

Hubble’s next discovery made it all snap into place. In 1929 he and his collaborator Milton Humason compared the redshifts of galaxies to the distances he had measured, and found a striking correlation: The farther the galaxies were, the faster they were receding. This is now known as
Hubble’s Law
: The apparent recession velocity of a galaxy is proportional to its distance from us, and the constant of proportionality is known as the
Hubble constant
.
³⁶

Hidden within this simple fact—the farther away things are, the faster they are receding—lies a deep consequence: We are not at the center of some giant cosmic migration. You might get the impression that we are somehow special, what with all of these galaxies moving way from us. But put yourself in the place of an alien astronomer within one of those other galaxies. If that astronomer looks back at us, of course they would see the Milky Way receding from them. But if they look in the opposite direction in the sky, they will also see galaxies moving away from them—because, from our perspective, those more distant galaxies are moving even faster. This is a very profound feature of the universe in which we live. There isn’t any particular special place, or central point away from which everything is moving. All of the galaxies are moving away from all of the other galaxies, and each of them sees the same kind of behavior. It’s almost as if the galaxies aren’t moving at all, but rather that the galaxies are staying put and space itself is expanding in between them.

Which is, indeed, precisely what’s going on, from the modern way of looking at things. These days we think of space not as some fixed and absolute stage through which matter moves, but as a dynamical and lively entity in its own right, according to Einstein’s general theory of relativity. When we say space is expanding, we mean that more space is coming into existence in between galaxies. Galaxies themselves are not expanding, nor are you, nor are individual atoms; anything that is held together by some local forces will maintain its size, even in an expanding universe. (Maybe you are expanding, but you can’t blame the universe.) A light wave, which is not bound together by any forces, will be stretched, leading to the cosmological redshift. And, of course, galaxies that are sufficiently far apart not to be bound by their mutual gravitational attraction will be moving away from one another.

This is a magnificent and provocative picture of the universe. Subsequent observations have confirmed the idea that, on the very largest scales, the universe is homogeneous: It’s more or less the same everywhere. Clearly the universe is “lumpy” on smaller scales (here’s a galaxy, there’s a void of empty space next to it), but if you consider a sufficiently large volume of space, the number of galaxies and the amount of matter within it will be essentially the same, no matter which volume you pick. And the whole shebang is gradually getting bigger; in about 14 billion years, every distant galaxy we observe will be twice as far away as it is today.

We find ourselves in the midst of an overall smooth distribution of galaxies, the space between them expanding so that every galaxy is moving away from every other.
³⁷
If the universe is expanding, what’s it expanding into? Nothing. When we’re talking about the universe, there’s no need to invoke something for it to expand into—it’s the universe—it doesn’t have to be embedded in anything else; it might very well be all there is. We’re not used to thinking like this, because the objects we experience in our everyday lives are all situated
within
space; but the universe
is
space, and there’s no reason for there to be any such thing as “outside.”

Likewise, there doesn’t have to be an edge—the universe could just continue on infinitely far in space. Or, for that matter, it could be finite, by wrapping back on itself, like the surface of a sphere. There is a good reason to believe we will never know, on the basis of actual observations. Light has a finite speed (1 light-year per year, or 300,000 kilometers per second), and there is only a finite time since the Big Bang. As we look out into space, we are also looking backward in time. Since the Big Bang occurred approximately 14 billion years ago, there is an absolute limit to how far we can peer in the universe.
³⁸
What we see is a relatively homogeneous collection of galaxies, about 100 billion of them all told, steadily expanding away from one another. But outside our observable patch, things could be very different.