From Eternity to Here (12 page)

So instead of appealing to the correct theory of quantum gravity, which we still don’t have, we can simply examine the contributions to the vacuum energy of virtual particles at energies below where quantum gravity becomes important. That’s the
Planck energy
, named after German physicist Max Planck, one of the pioneers of quantum theory, and it turns out to be about 2 billion joules (a conventional unit of energy).
⁴⁹
We can add up the contributions to the vacuum energy from virtual particles with energies ranging from zero up to the Planck energy, and then cross our fingers and compare with what we actually observe.

The result is a complete fiasco. Our simple estimate of what the vacuum energy should be comes out to about 10
¹⁰⁵
joules per cubic centimeter. That’s a lot of vacuum energy. What we actually observe is about 10
^-15
joules per cubic centimeter. So our estimate is larger than the experimental value by a factor of 10
¹²⁰
—a 1 followed by 120 zeroes. Not something we can attribute to experimental error. This has been called the biggest disagreement between theoretical expectation and experimental reality in all of science. For comparison, the total number of particles in the observable universe is only about 10
⁸⁸
; the number of grains of sand on all the Earth’s beaches is only about 10
²⁰
.

The fact that the vacuum energy is so much smaller than it should be is a serious problem: the “cosmological constant problem.” But there is also another problem: the “coincidence problem.” Remember that vacuum energy maintains a constant density (amount of energy per cubic centimeter) as the universe expands, while the density of matter dilutes away. Today, they aren’t all that different: Matter makes up about 25 percent of the energy of the universe, while vacuum energy makes up the other 75 percent. But they are changing appreciably with respect to each other, as the matter density dilutes away with the expansion and the vacuum energy does not. At the time of recombination, for example, the energy density in matter was a billion times larger than that in vacuum energy. So the fact that they are somewhat comparable today, uniquely in the history of the universe, seems like a remarkable coincidence indeed. Nobody knows why.

These are serious problems with our theoretical understanding of vacuum energy. But if we put aside our worries concerning why the vacuum energy is so small, and why it’s comparable in density to the energy in matter, we are left with a phenomenological model that does a remarkable job of fitting the data. (Just like Carnot and Clausius didn’t need to know about atoms to say useful things about entropy, we don’t need to understand the origin of the vacuum energy to understand what it does to the expansion of the universe.) The first direct evidence for dark energy came from observations of supernovae in 1998, but since then a wide variety of methods have independently confirmed the basic picture. Either the universe is accelerating under the gentle influence of vacuum energy, or something even more dramatic and mysterious is going on.

THE DEEPEST FUTURE

As far as we can tell, the density of vacuum energy is unchanging as the universe expands. (It could be changing very slowly, and we just haven’t been able to measure the changes yet—that’s a major goal of modern observational cosmology.) We don’t know enough about vacuum energy to say for sure what will happen to it indefinitely into the future, but the obvious first guess is that it will simply stay at its current value forever.

If that’s true, and the vacuum energy is here to stay, it’s straightforward to predict the very far future of our universe. The details get complicated in an interesting way, but the outline is relatively simple.
⁵⁰
The universe will continue to expand, cool off, and become increasingly dilute. Distant galaxies will accelerate away from us, becoming more and more redshifted as they go. Eventually they will fade from view, as the time between photons that could possibly reach us becomes longer and longer. The entirety of the observable universe will just be our local group of gravitationally bound galaxies.

Galaxies don’t last forever. The stars in them burn their nuclear fuel and die. Out of the remnant gas and dust more stars can form, but a point of diminishing returns is reached, after which all of the stars in the galaxy are dead. We are left with white dwarfs (stars that once burned, and ran out of fuel), brown dwarfs (stars that never burned in the first place), and neutron stars (stars that used to be white dwarfs but collapsed further under the pull of gravity). These objects may or may not be stable in their own right; our best current theoretical guess is that the protons and neutrons that make them up aren’t perfectly stable themselves but will eventually decay into lighter particles. If that’s true (and admittedly, we’re not sure), the various forms of dead stars will eventually dissipate into a thin gas of particles that disperse into the void. It won’t be quick; a reasonable estimate is 10
⁴⁰
years from now. For comparison, the current universe is about 10
¹⁰
years old.

Besides stars, there are also black holes. Most large galaxies, including our own, have giant black holes at the center. In a galaxy the size of the Milky Way, with about 100 billion stars, the black hole might be a few million times as massive as the Sun—big compared to any individual star, but still small compared to the galaxy as a whole. But it will continue to grow, sweeping up whatever unfortunate stars happen to fall into it. Ultimately, however, all of the stars will have been used up. At that point, the black hole itself begins to evaporate into elementary particles. That’s the remarkable discovery of Stephen Hawking from 1976, which we’ll discuss in detail in Chapter Twelve: “black holes ain’t so black.” Due once again to quantum fluctuations, a black hole can’t help but gradually radiate out into the space around it, slowly losing energy in the process. If we wait long enough—and now we’re talking 10
¹⁰⁰
years or so—even the supermassive black holes at the centers of galaxies will evaporate away to nothing.

Regardless of how the details play out, we are left with the same long-term picture. Other galaxies move away from us and disappear; our own galaxy will evolve through various stages, but the end result is a thin gruel of particles dissipating into the void. In the very far future, the universe becomes once again a very simple place: It will be completely empty, as empty as space can be. That’s the diametric opposite of the hot, dense state in which the universe began; a vivid cosmological manifestation of the arrow of time.

THE ENTROPY OF THE UNIVERSE

An impressive number of brain-hours on the part of theoretical physicists have been devoted to the question of why the universe evolved in this particular fashion, rather than in some other way. It’s certainly possible that this question simply has no answer; perhaps the universe is what it is, and the best we can do is to accept it. But we are hopeful, not without reason, that we can do more than accept it—we can explain it.

Given perfect knowledge of the laws of physics, the question “Why has the universe evolved in the fashion it has?” is equivalent to “Why were the initial conditions of the universe arranged in the way they were?” But that latter formulation is already sneaking in an implicit notion of time asymmetry, by privileging past conditions over future conditions. If our understanding of the fundamental, microscopic laws of nature is correct, we can specify the state of the universe at
any
time, and from there derive both the past and the future. It would be better to characterize our task as that of understanding what would count as a natural history of the universe as a whole.
⁵¹

There is some irony in the fact that cosmologists have underappreciated the importance of the arrow of time, since it is arguably the single most blatant fact about the evolution of the universe. Boltzmann was able to argue (correctly) for the need for a low-entropy boundary condition in the past, without knowing anything about general relativity, quantum mechanics, or even the existence of other galaxies. Taking the problem of entropy seriously helps us look at cosmology in a new light, which might suggest some resolutions to long-standing puzzles.

But first, we need to be a little more clear about what exactly we mean about “the entropy of the universe.” In Chapter Thirteen we will discuss the evolution of entropy in our observable universe in great detail, but the basic story goes as follows:

1. In the early universe, before structure forms, gravity has little effect on the entropy. The universe is similar to a box full of gas, and we can use the conventional formulas of thermodynamics to calculate its entropy. The total entropy within the space corresponding to our observable universe turns out to be about 10
⁸⁸
at early times.

2. By the time we reach our current stage of evolution, gravity has become very important. In this regime we don’t have an ironclad formula, but we can make a good estimate of the total entropy just by adding up the contributions from black holes (which carry an enormous amount of entropy). A single supermassive black hole has an entropy of order 10
⁹⁰
, and there are approximately 10
¹¹
such black holes in the observable universe; our total entropy today is therefore something like 10
¹⁰¹
.

3. But there is a long way to go. If we took all of the matter in the observable universe and collected it into a single black hole, it would have an entropy of 10
¹²⁰
. That can be thought of as the maximum possible entropy obtainable by rearranging the matter in the universe, and that’s the direction in which we’re evolving.
⁵²

Our challenge is to explain this history. In particular, why was the early entropy, 10
⁸⁸
, so much lower than the maximum possible entropy, 10
¹²⁰
? Note that the former number is much, much, much smaller than the latter; appearances to the contrary are due to the miracle of compact notation.

The good news is, at least the Big Bang model provides a context in which we can sensibly address this question. In Boltzmann’s time, before we knew about general relativity or the expansion of the universe, the puzzle of entropy was even harder, simply because there was no such event as “the beginning of the universe” (or even “the beginning of the observable universe”). In contrast, we are able to pinpoint exactly when the entropy was small, and the particular form that low-entropy state took; that’s a crucial step in trying to explain why it was like that.

It’s possible, of course, that the fundamental laws of physics simply aren’t reversible (although we’ll give arguments against that later on). But if they are, the low entropy of our universe near the Big Bang leaves us with two basic possibilities:

1. The Big Bang was truly the beginning of the universe, the moment when time began. That may be because the true laws of physics allow spacetime to have a boundary, or because what we call “time” is just an approximation, and that approximation ceases to be valid near the Big Bang. In either case, the universe began in a low-entropy state, for reasons over and above the dynamical laws of nature—we need a new, independent principle to explain the initial state.

2. There is no such thing as an initial state, because time is eternal. In this case, we are imagining that the Big Bang isn’t the beginning of the entire universe, although it’s obviously an important event in the history of our local region. Somehow our observable patch of spacetime must fit into a bigger picture. And the way it fits must explain why the entropy was small at one end of time, without imposing any special conditions on the larger framework.

As to which of these is the correct description of the real world, the only answer is that we don’t know. I will confess to a personal preference for Option 2, as I think it would be more elegant if the world were described as a nearly inevitable result of a set of dynamical laws, without needing an extra principle to explain why it appears precisely this way. Turning this vague scenario into an honest cosmological model will require that we actually take advantage of the mysterious vacuum energy that dominates our universe. Getting there from here requires a deeper understanding of curved spacetime and relativity, to which we now turn.

PART TWO

TIME IN EINSTEIN’S UNIVERSE

4

TIME IS PERSONAL

Time travels in divers paces with divers persons.

—William Shakespeare, As You Like It

When most people hear “scientist,” they think “Einstein.” Albert Einstein is an iconic figure; not many theoretical physicists attain a level of celebrity in which their likeness appears regularly on T-shirts. But it’s an intimidating, distant celebrity. Unlike, say, Tiger Woods, the precise achievements Einstein is actually famous
for
remain somewhat mysterious to many people who would easily recognize his name.
⁵³
His image as the rumpled, absentminded professor, with unruly hair and baggy sweaters, contributes to the impression of someone who embodied the life of the mind, disdainful of the mundane realities around him. And to the extent that the substance of his contributions is understood—equivalence of mass and energy, warping of space and time, a search for the ultimate theory—it seems to be the pinnacle of abstraction, far removed from everyday concerns.