by Seth Lloyd
This conventional history of the universe is not as sexy as some versions, and dairy products enter into only its later stages, but unlike older creation myths, the scientific one has the virtue of being consistent with known scientific laws and observations. And even though it is phrased in terms of physics, the conventional history of the universe still manages to make a pretty good story. It has drama and uncertainty, and many questions remain: How did life arise? Why is the universe so complex? What is the future of the universe and of life in particular? When we look into the Milky Way, our own galaxy, we see many stars much like our own. When we look beyond, we see many galaxies apparently much like the Milky Way. There is a scripted quality to what we see, in which the same astral dramas are played out again and again by different stellar actors in different places. If the universe is in fact infinite in extent, then somewhere, eventually, every possible scenario allowed by the laws of physics will be enacted. The story of the universe is a kind of cosmic soap opera whose actors play out all possible permutations of the drama.
Energy: The First Law of Thermodynamics
Let’s get acquainted with the major players in the cosmic soap. In conventional cosmology, the primary actor is energy—the radiant energy in light and the mass energy in protons, neutrons, and electrons. What is energy? As you may have learned in middle school, energy is the ability to do work. Energy makes physical systems do things.
Famously, energy has the feature of being conserved: it can take different forms—heat, work, electrical energy, mechanical energy—but it is never lost. This is known as the first law of thermodynamics. But if energy is conserved, and if the universe started from nothing, then where did all of the energy come from? Physics provides an explanation.
Quantum mechanics describes energy in terms of quantum fields, a kind of underlying fabric of the universe, whose weave makes up the elementary particles—photons, electrons, quarks. The energy we see around us, then—in the form of Earth, stars, light, heat—was drawn out of the underlying quantum fields by the expansion of our universe. Gravity is an attractive force that pulls things together. (As high school students will tell you, “Gravity sucks.”) As the universe expands (which it continues to do), gravity sucks energy out of the quantum fields. The energy in the quantum fields is almost always positive, and this positive energy is exactly balanced by the negative energy of gravitational attraction. As the expansion proceeds, more and more positive energy becomes available, in the form of matter and light—compensated for by the negative energy in the attractive force of the gravitational field.
The conventional history of the universe pays great attention to energy: How much is there? Where is it? What is it doing? By contrast, in the story of the universe told in this book, the primary actor in the physical history of the universe is information. Ultimately, information and energy play complementary roles in the universe: Energy makes physical systems do things. Information tells them what to do.
Entropy: The Second Law of Thermodynamics
If we could look at matter at the atomic scale, we would see atoms dancing and jiggling every which way at random. The energy that drives this random atomic dance is called heat, and the information that determines the steps of this dance is called entropy. More simply, entropy is the information required to specify the random motions of atoms and molecules—motions too small for us to see. Entropy is the information contained in a physical system that is invisible to us.
Entropy is a measure of the degree of molecular disorder existing in a system: it determines how much of the system’s thermal energy is unavailable for conversion into mechanical work—how much of its energy is useful. The second law of thermodynamics states that the entropy of the universe as a whole does not decrease; in other words, the amount of unusable energy is increasing. Manifestations of the second law are all around us. Hot steam can run a turbine and do useful work. As steam cools, its jiggling molecules transfer some of their disorder into increased disorder in the surrounding air, heating it up. As the molecules of steam jiggle slower and slower, the air molecules jiggle faster and faster, until steam and air are at the same temperature. When the difference in temperatures is minimized, the entropy of the system is maximized. But room temperature steam will do no work.
Here is yet another way to conceive of entropy. Most information is invisible. The number of bits of information required to characterize the dance of atoms vastly outweighs the number of bits we can see or know. Consider a photograph: It has an intrinsic graininess determined by the size of the grains of silver halide that make up the photographic film—or, if it is a digital photograph, by the number of pixels that make up the digital image on a screen. A high-quality digital image can register almost a billion bits of visible information. How did I come up with that number? One thousand pixels per inch is a high resolution, comparable to the best resolution that can be distinguished with the naked eye. At this resolution, each square inch of the photograph contains a million pixels. An 8- by 6-inch color photograph with 1,000 pixels per inch has 48 million pixels. Each pixel has a color. Digital cameras typically use 24 bits to produce 16 million colors, comparable to the number that the human eye can distinguish. So an 8- by 6-inch color digital photograph with 1,000 pixels per inch and 24 bits of color resolution has 1,152,000,000 bits of information. (An easier way to see how many bits are required to register a photograph is to look at how rapidly the memory space in your digital camera disappears when you take a picture. A typical digital camera takes high-resolution pictures with 3 million bytes—3 megabytes—of information. A byte is 8 bits, so each picture on the digital camera registers approximately 24 million bits.)
1,152,000,000 bits is a lot of information, but the amount of information required to describe the invisible jiggling of the atoms in the grains of silver halide of a non-digital photograph is much greater. To describe them would require more than a million billion billion bits (1024, or a 1 followed by 24 zeros). The invisible jiggling atoms register vastly more information than the visible photograph they make up. A photograph that registered the same amount of visible information as the invisible information in a gram of atoms would have to be as big as the state of Maine.
The number of bits registered by the jiggling atoms that make up the photographic image on film can be estimated as follows. A grain of silver halide is about a millionth of a meter across and contains about a trillion atoms. There are tens of billions of grains of silver halide in the photographic film. Describing where an individual atom (at room temperature) is in its infinitesimal dance requires 10 to 20 bits per atom. The total amount of information registered by the atoms in the photograph is thus 1023 bits. The billion (109) bits of information visible in the photograph, as represented by the digital image, represent only a tiny fraction of this total. The remainder of the information contained in the matter of the photograph is invisible. This invisible information is the entropy of the atoms.
Free Energy
The laws of thermodynamics guide the interplay between our two actors, energy and information. To experience another example of the first and second laws, take a bite of an apple. The sugars in the apple contain what is called free energy. Free energy is energy in a highly ordered form associated with a relatively low amount of entropy. In the case of the apple, the energy in sugar is stored not in the random jiggling of atoms but in the ordered chemical bonds that hold sugar together. It takes much less information to describe the form energy takes in a billion ordered chemical bonds than it does to describe that same energy spread among a billion jiggling atoms. The relatively small amount of information required to describe this energy makes it available for use: that’s why it’s called free.
Pick the apple, take a bite. You’ve ingested free energy. Your digestive system contains chemicals called enzymes that convert the apple’s sugars into glucose, a form of sugar that can be used directly by your muscles. Every gram of glucose contains a few kilocalories of free energy. Once you�
��ve digested the sugar, you can run miles on a few hundred kilocalories. (A calorie is the amount of energy required to raise one gram of water one degree Celsius. A kilocalorie, 1,000 calories, is what someone on a diet would normally call a Calorie: a teaspoonful of sugar contains ten kilocalories of free energy. One hundred kilocalories is enough energy to lift a VW Bug one hundred feet in the air!) While you run, the free energy in the sugar is converted into motion by your muscles. By the time you’re finished running, you’re hot: the free energy in the sugar has been converted into heat and work. The number of calories of heat and work exactly matches the calories of free energy in the apple’s sugar. In obedience to the first law of thermodynamics, the total amount of energy remains the same. (In obedience to the second law, the amount of information required to describe the extra jiggling of molecules in your hot muscles and sweaty skin is much greater than the amount of information required to describe the ordered chemical bonds in the apple’s sugar.)
Unfortunately, to reverse this process is not so easy. If you wanted to convert the energy in heat, which has lots of invisible information (or entropy), back into energy in chemical bonds, which has much less entropy, you would have to do something with that extra information. As we will discuss, the problem of finding a place for the extra bits in heat puts fundamental limits on how well engines, humans, brains, DNA, and computers can function.
In either scenario, though, it’s clear that energy and information (visible and invisible) are the two primary actors in the universal drama. The universe we see around us arises from the interplay between these two quantities, interplay governed by the first and second laws of thermodynamics. Energy is conserved. Information never decreases. It takes energy for a physical system to evolve from one state to another. That is, it takes energy to process information. The more energy that can be applied, the faster the physical transformation takes place and the faster the information is processed. The maximum rate at which a physical system can process information is proportional to its energy. The more energy, the faster the bits flip. Earth, air, fire, and water in the end are all made of energy, but the different forms they take are determined by information. To do anything requires energy. To specify what is done requires information. Energy and information are by nature (no pun intended) intertwined.
The Story of the Universe: Part Two
Now that our two protagonists have been introduced, let’s tell the story of the universe in terms of their interplay. It is this interplay—this back-and-forth between information and energy—that makes the universe compute.
Over the last century, advances in the construction of telescopes have led to ever more precise observations of the universe beyond our solar system. The past decade has been a particularly remarkable one for observations of the heavens. Ground-based telescopes and satellite observatories have generated rich data describing what the universe looks like now, as well as what it looked like in the past. (Because the speed of light is finite, when you look at a galaxy that’s a billion light-years away, you’re looking at an image from a billion years ago.) The historical nature of cosmic observation proves useful as we attempt to untangle the early history of the universe.
The universe began just under 14 billion years ago in a massive explosion. What happened before the Big Bang? Nothing.3 There was no time and no space. Not just empty space, but the absence of space itself. Time itself had a beginning. There is nothing wrong with beginning from nothing. For example, the positive numbers begin from zero (the “empty thing”). Before zero, there are no positive numbers. Before the Big Bang, there was nothing—no energy, no bits.
Then, all at once, the universe sprang into existence. Time began, and with it, space. The newborn universe was simple; the newly woven fabric of quantum fields contained only small amounts of information and energy. At most, it required a few bits of information to describe. In fact, if—as some physical theories speculate—there is only one possible initial state of the universe and only one self-consistent set of physical laws, then the initial state required no bits of information to describe. Recall that to generate information, there must be alternatives—e.g., 0 or 1, yes or no, this or that. If there were no alternatives to the initial state of the universe, then exactly zero bits of information were required to describe it; it registered zero bits. This initial paucity of information is consistent with the notion that the universe sprang from nothing.
As soon as it began, though, the universe began to expand. As it expanded, it pulled more and more energy out of the underlying quantum fabric of space and time. Current physical theories suggest that the amount of energy in the early universe grew very rapidly (a process called “inflation”), while the amount of information grew more slowly. The early universe remained simple and orderly: it could be described by just a few bits of information. The energy that was created was free energy.
This paucity of information did not last for long, however. As the expansion continued, the free energy in the quantum fields was converted into heat, increasing entropy, and all sorts of elementary particles were created. These particles were hot: they jiggled around with a vengeance. To describe this jiggling would take a lot of information. After a billionth of a second—the amount of time it takes light to travel about a foot—had passed, the amount of information contained within the universe was on the order of 100 million billion billion billion billion billion (1050) bits. That’s approximately one bit for every atom that makes up the Earth. To store that much information visually would require a photograph the size of the Milky Way. The Big Bang was also a Bit Bang.
As the energy in the universe changed its form, the universe also processed and transformed its bits, filling up its “memory register” with the results of this information processing. After that billionth of a second, the universe had performed about 10,000 billion billion billion billion billion billion billion (1067) elementary operations, or “ops,” on the bits it registered. A lot had happened. But what was the universe computing during this initial billionth of a second? Science fiction writers have speculated that entire civilizations could have arisen and declined during this time—a time very much shorter than the blink of an eye. We have no evidence of these fast-living folk. More likely, these early ops consisted of elementary particles bouncing off one another in random fashion.
After this first billionth of a second, the universe was very hot. Almost all of the energy that had been drawn into it was now in the form of heat. Lots of information would have been required to describe the infinitesimal jigglings of the elementary particles in this state. In fact, when all matter is at the same temperature, entropy is maximized. There was very little free energy—that is, order—at this stage, making the moments after the Big Bang a hostile time for processes like life. Life requires free energy. Even if there were some form of life that could have withstood the high temperatures of the Big Bang, that life-form would have had nothing to eat.
As the universe expanded, it cooled down. The elementary particles jiggled around more slowly. The amount of information required to describe their jiggles stayed almost the same, though, increasing gradually over time. It might seem that slower jiggles would require fewer bits to describe, and it’s true that fewer bits were required to describe their velocities. But, at the same time, the amount of space in which they were jiggling was increasing, requiring more bits to describe their positions. Thus, the total amount of information remained constant or increased in accordance with the second law of thermodynamics.
As the jiggles got slower and slower, bits and pieces of the cosmic soup began to condense out. This condensation produced some of the familiar forms of matter we see today. When the amount of energy in a typical jiggle became less than the amount of energy required to hold together some form of composite particle—a proton, for example—those particles formed. When the jiggles of the constituent parts—quarks, in the case of a proton—were no longer sufficiently energetic to maintain them as distinct pa
rticles, they stuck together as a composite particle that condensed out of the cosmic soup. Every time a new ingredient of the soup condensed out, there was a burst of entropy—new information was written in the cosmic cookbook.
Particles condensed out of the jiggling soup in order of the energy required to bind them together. Protons and neutrons—the particles that make up the nuclei of atoms—condensed out a little more than a millionth of a second after the Big Bang, when the temperature was around 10 million million degrees Celsius. Atomic nuclei began to form at one second, and about a billion degrees. After three minutes, the nuclei of the lightweight atoms—hydrogen, helium, deuterium, lithium, beryllium, and boron—had condensed. Electrons were still whizzing around too fast, though, for these nuclei to capture them and form complete atoms. Three hundred eighty thousand years after the Big Bang, when the temperature of the universe had dropped to a little less than 10,000 degrees Celsius, electrons had finally cooled enough to be captured, and stable atoms formed.
Order from Chaos (the Butterfly Effect)
Until the formation of atoms, almost all the information in the universe lay at the level of the elementary particle. Nearly all bits were registered by the positions and velocities of protons, electrons, and so forth. On any larger scale, the universe still contained very little information: it was featureless and uniform. (How uniform was it? Imagine the surface of a lake on a windless morning so calm that the reflections of the trees are indistinguishable from the trees themselves. Imagine the earth with no mountain larger than a molehill. The early universe was more uniform still.)
