The pioneers of the Steady State theory (unlike some of their later followers) were not crackpots. They understood that Hubble had discovered the expansion of the universe, and they respected the data. So how can the universe be expanding without diluting and cooling down? The answer they suggested was that matter was continually being created in between the galaxies, precisely balancing the dilution due to the expansion of the universe. (You don’t need to make much: about one hydrogen atom per cubic meter every billion years. It’s not like your living room will start filling up.) Creation of matter wouldn’t happen all by itself; Hoyle invented a new kind of field, called the C-field, which he hoped would do the trick, but the idea never really caught on among physicists.
From our jaded modern perspective, the Steady State model seems like a lot of superstructure constructed on the basis of some fairly insubstantial philosophical presuppositions. But many great theories begin that way, before they are confronted with the harsh realities of data; Einstein certainly leaned on his own philosophical preferences during the construction of general relativity. But unlike relativity, when the data ultimately confronted the Steady State model, the result was not pretty.44 The last thing you would expect from a model in which the temperature of the universe remains constant is a relic background radiation that indicates a hot beginning. After Penzias and Wilson discovered the microwave background, support for the Steady State theory crumbled, although there remains to this day a small cadre of true believers who invent ingenious ways of avoiding the most straightforward interpretation of the data.
Nevertheless, thinking about the Steady State model brings home the perplexing nature of time in the Big Bang model. In the Steady State cosmology, there was still unmistakably an arrow of time: Entropy increased, without limit, in the same direction, forever and ever. In a very legitimate sense, the problem of explaining the low-entropy initial conditions of the universe would be infinitely bad in a Steady State universe; whatever those conditions were, they were infinitely far in the past, and the entropy of any finite-sized system today would have been infinitesimally small. One could imagine that considerations of this form might have undermined the Steady State model from the start, if cosmologists had taken the need to explain the low entropy of the early universe seriously.
In the Big Bang picture, things don’t seem quite as hopeless. We still don’t know why the early universe had a low entropy, but at least we know when the early universe was: It was 14 billion years ago, and its entropy was small but not strictly zero. Unlike in the Steady State model, in the context of the Big Bang you can at least put your finger directly on where (really “when”) the problem is located. Whether or not this is really an improvement can’t be decided until we understand cosmology within a more comprehensive framework.
BUT IT IS ACCELERATING
We know a good deal about the evolution of the universe over the last 14 billion years. What’s going to happen in the future?
Right now the universe is expanding, becoming increasingly colder and ever more dilute. For many years the big question in cosmology had been, “Will expansion continue forever, or will the universe eventually reach a maximum size and begin to contract toward a Big Crunch at the end of time?” Debating the relative merits of these alternatives was a favorite parlor game among cosmologists ever since the early days of general relativity. Einstein himself favored a universe that was finite in both space and time, so he liked the idea of an eventual re-collapse. Lemaître, in contrast, preferred the idea that the universe would continue to cool off and expand forever: ice, rather than fire.
Performing measurements that would decide the question empirically turned out to be more difficult. General relativity would seem to make a clear prediction: As the universe expands, the gravitational force between galaxies pulls all of them together, working to slow the expansion down. The question was simply whether there was enough matter in the universe to actually cause a collapse, or whether it would expand ever more gradually but for all eternity. For a long time it was a hard question to answer, as observations seemed to indicate that there was almost enough matter to reverse the expansion of the universe—but not quite enough.
The breakthrough occurred in 1998, from a completely different method. Rather than measuring the total amount of mass in the universe, and comparing with theory to determine whether there was enough to eventually reverse the universe’s expansion, one could go out and directly measure the rate at which the expansion was slowing down. Easier said than done, of course. Basically what one had to do was what Hubble had done years before—measure both distances and apparent velocities of galaxies, and look at the relationship between them—but to enormously higher precision and at much greater distances. The technique eventually used was to search for Type Ia supernovae, exploding stars that not only have the virtue of being very bright (and therefore visible over cosmological distances), but also have almost the same brightness in every event (so that the apparent brightness can be used to deduce the distance to the supernova).45
The hard work was done by two teams: one led by Saul Perlmutter of Lawrence Berkeley National Laboratory, and one led by Brian Schmidt of Mount Stromlo Observatory in Australia. Perlmutter’s group, which contained a number of particle physicists converted to the cause of cosmology, started earlier, and had championed the supernova technique in the face of considerable skepticism. Schmidt’s group, which included a number of experts on supernova astronomy, started later but managed to catch up. The teams maintained a rivalry that was often friendly and occasionally less so, but they both made crucial contributions, and rightfully share the credit for the ultimate discovery.
As it happens, Brian Schmidt and I were office mates in graduate school at Harvard in the early 1990s. I was the idealistic theorist, and he was the no-nonsense observer. In those days, when the technology of large-scale surveys in astronomy was just in its infancy, it was a commonplace belief that measuring cosmological parameters was a fool’s errand, doomed to be plagued by enormous uncertainties that would prevent us from determining the size and shape of the universe with anything like the precision we desired. Brian and I made a bet concerning whether we would be able to accurately measure the total matter density of the universe within twenty years. I said we would; Brian was sure we wouldn’t. We were poor graduate students at the time, but purchased a small bottle of vintage port, to be secreted away for two decades before we knew who had won. Happily for both of us, we learned the answer long before then; I won the bet, due in large part to the efforts of Brian himself. We split the bottle of port on the roof of Harvard’s Quincy House in 2005.
And the answer is: The universe isn’t decelerating at all; it’s actually accelerating! If you were to measure the apparent recession velocity of a galaxy, and (hypothetically) came back a billion years later to measure it again, you would find that the velocity was now higher.46 How can that be reconciled with the supposed prediction of general relativity that the universe should be slowing down? Like most such predictions of general relativity, there are hidden assumptions: in this case, that the primary source of energy in the universe consists of matter.
Figure 9: The accelerating universe.
To a cosmologist, matter is shorthand for “any collection of particles, each of which is moving much more slowly than the speed of light.” (If particles are moving at or close to the speed of light, cosmologists refer to them as “radiation,” whether or not they are actually electromagnetic radiation in the usual sense.) Einstein taught us long ago that particles have energy, even when they’re not moving at all: E = mc2 means that the energy of a perfectly stationary massive particle is given by its mass times the speed of light squared. For our present purposes, the crucial aspect of matter is that it dilutes away as the universe expands.47 What general relativity actually predicts is that the expansion should be decelerating, as long as the energy is diluting away. If it’s not—if the density of energy, the amount of energy in each cubic cen
timeter or cubic light-year of space, is approximately constant—then that energy provides a perpetual impulse to the expansion of space, and the universe will actually be accelerating.
It’s possible, of course, that general relativity is not the correct theory of gravity on cosmological scales, and that possibility is one that physicists take very seriously. It seems more likely, however, that general relativity is correct, and the observations are telling us that most of the energy in the universe is not in the form of “matter” at all, but rather in the form of some stubbornly persistent stuff that sticks around even as space expands. We’ve dubbed that mysterious stuff “dark energy,” and the nature of the dark energy is very much a favorite research topic for modern cosmologists, both theorists and observers.
We don’t know much about dark energy, but we do know two very crucial things: It’s nearly constant throughout space (the same amount of energy from place to place), and also nearly constant in density through time (the same amount of energy per cubic centimeter at different times). So the simplest possible model for dark energy would be one featuring an absolutely constant density of energy through all space and time. And in fact, that’s an old idea, dating back to Einstein: He called it “the cosmological constant,” and these days we often call it “vacuum energy.” (Some people may try to convince you that there is some difference between vacuum energy and the cosmological constant—don’t fall for it. The only difference is which side of the equation you put it on, and that’s no difference at all.)
What we’re suggesting is that every cubic centimeter of space—out in the desolate cold between the galaxies, or at the center of the Sun, or right in front of your face—there is a certain amount of energy, over and above whatever comes from the particles and photons and other things that are actually located in that little cube. It’s called “vacuum energy” because it’s present even in a vacuum, in a perfectly empty space—a minimum amount of energy inherent in the fabric of spacetime itself.48 You can’t feel it, you can’t see it, you can’t do anything with it, but it is there. And we know it is there because it exerts a crucial influence on the universe, imparting a gentle push that causes distant galaxies to accelerate away from us.
Unlike the gravity caused by ordinary matter, the effect of vacuum energy is to push things apart rather than pull them together. When Einstein first proposed the cosmological constant in 1917, his motivation was to explain a static universe, one that wasn’t expanding or contracting. This wasn’t a misguided philosophical stance—it was the best understanding according to the astronomy of the day; Hubble wouldn’t discover the expansion of the universe until 1929. So Einstein imagined a universe in delicate balance between the pull of gravity among galaxies and the push of the cosmological constant. Once he learned of Hubble’s discovery, he regretted ever introducing the cosmological constant—had he resisted the temptation, he might have predicted the expansion of the universe before it was discovered.
THE MYSTERY OF VACUUM ENERGY
In theoretical physics, it’s not easy to un-invent a concept. The cosmological constant is the same as the idea of vacuum energy, the energy of empty space itself. The question is not “Is vacuum energy a valid concept?”—it’s “What value should we expect the vacuum energy to have?”
Modern quantum mechanics implies that the vacuum is not a boring place; it’s alive with virtual particles. A crucial consequence of quantum mechanics is Werner Heisenberg’s uncertainty principle: It’s impossible to pin down the observable features of any system into one unique state with perfect precision, and that includes the state of empty space. So if we were to look closely enough at empty space, we would see particles flashing into and out of existence, representing quantum fluctuations of the vacuum itself. These virtual particles are not especially mysterious or hypothetical—they are definitely there, and they have measurable effects in particle physics that have been observed many times over.
Virtual particles carry energy, and that energy contributes to the cosmological constant. We can add up the effects of all such particles to obtain an estimate for how large the cosmological constant should be. But it wouldn’t be right to include the effects of particles with arbitrarily high energies. We don’t believe that our conventional understanding of particle physics is adequate for very high-energy events—at some point, we have to take account of the effects of quantum gravity, the marriage of general relativity with quantum mechanics, which remains an incomplete theory at the moment.
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 10105 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 10120—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 1088; the number of grains of sand on all the Earth’s beaches is only about 1020.
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 u
niverse 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 1040 years from now. For comparison, the current universe is about 1010 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 10100 years or so—even the supermassive black holes at the centers of galaxies will evaporate away to nothing.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 8
