The Fabric of the Cosmos: Space, Time, and the Texture of Reality (22 page)

When I first encountered this idea many years ago, it was a bit of a shock. Up until that point, I had thought I understood the concept of entropy fairly well, but the fact of the matter was that, following the approach of textbooks I'd studied, I'd only ever considered entropy's implications for the future. And, as we've just seen, while entropy applied toward the future confirms our intuition and experience, entropy applied toward the past just as thoroughly contradicts them. It wasn't quite as bad as suddenly learning that you've been betrayed by a longtime friend, but for me, it was pretty close.

Nevertheless, sometimes it's good not to pass judgment too quickly, and entropy's apparent failure to live up to expectations provides a case in point. As you're probably thinking, the idea that all we're familiar with just popped into existence is as tantalizing as it is hard to swallow. And it's not "merely" that this explanation of the universe challenges the veracity of everything we hold to be real and important. It also leaves critical questions unanswered. For instance, the more ordered the universe is today— the greater the dip in Figure 6.4—the more surprising and unlikely is the statistical aberration required to bring it into existence. So if the universe could have cut any corners, making things look more or less like what we see right now while skimping on the actual amount of order, probabilistic reasoning leads us to believe it would have. But when we examine the universe, there seem to be numerous lost opportunities, since there are many things that are more ordered than they have to be. If Michael Jackson never recorded
Thriller
and the millions of copies of this album now distributed worldwide all got there as part of an aberrant fluctuation toward lower entropy, the aberration would have been far less extreme if only a million or a half-million or just a few albums had formed. If evolution never happened and we humans got here via an aberrant jump toward lower entropy, the aberration would have been far less extreme if there weren't such a consistent and ordered evolutionary fossil record. If the big bang never happened and the more than 100 billion galaxies we now see arose as an aberrant jump toward lower entropy, the aberration would have been less extreme if there were 50 billion, or 5,000, or just a handful, or just one galaxy. And so if the idea that our universe is a statistical fluctuation—a happy fluke—has any validity, one would need to address how and why the universe went so far overboard and achieved a state of
such
low entropy.

Even more pressing, if you truly can't trust memories and records, then you also can't trust the laws of physics. Their validity rests on numerous experiments whose positive outcomes are attested to only by those very same memories and records. So all the reasoning based on the time-reversal symmetry of the accepted laws of physics would be totally thrown into question, thereby undermining our understanding of entropy and the whole basis for the current discussion. By embracing the conclusion that the universe we know is a rare but every-so-often-expectable statistical fluctuation from a configuration of total disorder, we're quickly led into a quagmire in which we lose all understanding, including the very chain of reasoning that led us to consider such an odd explanation in the first place.
¹⁴

Thus, by suspending disbelief and diligently following the laws of physics and the mathematics of entropy—concepts which in combination tell us that it is overwhelmingly likely that disorder will increase both toward the future
and
toward the past from any given moment—we have gotten ourselves neck deep in quicksand. And while that might not sound pleasant, for two reasons it's a very good thing. First, it shows with precision why mistrust of memories and records—something at which we intuitively scoff—doesn't make sense. Second, by reaching a point where our whole analytical scaffolding is on the verge of collapse, we realize, forcefully, that we
must
have left something crucial out of our reasoning.

Therefore, to avoid the explanatory abyss, we ask ourselves: what new idea or concept, beyond entropy and the time symmetry of nature's laws, do we need in order to go back to trusting our memories and our records—our experience of room-temperature ice cubes melting and not unmelting, of cream and coffee mixing but not unmixing, of eggs splattering but not unsplattering? In short, where are we led if we try to explain an asymmetric unfolding of events in spacetime, with entropy to our future higher, but entropy to our past
lower
? Is it possible?

It is. But only if things were very special early on.
¹⁴

To see what this means, let's take the example of a pristine, low-entropy, fully formed egg. How did this low-entropy physical system come into being? Well, putting our trust back in memories and records, we all know the answer. The egg came from a chicken. And that chicken came from an egg, which came from a chicken, which came from an egg, and so on. But, as emphasized most forcefully by the English mathematician Roger Penrose,
¹⁵
this chicken-and-egg story actually teaches us something deep and leads somewhere definite.

A chicken, or any living being for that matter, is a physical system of astonishingly high order. Where does this organization come from and how is it sustained? A chicken stays alive, and in particular, stays alive long enough to produce eggs, by eating and breathing. Food and oxygen provide the raw materials from which living beings extract the energy they require. But there is a critical feature of this energy that must be emphasized if we are to really understand what's going on. Over the course of its life, a chicken that stays fit takes in just about as much energy in the form of food as it gives back to the environment, mostly in the form of heat and other waste generated by its metabolic processes and daily activities. If there weren't such a balance of energy-in and energy-out, the chicken would get increasingly hefty.

The essential point, though, is that all forms of energy are not equal. The energy a chicken gives off to the environment in the form of heat is highly disordered—it often results in some air molecules here or there jostling around a touch more quickly than they otherwise would. Such energy has high entropy—it is diffuse and intermingled with the environment—and so cannot easily be harnessed for any useful purpose. To the contrary, the energy the chicken takes in from its feed has low entropy and is readily harnessed for important life-sustaining activities. So the chicken, and every life form in fact, is a conduit for taking in low-entropy energy and giving off high-entropy energy.

This realization pushes the question of where the low entropy of an egg originates one step further back. How is it that the chicken's energy source, the food, has such low entropy? How do we explain this aberrant source of order? If the food is of animal origin, we are led back to the initial question of how animals have such low entropy. But if we follow the food chain, we ultimately come upon animals (like me) that eat only plants. How do plants and their products of fruits and vegetables maintain low entropy? Through photosynthesis, plants use sunlight to separate ambient carbon dioxide into oxygen, which is given back to the environment, and carbon, which the plants use to grow and flourish. So we can trace the low-entropy, nonanimal sources of energy to the sun.

This pushes the question of explaining low entropy another step further back: where did our highly ordered sun come from? The sun formed about 5 billion years ago from an initially diffuse cloud of gas that began to swirl and clump under the mutual gravitational attraction of all its constituents. As the gas cloud got denser, the gravitational pull of one part on another got stronger, causing the cloud to collapse further in on itself. And as gravity squeezed the cloud tighter, it got hotter. Ultimately, it got hot enough to ignite nuclear processes that generated enough outwardflowing radiation to stem further gravitational contraction of the gas. A hot, stable, brightly burning star was born.

So where did the diffuse cloud of gas come from? It likely formed from the remains of older stars that reached the end of their lives, went supernova, and spewed their contents out into space. Where did the diffuse gas responsible for these early stars come from? We believe that the gas was formed in the aftermath of the big bang. Our most refined theories of the origin of the universe—our most refined
cosmological
theories—tell us that by the time the universe was a couple of minutes old, it was filled with a
nearly uniform hot gas
composed of roughly 75 percent hydrogen, 23 percent helium, and small amounts of deuterium and lithium. The essential point is that this gas filling the universe had extraordinarily
low
entropy. The big bang started the universe off in a state of low entropy, and that state appears to be the source of the order we currently see. In other words,
the current order is a cosmological relic.
Let's discuss this important realization in a little more detail.

Because theory and observation show that within a few minutes after the big bang, primordial gas was uniformly spread throughout the young universe, you might think, given our earlier discussion of the Coke and its carbon dioxide molecules, that the primordial gas was in a high-entropy, disordered state. But this turns out not to be true. Our earlier discussion of entropy completely ignored gravity, a sensible thing to do because gravity hardly plays a role in the behavior of the minimal amount of gas emerging from a bottle of Coke. And with that assumption, we found that uniformly dispersed gas has high entropy. But when gravity matters, the story is very different. Gravity is a universally attractive force; hence, if you have a large enough mass of gas, every region of gas will pull on every other and this will cause the gas to fragment into clumps, somewhat as surface tension causes water on a sheet of wax paper to fragment into droplets. When gravity matters, as it did in the high-density early universe, clumpiness—not uniformity—is the norm; it is the state toward which a gas tends to evolve, as illustrated in Figure 6.5.

Even though the clumps appear to be more ordered than the initially diffuse gas—much as a playroom with toys that are neatly grouped in trunks and bins is more ordered than one in which the toys are uniformly strewn around the floor—in calculating entropy you need to tally up the contributions from
all
sources. For the playroom, the entropy decrease in going from wildly strewn toys to their all being "clumped" in trunks and bins is more than compensated for by the entropy increase from the fat burned and heat generated by the parents who spent hours cleaning and arranging everything. Similarly, for the initially diffuse gas cloud, you find that the entropy decrease through the formation of orderly clumps is more than compensated by the heat generated as the gas compresses, and, ultimately, by the enormous amount of heat and light released when nuclear processes begin to take place.

Figure 6.5 For huge volumes of gas, when gravity matters, atoms and molecules evolve from a smooth, evenly spread configuration, into one involving larger and denser clumps.

This is an important point that is sometimes overlooked. The overwhelming drive toward disorder does not mean that orderly structures like stars and planets, or orderly life forms like plants and animals, can't form. They can. And they obviously do. What the second law of thermodynamics entails is that in the formation of order there is generally a more-than-compensating generation of disorder. The entropy balance sheet is still in the black even though certain constituents have become more ordered. And of the fundamental forces of nature, gravity is the one that exploits this feature of the entropy tally to the hilt. Because gravity operates across vast distances and is universally attractive, it instigates the formation of the ordered clumps—stars—that give off the light we see in a clear night sky, all in keeping with the net balance of entropy increase.

The more squeezed, dense, and massive the clumps of gas are, the larger the overall entropy. Black holes, the most extreme form of gravitational clumping and squeezing in the universe, take this to the limit. The gravitational pull of a black hole is so strong that nothing, not even light, is able to escape, which explains why black holes are black. Thus, unlike ordinary stars, black holes stubbornly hold on to all the entropy they produce: none of it can escape the black hole's powerful gravitational grip.
¹⁶
In fact, as we will discuss in Chapter 16, nothing in the universe contains more disorder—more entropy—than a black hole.
¹⁵
This makes good intuitive sense: high entropy means that many rearrangements of the constituents of an object go unnoticed. Since we can't see inside a black hole, it is impossible for us to detect
any
rearrangement of its constituents— whatever those constituents may be—and hence black holes have maximum entropy. When gravity flexes its muscles to the limit, it becomes the most efficient generator of entropy in the known universe.

We have now come to the place where the buck finally stops.
The ultimate source of order, of low entropy, must be the big bang itself.
In its earliest moments, rather than being filled with gargantuan containers of entropy such as black holes, as we would expect from probabilistic considerations, for some reason the nascent universe was filled with a hot, uniform, gaseous mixture of hydrogen and helium. Although this configuration has high entropy when densities are so low that we can ignore gravity, the situation is otherwise when gravity can't be ignored; then, such a uniform gas has extremely low entropy. In comparison with black holes, the diffuse, nearly uniform gas was in an extraordinarily low-entropy state. Ever since, in accordance with the second law of thermodynamics, the overall entropy of the universe has been gradually getting higher and higher; the overall, net amount of disorder has been gradually increasing. After about a billion years or so, gravity caused the primordial gas to clump, and the clumps ultimately formed stars, galaxies, and some lighter clumps that became planets. At least one such planet had a nearby star that provided a relatively low-entropy source of energy that allowed low-entropy life forms to evolve, and among such life forms there eventually was a chicken that laid an egg that found its way to your kitchen counter, and much to your chagrin that egg continued on the relentless trajectory to a higher entropic state by rolling off the counter and splattering on the floor. The egg splatters rather than unsplatters because it is carrying forward the drive toward higher entropy that was initiated by the extraordinarily low entropy state with which the universe began. Incredible order at the beginning is what started it all off, and we have been living through the gradual unfolding toward higher disorder ever since.

This
is the stunning connection we've been leading up to for the entire chapter.
A splattering egg tells us something deep about the big
bang.
It tells us that the big bang gave rise to an extraordinarily ordered nascent cosmos.

The same idea applies to all other examples. The reason why tossing the newly unbound pages of
War and Peace
into the air results in a state of higher entropy is that they
began
in such a highly ordered, low entropy form. Their initial ordered form made them ripe for entropy increase. By contrast, if the pages initially were totally out of numerical order, tossing them in the air would hardly make a difference, as far as entropy goes. So the question, once again, is: how did they become so ordered? Well, Tolstoy wrote them to be presented in that order and the printer and binder followed his instructions. And the highly ordered bodies and minds of Tolstoy and the book producers, which allowed them, in turn, to create a volume of such high order, can be explained by following the same chain of reasoning we just followed for an egg, once again leading us back to the big bang. How about the partially melted ice cubes you saw at 10:30 p.m.? Now that we are trusting memories and records, you remember that just before 10 p.m. the bartender put fully formed ice cubes in your glass. He got the ice cubes from a freezer, which was designed by a clever engineer and fabricated by talented machinists, all of whom are capable of creating something of such high order because they themselves are highly ordered life forms. And again, we can sequentially trace their order back to the highly ordered origin of the universe.